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Engineering Applications of Computational Methods 5
LinmiTao
Atif Mughees
Deep Learning
for Hyperspectral
Image Analysis
and Classification

Engineering Applications of Computational
Methods
Volume 5
Series Editors
Liang Gao, State Key Laboratory of Digital Manufacturing Equipment
and Technology, Huazhong University of Science and Technology,
Wuhan, Hubei, China
Akhil Garg, School of Mechanical Science and Engineering, Huazhong University
of Science and Technology, Wuhan, Hubei, China

The book series Engineering Applications of Computational Methods addresses the
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expand their knowledge of computational methods.
More information about this series at http://www.springer.com/series/16380

Linmi Tao • Atif Mughees
Deep Learning
for Hyperspectral Image
Analysis and Classiﬁcation
123

Linmi Tao
Department of Computer Science
and Technology
Tsinghua University
Beijing, China
Atif Mughees
Department of Computer Science
and Technology
Tsinghua University
Beijing, China
ISSN 2662-3366 ISSN 2662-3374 (electronic)
Engineering Applications of Computational Methods
ISBN 978-981-33-4419-8 ISBN 978-981-33-4420-4 (eBook)
https://doi.org/10.1007/978-981-33-4420-4
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
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This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
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Singapore

Preface
With the rapid development in the field of science and technology, the
Hyperspectral Image (HSI) analysis, being extensively broader and advanced
technology, has acquired the wide as well as significant advancement in the con-
ceptual, theoretical, and application level and has become an established discipline.
It takes into account hundreds of contiguous spectral channels to discover earth
resources that typical traditional vision sensors are unable to identify.
This book is an outcome of research efforts in machine learning based HSI
processing over a decade, which is a new methodology from the HSI perspective.
The title of the book “Deep Learning for Hyperspectral Image Understanding”
represents that the main purpose of the book is to explore and define novel machine
learning methods and techniques for the analysis and classification of the hyper-
spectral remote sensing scenes by incorporating spectral and spatial characteristics
of the image. In particular, the prime target is on investigation and optimization of
deep learning based deep feature extraction strategies. Furthermore, in the last
chapter, we present the unsupervised traditional technique of sparse coding to
effectively extract spatial features and design a framework to detect the redundancy
and noise in the high-dimensional data. We hope the readers can experience both
the merits and demerits of supervised deep learning versus the unsupervised sparse
scheme in HSI area.
An important factor that makes this book different from other HSI books is that
this book exploits theory, application, and analysis of HSI, starting from noise
detection removal, deep learning based feature extraction and finally classification.
The book is structured according to the deep learning methods in a sequentially
associated chapters that are logically related to each other and can be studied
backward and forward for additional details. More specifically, most of the
experiments, simulated results, graphs, and experimental analysis comparisons have
been organized to have a consistent and logical organization of both the HSI
content and learning methods. Techniques are combined in such an integrated
structure that readers can easily understand how the concepts were established and
evolved.
v

This book can be considered as a complete recipe that covers techniques for HSI
analysis. Some of these techniques such as unsupervised HSI noise detection
removal, segmentation, and feature extraction are established and matured for
practical implementation. They are evaluated and analyzed with extreme detail.
Various deep learning techniques established in the book will also become really
useful for the coming years. For this reason, we have made the book self-sufﬁcient
so that readers can effortlessly understand and implement the algorithms without
much struggle. In doing so, we have incorporated comprehensive mathematical
sources and experiments for explanation.
Tsinghua, Beijing, China Linmi Tao
August 2020 Atif Mughees
vi Preface

Acknowledgements
We owe much recognition to people who deserve our heartfelt appreciation. These
individuals are my former Ph.D. students, Dr. Sami ul Haq, Mr. Xiaoqi Chen, and
Dr. Rucheng Du. This book cannot be concluded and completed without their
efforts and contributions. We would like to deeply thank Dr. Sami ul Haq for his
valuable Ph.D. research on sparse coding, which is presented in the book.
This book comprises HSI work that has been researched and completed over a
decade in the Department of Computer Science and Technology, Tsinghua
University; BNRist; and Key Laboratory of Pervasive Computing, Ministry of
Education; Beijing, China.
Finally, we thank the National Natural Science Foundation of China for the
fundings under Grant 61672017 and 61272232.
vii

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Applications of Hyperspectral Images . . . . . . . . . . . . . . . . . . . . . 2
1.2 Challenges in Hyperspectral Image Classification . . . . . . . . . . . . . 2
1.3 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Research Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Noise Reduction/Band Categorization of HSI . . . . . . . . . . 6
1.4.2 Unsupervised Hyperspectral Image Segmentation . . . . . . . 7
1.4.3 Deep Learning Based HSI Classification Techniques . . . . . 8
1.5 Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Hyperspectral Image and Classification Approaches. . . . . . . . . . . . . 13
2.1 Introduction to Hyperspectral Imaging . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Hyperspectral Imaging System . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Why Hyperspectral Remote Sensing . . . . . . . . . . . . . . . . . 15
2.2 Review of Machine Learning Based Approaches
for Hyperspectral Image Classification . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Hyperspectral Image Interpretation Taxonomy . . . . . . . . . . 18
2.3 Hyperspectral Remote Sensing Image Dataset Description . . . . . . 20
2.3.1 Indian Pine: AVIRIS Dataset . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Pavia University: ROSIS Dataset . . . . . . . . . . . . . . . . . . . 21
2.3.3 Houston Image: AVIRIS Dataset . . . . . . . . . . . . . . . . . . . 21
2.3.4 Salinas Valley: AVIRIS Dataset . . . . . . . . . . . . . . . . . . . . 23
2.3.5 Moffett Image: AVIRIS Dataset . . . . . . . . . . . . . . . . . . . . 23
2.3.6 Washington DC Mall Hyperspectral Dataset . . . . . . . . . . . 24
2.4 Classification Evaluation Measures . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.1 HSI Noise/Redundancy Detection . . . . . . . . . . . . . . . . . . . 27
2.5.2 Deep Learning Based Algorithms . . . . . . . . . . . . . . . . . . . 29
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
ix

3 Unsupervised Hyperspectral Image Noise Reduction
and Band Categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1 Proposed Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1 Preprocessing Toward Initial Segmentation . . . . . . . . . . . . 42
3.1.2 Cluster-Size Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.3 Cluster-Shift Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.4 Cluster Spatial-Spectral Contextual Difference Factor . . . . . 43
3.1.5 Band-Noise Factor (BNF) . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.6 The HSI Process and Noise Model . . . . . . . . . . . . . . . . . . 44
3.1.7 Noise Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.1 HSI Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.2 Synthetic Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.3 Experiments on Real HS Data . . . . . . . . . . . . . . . . . . . . . 49
3.2.4 Discussion of rET Parameters . . . . . . . . . . . . . . . . . . . . . . 56
3.2.5 Discussion of Weight-Subfactor Parameters . . . . . . . . . . . . 56
3.2.6 Noise-Level Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.7 HSI Classiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Summary of the Proposed Unsupervised Hyperspectral Image
Noise Reduction and Band Categorization Method . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4 Hyperspectral Image Spatial Feature Extraction
via Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1.1 Preprocessing Toward Initial Segmentation . . . . . . . . . . . . 72
4.1.2 Boundary Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1.3 Channel–Group Merge Criteria . . . . . . . . . . . . . . . . . . . . . 77
4.2 Experimental Approach and Analysis. . . . . . . . . . . . . . . . . . . . . . 78
4.2.1 Hyperspectral Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2.2 Adjustment of Weight Factors . . . . . . . . . . . . . . . . . . . . . 79
4.2.3 Grouping and Merging Methods . . . . . . . . . . . . . . . . . . . . 80
4.2.4 Experimental Results and Comparison . . . . . . . . . . . . . . . 80
4.2.5 Evaluation Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Summary of the Proposed Hyperspectral Image Spatial Feature
Extraction via Segmentation Method . . . . . . . . . . . . . . . . . . . . . . 83
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5 Integrating Spectral-Spatial Information for Deep Learning
Based HSI Classiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.1 Band Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.2 Hyper-Segmentation-Based Spatial Feature Extraction . . . . 89
x Contents

5.2 SAE Based Shape-Adaptive Deep Learning for Hyperspectral
Image Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.1 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2.2 Experimental Results and Performance Comparisons . . . . . 93
5.2.3 Summary of the Proposed Integration of Spectral-Spatial
Information Method for Deep Learning Based HSI
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3 DBN-Based Shape-Adaptive Deep Learning for Hyperspectral
Image Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4 Hyper-Segmentation Based DBN for HSI Classification . . . . . . . . 102
5.4.1 Extraction of Spectral-Spatial Information of Spatial
Segments via DBN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.4.3 Summary of the Proposed DBN-Based Shape-Adaptive
Deep Learning Method for Hyperspectral Image
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.5 PCANet-Based Boundary-Adaptive Deep Learning for
Hyperspectral Image Classification . . . . . . . . . . . . . . . . . . . . . . . 105
5.5.1 SANet-Based Spectral-Spatial Classification Network . . . . 107
5.5.2 Experimental Analysis and Performance Comparisons . . . . 110
5.5.3 Parameter Setting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5.4 Summary of the Proposed PCANet-Based Boundary-
Adaptive Deep Learning Method for Hyperspectral Image
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.6 Summary of the Proposed Deep Learning Based Methods
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6 Multi-Deep Net Based Hyperspectral Image Classification . . . . . . . . 119
6.1 Multi-Deep Belief Network-Based Spectral–Spatial
Classification of Hyperspectral Image . . . . . . . . . . . . . . . . . . . . . 120
6.1.1 Spectral-Adaptive Segmented DBN for HSI
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.1.2 Spectral–Spatial Feature Extraction by Segmented
DBN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.1.4 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.1.5 Spectral–Spatial HSI Classification . . . . . . . . . . . . . . . . . . 130
6.1.6 Summary of the Proposed Multi-Deep Net-Based
Hyperspectral Image Classification Method . . . . . . . . . . . . 133
6.2 Hyperspectral Image Classification Based on Deep Auto-Encoder
and Hidden Markov Random Field . . . . . . . . . . . . . . . . . . . . . . . 134
Contents xi

6.3.1 HMRF-EM Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.3.2 Final Segmentation with Preserved Edges . . . . . . . . . . . . . 139
6.3.3 SAE Pixel-Wise Classification . . . . . . . . . . . . . . . . . . . . . 139
6.3.4 Majority Voting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.4 Experimental Results and Performance Comparisons . . . . . . . . . . 142
6.5 Summary of the Proposed Hyperspectral Image Classification
Method Based on Deep Auto-encoder and Hidden Markov
Random Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.6 Hyperspectral Image Classification Based on Hyper-
segmentation and Deep Belief Network . . . . . . . . . . . . . . . . . . . . 144
6.6.1 Proposed Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.6.2 Experimental Results and Performance Comparison . . . . . . 151
6.7 Summary of the Proposed Deep Learning-Based Methods
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7 Sparse-Based Hyperspectral Data Classification . . . . . . . . . . . . . . . . 159
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.2 Related Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.3 Proposed Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.3.1 Sparse Representation for Hyperspectral Data
Using a Few Labeled Samples . . . . . . . . . . . . . . . . . . . . . 165
7.3.2 Homotopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7.3.3 Sparse Ensemble Framework . . . . . . . . . . . . . . . . . . . . . . 171
7.4 Experimental Results and Comparison . . . . . . . . . . . . . . . . . . . . . 175
7.4.1 Effect of Parameter Selection on Classification
Accuracy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.4.2 AVIRIS Hyperspectral Image . . . . . . . . . . . . . . . . . . . . . . 177
7.4.3 Washington DC Mall Image . . . . . . . . . . . . . . . . . . . . . . . 188
7.4.4 Kennedy Space Center and Salina A Hyperspectral
Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
7.4.5 Time Comparison of General LP Sparse
and Homotopy-Based Sparse Representations . . . . . . . . . . 193
7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
7.5.1 Sparsity of Computed Solution . . . . . . . . . . . . . . . . . . . . . 193
7.5.2 Sparse Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7.5.3 Sparse Solution Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 197
7.5.4 Sparse Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
8 Challenges and Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.1 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
xii Contents

Chapter 1
Introduction
The human curiosity to discover and apprehend the universe always results in expand-
ing the limits of science and technology, remote sensing is yet another addition.
Remote Sensing (RS) is the area of science that deals with observation, collection,
and analysis of information associated with objects or events under study, without
making physical contact. The launch of the first satellite in 1957, opened new doors
for a wealth of information particularly for Earth Observation (EO). Space-borne
and airborne platforms equipped with powerful sensors make it possible to acquire
detailed information from the surface of the earth. Hyperspectral imaging sensors
have the capability of capturing the detailed spectral characteristics of the received
light in the sensor’s covered area.
Image spectroscopy also known as hyperspectral imaging is a process of measur-
ing the spectral signatures/chemical composition of the scene under airborne/space-
borne sensor’s field of view. Hyperspectral image comprises of detailed spectral and
spatial information of each material in a specified scene. Sensors capture hundreds
of narrow, contiguous spectral channels in the wavelength range of visible through
near infrared hence provide huge spectral and spatial information of the surface of
earth. Each pixel comprises a vector, where each value corresponds to a particular
spectral signature across a sequence of continuous, narrow spectral bands and also
contains detailed spatial characteristics. The size of the vector is equal to the total
number of spectral channels that a particular sensor is capable of capturing. In case
of hyperspectral imaging sensors, they are capable of acquiring hundreds of spec-
tral channels. The availability of such a detailed information makes it possible to
accurately discriminate materials of interest with enhanced classification accuracy.
Classification of high-dimensional hyperspectral data is a challenging task.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. Tao and A. Mughees, Deep Learning for Hyperspectral Image Analysis
and Classification, Engineering Applications of Computational Methods 5,
https://doi.org/10.1007/978-981-33-4420-4_1
1

2 1 Introduction
1.1 Applications of Hyperspectral Images
HSI have been widely used in analyzing the earth’s surface due to its high distinctive
capability to classify and discriminate different materials, which in turn has opened
new doors for a vast range of applications such as mineral detection, precision farm-
ing, urban planning, environmental monitoring and management, and surveillance.
In the past decade, hyperspectral imaging has pushed the science boundaries by pro-
viding a great deal of information and solving challenging problems such as scene
analysis [2], environmental changes [3], and object classification [4]. Hyperspec-
tral Imaging contains numerous applications. The power of full spectral information
combined with the rich spatial information opens up enormous capabilities such as
• Agriculture—crop identification, area determination, and condition monitoring:
HSI consisting of fields, crops can be employed for precision agriculture to manage
and monitor the farming process. The hyperspectral images can be utilized for farm
optimization and spatially enabled organization of procedural operations. The data
can assist to locate the area and level of crop stress and then can be utilized to
optimize the use of agricultural chemicals. The major application involves crop
classification, crop damage assessment, and crop production estimation.
• Ecological Science: Hyperspectral images can be used in the classification of
distinct ecological regions, based on their geology, structure, soils, plants, envi-
ronment conditions, and aquatic resources.
• Geological science: Hyperspectral image techniques are now being increasingly
utilized for preparing geological maps and extract the basic geological material
which is utilized for further detailed analysis.
• SurveillanceandMilitaryApplications:Enrichedspectral-spatialinformationcon-
tained in hyperspectral images has enormous military and surveillance applica-
tions. It enables us to keep a watch on military build-ups, and troop movements in
the area under study.
Remote sensing scene can also be seen as a pile of scenes taken in diverse wavelengths
(spectral bands), which results in a hyperspectral image. Specifically, each spectral
channel of the hyperspectral data cube represents a gray-level image as presented in
Fig.1.1. The size of the 3D data cube is L1 × L2 × S where L1 × L2 is the size of
each spectral channel while S is the total count of spectral bands. More specifically,
hyperspectral scene is divided into spectral and spatial characteristics.
1.2 Challenges in Hyperspectral Image Classification
Classifying HSI image into its land cover classes is fundamental, crucial, and decisive
advantage of hyperspectral scene and has many major applications in almost all fields.
However, supervised classification techniques in general, require plenty of labeled
samples for different stages such as training, testing, validation, and parameter fine-
tuning. This problem becomes more serious in remote sensing as it is very difficult

1.2 Challenges in Hyperspectral Image Classification 3
Fig. 1.1 3D cube of HSI data [1]
and sometimes impossible to get the labeled data and if its available, it is very costly
and limited. High spectral data and detailed spatial characteristics make HSI analysis
a challenging task as it is really strenuous to get the spectral-spatial features without
data complexity. Following are some of the challenges:
1. Effect of noise and other atmospheric factors: Factors such as illumination
and multi-scattering in the acquisition process, noise, and redundancy causes sig-
nificant difficulties in HSI classification. The analysis of the scenes turns out to
be really challenging due to the high spectral redundancy, noise and uncertainty
sources observed. Source of illumination may affect the spectral signatures as
object illuminated through different sources may have different spectral charac-
teristics at one time.
2. Curse of dimensionality: Large ratio between the presence of a huge number
of bands in HSI and availability of a small amount of training data makes the
analysis of remote sensing scene a challenging task. Methods based on machine
learning techniques, this problem makes things even worse as with increase in
dimensionality, the amount of labeled data required to attain a statistically reliable
result also rise as the volume of parameters to be predicted increases with dimen-
sionality. Optimizing such a large number of parameters become challenging,
complex, and time- consuming [5].
3. Integration of spectral-spatial information: Recent advancements in remote
sensor technology delivers rich spatial information along with the spectral data.
Spatial and spectral domains are entirely different, each carries distinctive charac-

4 1 Introduction
teristics and properties. Contextual information comprises edges, object shapes,
structures, different textures, and contextual information. While spectral informa-
tion consists of distinct spectral characteristics of the scene and depicts material-
related properties. For an effective and accurate classification, it is recently dis-
covered that exploiting spectral and spatial information plays a vital role. Due
to their different nature, it is still an open research area as to how to merge the
spectral and spatial information for effective classification.
4. Classification of Diverse Classes in the Presence of Limited Training data:
Process of labeling each Hyperspectral Image (HSI) pixel according to the class
it belongs is called HSI classification. One of the most vital limitations of HSI is
the availability of limited training data as its difficult, expensive and sometimes
impossible to label the HSI data which makes the classification a challenging
task as most of the classifiers and feature extraction techniques require plenty of
training data. Moreover, some HSI datasets include many classes within a small
size image which makes the classification even more difficult and complex.
It is therefore highly desirable to design a classifier that can efficiently utilize the
spectral and spatial data and can handle the high dimensionality of HSI data. More-
over, the detection and removal of redundancy and noise is also an open issue.
1.3 Research Objective
The main purpose of the book is to explore and define novel approaches for the anal-
ysis and classification of the hyperspectral remote sensing scenes by incorporating
spectral and spatial characteristics of the image. In addition, we develop techniques
to effectively extract spatial features in unsupervised manner and design a frame-
work to detect the redundancy and noise in the high-dimensional data. In particular,
the prime target is on investigation and optimization of deep learning based deep
feature extraction strategies, for the extraction and integration of spectral and spatial
characteristics for powerful HSI classification. The framework of the proposed hyper-
spectral remote sensing image analysis is presented in Fig.1.2. In recent years, deep
learning based architectures, which can extract deep and discriminative features in a
hierarchical manner, have gained more attention. Deep learning has recently proved
its effectiveness in extracting useful features in HSI classification. However, various
problems associated with the computational cost and effective extraction of class-
specific statistics need further investigation. The high dimensionality of the HSI data,
which contains redundant and noisy information, and which also leads to Hughes
phenomena is also an open issue.
In order to address and overcome the above-mentioned challenges and limitations,
which obstructs the HSI analysis, the following objectives are established:
• Deeply explore the behavior and performance, in terms of complexity and clas-
sification accuracy, of deep learning based architectures/algorithms in the remote
sensing field, under various experimental arrangements and based on that design

1.3 Research Objective 5
Fig. 1.2 General framework
for hyperspectral image
analysis
effective deep learning based classification methods for improved classification
performance.
• Develop an innovative methodology for spatial feature extraction, information
redundancy, and noise issues by exploiting the adaptive boundary adjustment based
technique.
• Define an approach for integrating both spectral and spatial characteristics within
a deep learning based classification framework.
• Design a novel strategy to address the Hughes phenomenon for HSI classification
by exploiting tri-factor-based criteria.

6 1 Introduction
1.4 Research Achievements
This section briefly describes the research achievements presented in this book.
Detailed contribution is presented in Figs.1.3 and 1.4. In order to meet the above-
mentioned challenges, first, the proposed spectral feature extraction based band
categorization approach is discussed which can effectively detect and remove the
redundant and noisy data and at the same time retain the most discriminant informa-
tion. Secondly, unsupervised spatial feature extraction approach is proposed which
segments the spatially similar regions in HSI. Lastly, several deep-learning based
algorithms are developed which effectively extract and integrate the spectral-spatial
information for hyperspectral image classification which demonstrates improved
classification performance.
1.4.1 Noise Reduction/Band Categorization of HSI
The immense volume of the dimensional domain of Hyperspectral Scenes (HSIs)
including all of its complexity and intricacy which also involves a substantial amount
of duplication and noise is considered to be one of the persistent issue that results
in encumbrance and numerous obscurities in HSI analysis and for all the succeed-
ing application in general and HSI classification in particular. To handle the subject
issue, we developed a flexible edge detection based group-wise Band Categoriza-
tion (BC) algorithm that categorizes channels through the content and extent of
useful spectral data that exists in a particular channel. Moreover, it also addresses
Fig. 1.3 The major contribution of the book

1.4 Research Achievements 7
Fig. 1.4 General framework for hyperspectral image analysis along with contribution at each stage
the duplication/noise material deprived of negotiating the real content from the raw
hyperspectral data. As hyperspectral scene training data is demanding and complex
to acquire, an innovative unsupervised spectral-contextual flexible channel-noise
criteria-rooted design is formulated for band categorization which is rooted in capac-
ity of edge adaptation/modification and channel inter-association. Strong clustering
and edge-detection-rooted approaches contain two major concerns: channel associa-
tion and channel preference. Our developed technique anticipates mutually channel
correspondence as well as channel synergy. Here, channel preference is established
by the distinguishing and information content confined in each spectral channel.
1.4.2 Unsupervised Hyperspectral Image Segmentation
Hyperspectral Image (HSI) segmentation is believed to be the vital preprocessing
steps for successive applications and deep analysis to take full advantage of the
existing multispectral information. Unsupervised Segmentation devoid of dimen-
sional contraction procedure and without training samples is a persistent issue in
computer vision but a more serious and critical issue in hyperspectral imaging. An
innovative unsubstantiated spectral-contextual flexible edge modification/alteration
rooted architecture and a structure is designed for hyperspectral scene segmentation,
which is modified through biased clustering.

8 1 Introduction
This architecture utilizes and explores two major characteristics of hyperspectral
scene: spectral relationship and channel contextual preference. Spectral channel pref-
erence is demonstrated by the distinctive capability and information content confined
in individual channel, and flexible procedure is suggested to preserve the spectral
relationships in the spectral domain and to contest the real object in the contextual
domain. The developed methodology agrees on the scene to be exploited at multi-
ple segmentation points. Utilization of confined edge uniformity and self-similarity
characteristics from channel-cluster flexible edge alteration rooted procedure, and
concluding segmentation outcome rooted from the developed four diverse merging
measures employ a substantial consequence on the performance of the concluding
segmentation.
1.4.3 Deep Learning Based HSI Classification Techniques
DL can characterize and establish various stages of information to represent complex
associations between data. However, despite its advantages, deep learning cannot be
directly applied on HSI due to multiple reasons such as large number of bands
and limited available training data. HSI consists of hundred of bands, hence even
a small patch comprises very large data that results in a large number of neurons
in a pre-trained network. Similarly, very few labeled samples make the network,
difficult to train. Moreover, incorporating spatial contextual information along with
the spectral features for DL is also an open research problem. Furthermore, images
captured by different sensors exhibit different characteristics and generally present
great differences. Therefore, in this book multiple deep learning based classification
methods are proposed. In general integrating spatial information along with spectral
channels in the HSI classification process is of paramount importance [6] as with the
advancement in imaging technology, hyperspectral sensors can deliver an excellent
spatial resolution. In this regard, researchers have proposed certain techniques. In
the first category, classification techniques extracts the spatial and spectral features
before performing classification [7, 8]. In the second category, HSI classification
methods consist of incorporating spatial information into the classifier during the
classification process [9]. In the third category, classification methods attempt to
include spatial dependencies after the classification either by spatial regularization
or by decision rule [10]. However, all these spatial features need human knowledge.
In this book, several DL-based methods are developed and investigated to effectively
incorporate the spatial contextual information in an effective way. These methods can
be split into two major groups established on the integration of spatial information
and nature of network:
• Integration of spatial information prior to classification
1. Stacked auto-encoder based HSI classification,
2. Deep Belief Network based HSI classification,
3. PCANet based HSI classification.

• Integration of spatial information after classification
1. Stacked auto-encoder and Hidden Markov Random field based HSI classifica-
tion,
2. Deep Belief Network based HSI classification,
3. segmented DBN based HSI classification.
1.4.3.1 Stacked Auto-encoder Based Spectral-Spatial Classification of
HSI
Improving the classification accuracy of diverse classes in HSI is of preeminent con-
cern in remote sensing field. Recently, deep learning algorithms have established
their capability in HSI classification. However, despite its learning capability, fixed-
size scanning window in deep learning and its inability to integrate spatial contextual
information along with spectral features in deep network for improved performance
limits its capability. In this work, for spectral-spatial feature extraction, a spatial-
adaptive hyper-segmentation-based Stacked Auto-Encoder (SAHS-SAE) approach
is proposed, which adaptively modifies the scanning window size and explores spa-
tial contextual features within spectrally similar contiguous pixels for robust HSI
classification. The proposed approach includes two key methods–first, we developed
adaptive boundary movement based hyper-segmentation whose size and shape can
be adapted according to the spatial structures and which consists of spatially con-
tiguous pixels with similar spectral features, second, object-level classification using
Stacked Auto-Encoder (SAE) based decision fusion method is developed that inte-
grates spatial-segmented outcome and spectral information into an SAE framework
for robust spectral-spatial HSI classification. The proposed approach replaces the tra-
ditionalscanningwindowapproachforSAEwithobject-levelhyper-segments.More-
over, for robust classification, band preference and correlation-based band selection
approach is used to select only the most informative bands without compromising
the original content in HSI. Use of local structural regularity and spectral similarity
information from adaptive boundary adjustment based process, and fusion of spatial
context and spectral features into SAE has a significant effect on the accuracy of the
final HSI classification. Experimental results on real diverse hyperspectral imagery
with different contexts and resolutions validate the classification accuracy of the
proposed method over several well-known existing techniques.
1.4.3.2 Deep Belief Network Based Spectral-Spatial Classification of
HSI
Lately, the employment of deep learning based architectures in hyperspectral image
analyses has been matured and materialized. However, fusing contextual characteris-
tics along with spectral information in deep learning model is a persistent challenge.
This framework represents a distinguishing contextually modified deep belief net

10 1 Introduction
(SDBN) that effectually employs contextual characteristics inside spectrally match-
ing adjacent pixels for hyperspectral scene classification. In the developed frame-
work, scene is initially partitioned into flexible edge regulation rooted contextu-
ally comparable areas that possess the same spectral characteristics, succeeding
a structural feature mining and classification is commenced utilizing Deep Belief
Network (DBN) rooted outcome merging technique that joins contextually parti-
tioned contextual and spectral data into a DBN network for improved spectral-spatial
hyperspectral scene classification. Furthermore, for enhanced precision, channel par-
tiality/association rooted characteristic selection technique is utilized to choose the
spectral channels with maximum data devoid of conceding the real information in
the scene. Employment of indigenous contextual characteristics and spectral cor-
respondence from flexible edge regulation rooted technique, and incorporation of
contextual and spectral characteristics into DBN net fallouts into enhanced precision
of the concluding scene classification. Experimental demonstration of famous hyper-
spectral scenes designates the classification precision of the developed approach over
numerous prevailing approaches.
1.4.3.3 PCANet Based Spectral-Spatial Classification of HSI
Distribution of each pixel in the HSI scene to a corresponding class by employing
feature mining through well-known DL-based architecture has already demonstrated
greatperformance.Nevertheless,themultifacetednetmodel,wearisometrainingpro-
cedure and active employment of contextual material in deep network bounds the
employment and enactment of deep learning. In this portion of the book, for an oper-
ative spectral-contextual feature extraction, an improved deep network, contextual
flexible network (SANet) technique is developed that employs contextual character-
istics and spectral properties to create a further abridged deep network that results
in much improved feature mining for the subsequent procedural analysis. SANet
is recognized from the effective model of a principal component analysis net. Ini-
tially, contextual operational characteristic is mined and fused with useful spectral
bands succeeded by a structural classification by utilizing SANet rooted conclusion
merging technique. It merges contextual outcome and spectral features into a SANet
network for vigorous spectral-contextual scene analyses. A combination of confined
operational uniformity and spectral likeness into effective deep SANet has substan-
tial consequences on the classification enactment. Experimental demonstration on
prevalent regular HSI scenes exposes the performance of SANet approach that acted
much better with increased accuracies.
1.4.3.4 Segmented DBN Based HSI Classification
Deep learning based deep belief networks have lately been designed for feature
extraction in hyperspectral scenes. Deep belief net, as deep learning based archi-
tecture, has been utilized in hyperspectral scene analyses for shallow and invariant

features extraction. Nevertheless, DBN architecture has to face and handle numerous
spectral characteristics and high spatial resolution from hyperspectral cube, which
leads to the intricacy and inability to mine true exact invariant characteristics, hence
the ability of this DL architecture damages badly in front of the hyperspectral chal-
lenges. Furthermore, dimensionality reduction based solution to the subject problem
results in damage of valued spectral data, which further lowers the accuracy. To
handle this issue, this section develops a spectral-variational segmented DBN (SAS-
DBN) for spectral-contextual hyperspectral classification that explores the invariant
deep characteristics by partitioning the real spectral channels into tiny groups of
associated spectral channels and applying deep belief net to each individual group
of channels independently. Additionally, contextual characteristics are also merged
by initially employing hyper-segmentation on the scene. The performance of this
approach improved the classification accuracy as expected. By indigenously employ-
ing DBN-rooted characteristics mining to every individual channel group decreases
the computational intricacy and simultaneously leads to improved data mining and,
therefore, enhanced precision is acquired. Overall, employing spectral characteris-
tics effectually through partitioned DBN procedure and contextual characteristics
by flexible-segmentation and addition of spectral and contextual characteristics for
scene analyses made a foremost impact on the accuracy of classification. Experimen-
tal analyses of the developed approach on prevailing hyperspectral typical scenes
with diverse contextual features and resolutions launch the worth of the developed
approach where the outcome is similar to numerous newly developed hyperspectral
classification approaches.
1.4.3.5 Stacked Auto-encoder and Markov Random Field Based HSI
Classification
This technique develops a novel spectral-contextual hyperspectral scene classify-
ing methodology built on invariant characteristics mining by utilizing Stack-Auto-
Encoders (SAE) along with unsupervised hyperspectral segmentation. Precisely, ini-
tially, the SAE architecture is employed as a standard spectral feature-rooted classi-
fier for invariant characteristic mining. Subsequently, contextual subjugated feature is
obtained by utilizing operative edge regularization focused segmentation approach.
Lastly, the supreme voting based feature is employed to fuse the spectral mined
characteristics and contextual associations, that forms a precise classification map.
1.5 Organization of the Book
The rest of the book is arranged as follows: Chap.2 briefly provides a description
of hyperspectral imaging, and several deep learning based classification techniques
for hyperspectral image classification. Chapter 3 presents the proposed boundary
adjustment based band selection/categorization approach for effective spectral fea-

12 1 Introduction
ture extraction. Moreover, Chap.4 includes the proposed approach for spatial feature
extraction through Adaptive boundary adjustment based criteria. Chapter5 intro-
duces a novel concept of adaptive window size and spatial feature fusion for opti-
mized deep learning feature extraction. It presents a new methodology that integrates
the findings of Chaps.3 and 4, by integrating the spectral and spatial information in
a deep learning architecture for HSI classification. Chapter6 presents the strategies
for incorporating the spatial information and exploiting the spectral channels for
HSI classification. Chapter7 presents the sparse-based deep learning solution of HSI
classification. Finally, Chap.8 summarizes this book.
References
1. http://www.markelowitz.com/Hyperspectral.html
2. Marin-Franch I, Foster DH (2013) Estimating information from image colors: an application
to digital cameras and natural scenes. IEEE Trans Pattern Anal Mach Intell 35(1):78–91
3. Kim SJ, Deng F, Brown MS (2011) Visual enhancement of old documents with hyperspectral
imaging. Pattern Recognit 44(7):1461–1469
4. Fu Z, Robles-Kelly A, Zhou J (2011) MILIS: multiple instance learning with instance selection.
IEEE Trans Pattern Anal Mach Intell 33(5):958–977
5. Hughes G (1968) On the mean accuracy of statistical pattern recognizers. IEEE Trans Inf
Theory 14(1):55–63
6. Plaza A, Plaza J, Martin G (2009) Incorporation of spatial constraints into spectral mixture
analysis of remotely sensed hyperspectral data. In: IEEE international workshop on machine
learning for signal processing, 2009. MLSP 2009. IEEE, pp 1–6
7. Li J, Marpu PR, Plaza A, Bioucas-Dias JM, Benediktsson JA (2013) Generalized composite
kernel framework for hyperspectral image classification. IEEE Trans Geosci Remote Sens
51(9):4816–4829
8. Zhou Y, Peng J, Chen CP (2015) Extreme learning machine with composite kernels for hyper-
spectral image classification. IEEE J Sel Top Appl Earth Obs Remote Sens 8(6):2351–2360
9. Chen Y, Nasrabadi NM, Tran TD (2013) Hyperspectral image classification via kernel sparse
representation. IEEE Trans Geosci Remote Sens 51(1):217–231
10. FauvelM,BenediktssonJA,ChanussotJ,SveinssonJR(2008)Spectralandspatialclassification
of hyperspectral data using SVMS and morphological profiles. IEEE Trans Geosci Remote Sens
46(11):3804–3814

Chapter 2
Hyperspectral Image and Classification
Approaches
2.1 Introduction to Hyperspectral Imaging
Recent developments in remote sensing technology and geographical data have
directedthewayfortheadvancementofhyperspectralsensors.HyperspectralRemote
Sensing (HRS), also known as imaging spectroscopy, is a comparatively new tech-
nology that is presently under investigation by researchers and scientists for its vast
range of applications such as target detection, minerals identification, vegetation,
and identification of human structures and backgrounds. HRS integrates imaging
and spectroscopy in a distinct structure that generally consists of huge data sets and
needs a modern state-of-the-art analysis techniques. Electromagnetic spectrum of
light is shown in Fig.2.1. Hyperspectral images mostly consist of spectral channels
in the range of about 100–200 in the narrow bandwidth range of 5–10 nm, while,
multispectral images generally consist of 5–10 spectral channels in large bandwidth
range, i.e., 70–400 nm.
2.1.1 Hyperspectral Imaging System
When the light interacts with the earth’s surface, 5 mechanisms can happen, either
the light can scatter in many directions, reflect in a single direction, absorbed as a
energyandstoredinthatmaterialortransmittedorpassesthrough.Figure2.2presents
a detailed process. If we only consider the reflection component, the reflection of
sun’s energy by any earth material creates a distinct footprint specifically known as
the spectral signature of that particular material. The location and shape of these
unique spectral signatures enable us to identify the different types of the land surface
features.
13

14 2 Hyperspectral Image and Classification Approaches
Fig. 2.1 Electromagnetic spectrum [1]
Fig. 2.2 Electromagnetic radiation’s interaction in the atmosphere and Earth’s surface [2]

2.1 Introduction to Hyperspectral Imaging 15
2.1.1.1 Bands and Wavelengths
Each of the bands in the 200 bands of HSI is associated with the particular wave-
length region. For instance, the wavelength region between 700 and 705 nm might be
associated with one band as captured by an imaging spectrometer. Spectral resolu-
tion is associated with a number of bands. But it is not only the number of bands but
also band range (bandwidth). Smaller the bandwidth, better is the spectral resolution
and vice versa. This is the main difference in multispectral and hyperspectral, i.e.,
spectral resolution is higher in hyperspectral than in narrow-band observation.
Hyperspectral imaging is a process of collecting and processing of information
across the electromagnetic spectrum with hundreds of spectral bands. Figure2.3
presents the difference between broadband, multispectral, hyperspectral, and ultra-
spectral (spectral sensing). First is panchromatic, the entire visible region falls into
one observation. In multispectral, the same visible region is broken down into more
broad spectral channels. Whereas, in case of hyperspectral image, the same region
is divided into hundreds of bands. As the spectral capability increases, the power
of analysis also increases, the kind of detailed information that you can retrieve
also increases. In hyperspectral image, for each image, you have a large number of
observations depending on the number of bands you have through which you can
identify the ground material by matching its spectral signature.
2.1.2 Why Hyperspectral Remote Sensing
Most of the earth surface materials have diagnostic absorption features in the 400–
2500 nm range of the electromagnetic spectrum. These features are of a very narrow
spectral appearance. These materials can only be identified if the spectrum is sampled
at sufficiently high spectral resolution.
Human eye can only detect the reflective energy in the visible region of the elec-
tromagnetic spectrum, i.e., 0.4–0.7 µm. On the other hand, advanced hyperspectral
sensors capture data in the form of image, sensing a part of the electromagnetic radi-
ation reflected from the Earth’s surface in a range of wavelengths including visible,
near-infrared, and short-wavelength infrared regions of the electromagnetic spectrum
as described in Fig. 2.4.
2.2 Review of Machine Learning Based Approaches for
Hyperspectral Image Classification
In order to classify, identify, and analyze the chemical composition of objects in the
area, hyperspectral acquiring devices enable scene contents to be remotely analyzed.
Hyperspectral images of earth observation satellites and aircraft have therefore been

Fig. 2.3 Difference between multispectral and hyperspectral data [3]
Fig. 2.4 Hyperspectral data cube [4]

2.2 Review of Machine Learning Based Approaches for Hyperspectral … 17
increasingly important for agriculture, environmental surveillance, urban develop-
ment, mining and defense purposes. Hyperspectral scenes of earth observation satel-
lites and aircraft have therefore been increasingly important for agriculture, envi-
ronmental surveillance, urban development, mining, and defense purposes. Machine
Learning (ML) algorithms have become a crucial method for modern hyperspec-
tral imaging research due to their extraordinary predictive ability. For remote sens-
ing scholars and scientists, thus a sound knowledge of ML techniques has become
extremely important. This section of the chapter examines and analyzes newly devel-
oped algorithms in the research community for ML learning based hyperspectral
scene classification. These techniques are organized by scene evaluation as well as
the ML algorithm and produce a dual visualization of the scene assessment and dif-
ferent kinds of machine learning based scene analysis algorithms. Both hyperspectral
images interpretation and ML techniques are covered in this section (Fig.2.4).
In the areas such as agricultural production, environmental sciences, wildlife, min-
eral extraction and rapid urbanization, security and aerospace science, hyperspectral
imagery is considered as a good remotely sensed tool for studying the chemical
structure of earth resources. Remote sensing, sometimes regarded as spectroscopy
image acquisition, measures the transmitted or released electromagnetic radiation
throughout the image from visible to infrared frequencies into multiple of hundreds
of associated spectral relations. Every pixel in a hyperspectral scene has a vector
consisting of hundreds of components, the scale factor is recognized as the spectral
range, that measure the reflective or emitting radiation. Hyperspectral images can
therefore be perceived as a 3-dimensional data model comprising of 2 contextual
axes that carry relevant data regarding object placement and a spectral axis that car-
ries data regarding the chemical texture of elements. This frequency range acquires
chemical features as these atoms or molecule structures are controlled by the inter-
face among light at distinct frequencies and components. Aerial and satellite-based
hyperspectral devices can capture scenes and also can design the earth surface and
earth usage, identify and localize structures, or interpret the substances’ physiolog-
ical characteristics over a broad geographic region. Hyperspectral scenes, which
consist of hundreds of channels, cannot be evaluated just like color scenes as there
are only 3 channels in RGB scenes. Hence, computer vision approaches are designed
to obtain expressive data from the scenes. ML and computer vision rooted techniques
have demonstrated their accuracy in this regard, because they have the capability to
inevitably pick the association among the spectral information acquired at each spa-
tial location in the scene and the characteristics which are required to be acquired. In
terms of managing distortion and ambiguities, they possess much more robustness in
comparison to conventional approaches, like hand-engineered standardized indices
and physics rooted architectures. The practitioners associated with the hyperspectral
field has revealed a prodigious curiosity in ML in general and in deep learning in
specific.
This section targets to deliver a wide-ranging exposure of not only hyperspectral
scene classification job but also ML and specifically deep learning algorithmic views.
All the approaches summarized in this section are mature published studies. These
approaches are capable of analyzing electromagnetic emission as well as reflective

Fig. 2.5 Hyperspectral image interpretation [5]
scenes, except presented the other way around. The hyperspectral image exploration
goal is characterized as earth surface classification [39], object localization [222],
unmixing [29], and somatic factor assessment [278]. The major aim of this section
is to get the reader familiarized with newly researched HSI classification techniques,
classify a technique either by hyperspectral image job or an ML algorithm and
investigation of existing tendencies and challenges including upcoming directions.
2.2.1 Hyperspectral Image Interpretation Taxonomy
The attribute of the surface component which governs the degree of the reflective
energy is the angular reflection of the surface. Nevertheless, the energy entering the
receptor involves inputs from the atmospheric dispersion, which can be extracted
by utilizing the environmental adjustment approaches [101] for the estimation of the
surface reflection. Therefore, the pixel values in the hyperspectral scene are evaluated
at the radiance or reflective level. The reflective characteristic of a scene is further
favored for HSI scene exploration due to the surface characteristic of the reflective
attribute as shown in Fig.2.5. Moreover, the scene containing reflective attributes
generates enhanced results due to a reduction in the environmental intervention.
Hyperspectral scenes can be analyzed in 4 discrete fields: land cover mapping, target

2.2 Review of Machine Learning Based Approaches for Hyperspectral … 19
Fig. 2.6 Hyperspectral image interpretation [5]
identification, spectral unmixing, and physiological factor assessment, as depicted
in Fig.2.6.
2.2.1.1 Land Surface Mapping
Earth surface mapping [39] is the procedure of detecting the substance to which each
pixel of the HSI scene belongs to. The objective is to generate a map presenting the
diverse distribution of several substances over a terrestrial region captured by an HSI
device. Important uses of surface mapping includes plant types taxonomy [69], city
image organization [74], mineral detection [218], and variation investigation [238].
Numerous surfaceareamappingtechniques involveaprecedinginformationabout
thecategoriesofsubstancesthatexistintheimageincludingthespectralsignaturethat
belong to that particular substance. In general, this data is supplied by professionals
from pixel values obtained from the field, or altered from a given spectrum collection.
Nevertheless, several surface area mapping approaches do not need preceding data
for the image substance.
2.2.1.2 Target Identification
The role of target identification [191] in a hyperspectral scene is to identify and
localize the destination structures provided the spectral signature of a particular

structure. The size of the target structure can vary from a few pixels to even smaller
than a pixel. Targets that are less than a pixel size are difficult to detect.
Task linked to target identification is anomaly detection that involves identifying
the unusual objects resent in the HSI scene.
2.2.1.3 Spectral Unmixing
The electromagnetic radiance acquired by each pixel of the HSI scene is hardly
returned from a distinct surface of a distinct substance. Scenes captured through
aerial or satellite have a resolution of more than one meter, i.e., each pixel represents
an area which mostly is more than one meter. Hence, it is highly possible that the
particular area consists of different or sometimes numerous different materials. For
instance, in an image captured from an urban area, each pixel may contain several
materials including man-made structures, roads, trees, etc. Hence spectral signature
obtained for each pixel may contain spectral characteristics of different materials.
HSI unmixing is the procedure of reconstructing the quantities of uncontaminated
substance at every pixel level of the scene.
2.3 Hyperspectral Remote Sensing Image Dataset
Description
To evaluate the classification performance, all the researchers [6] in the HSI clas-
sification research community utilizes these available standard real hyperspectral
data sets captured by different sensors at different times at different locations. These
datasets propose challenging classification tasks due to the presence of both rural and
urban areas as well as small man-made and natural structures. Mostly, in the existing
literature, two datasets at each time, are considered to demonstrate the validation and
accuracy of the proposed techniques for HSI classification. A detailed description of
each dataset in tabular form is given in Table2.1. A brief description of each dataset
is given below.
2.3.1 Indian Pine: AVIRIS Dataset
Indian Pine dataset was acquired through Airborne Visible Infrared Imaging Spec-
trometer (AVIRIS) sensor in 1992 over the pines region of Northwestern Indiana. It
consists of spatial size of 145 × 145 with a ground resolution of 17 m. It contains
224 spectral bands in the wavelength range 0.4–2.5 m, with a spectral resolution of
10 nm and a spatial resolution of 20 m. Out of 224, 24 noisy bands due to water
absorption were removed resulting in 200 spectral channels. As shown in Fig.2.7,

2.3 Hyperspectral Remote Sensing Image Dataset Description 21
(a) False-color Image (b) Ground Truth (c) Classes
Fig. 2.7 Indian Pine dataset with 16 classes
it contains 16 different land cover agricultural classes. False-color composition and
ground truth are presented in Fig.2.7. This dataset is considered to be one of the chal-
lenging datasets due to its low spatial resolution, small structural size, and presence
of mixed pixels.
2.3.2 Pavia University: ROSIS Dataset
The Pavia University Scene was collected by Reflective Optics System Imaging
Spectrometer (ROSIS) sensor over Pavia University, Italy. The Pavia scene comprises
of a spatial size of 610 × 340 and a spectral size of 115 channels. The spatial size
of the scene is 1.3 m/pixel while the spectral range is 0.43–0.86 µm. A total of 12
noisy bands were removed owing to water absorption with 103 remaining bands. Nine
standard classes are utilized for Pavia scene classification. The false-color composite
is described in Fig.2.8. This dataset comprises both man-made structures and green
areas.
2.3.3 Houston Image: AVIRIS Dataset
The Houston database was collected by AVIRIS sensor over the University of Hous-
ton, and neighboring urban region. It contains 144 spectral bands with a spectral
resolution of 380 × 1050 nm and a spatial area of 349 × 1905. It consists of 15 dif-
ferent ground cover classes as shown in the false-color composite and ground truth
in Fig.2.9.

(a) False-color Image (b) Ground Truth (c) Ground Truth
Fig. 2.8 Pavia University dataset with 9 classes
(a) Houston University
(b) Ground Truth and Classes
Fig. 2.9 Houston University dataset with 15 classes

2.3 Hyperspectral Remote Sensing Image Dataset Description 23
(a) False-color Image (b) Ground Truth (c) Ground Truth
Fig. 2.10 Salinas dataset with 16 classes
2.3.4 Salinas Valley: AVIRIS Dataset
Salinas Valley image was captured by the AVIRIS sensor over the Salinas Valley,
California. It comprises of 224 channels originally but 20 water absorption bands
were discarded. It is characterized by a high spatial resolution of 3.7 m/pixel. Salinas
Valley ground truth consists of 16 classes including soil, green fields. The area
covered comprises 512 lines by 217 samples. The terrain and boundaries are shown
in Fig.2.10.
2.3.5 Moffett Image: AVIRIS Dataset
Moffettwasacquiredin1997bytheAVIRISsensoroverMoffettField,atthesouthern
end of the San Francisco Bay, California.1
The image depicted in Fig.2.11 has 224
spectral bands, a nominal bandwidth of 10 nm, and a dimensional of 512 × 614. It
consists of a part of a lake and a coastal area composed of vegetation and soil.
1[Online] http://aviris.jpl.nasa.gov/html/aviris.freedata.html.

Fig. 2.11 Moffett Field dataset
Table 2.1 Dataset specifications
Dataset Image size Classes Bands Labeled
pixels
Wavelength
range (nm)
Spatial
resolution
(m)
Indian Pine 145 × 145 16 200 10,249 400–2,500 20
Pavia
University
340 × 610 9 103 42,776 430–860 1.3
Salinas 512 × 217 16 200 54,129 400–2,500 3.7
Houston
University
349 × 1905 15 144 2.5 380–1,050 −
Moffett
Field
512 × 614 − 224 − − −
2.3.6 Washington DC Mall Hyperspectral Dataset
This dataset was acquired by utilizing a Hyperspectral Digital Imagery Collection
Experiment (HYDICE) sensor. It comprises 210 spectral channels in the series of
0.4–2.4 um. However, 19 channels were rejected because of water absorption. This
hyperspectral image comprises of 1280 rows and 307 columns. In the experiment, 7
material classes were utilized that include Rooftop, Road, Trail, Grass, Tree, Water,
and Shadow as shown in Fig.2.12. The subject HSI is comparatively not as prob-
lematic as AVIRIS in terms of classification.

2.4 Classification Evaluation Measures 25
(a)
(b)
(c)
Fig. 2.12 Washington DC Mall dataset. a False-color representation of Washington DC. b Ground
truth. c Classes
2.4 Classification Evaluation Measures
In the hyperspectral Image analysis research community, classification performance
is estimated using the evaluation criterion’s based on overall accuracy (OA), Average
accuracy (AA), and kappa Coefficient (k) (Fig.2.12).
• Overall accuracy (OA): OA is the percentage of pixels correctly classified.
• Average accuracy (AA): AA is the mean of all the class-specific accuracies over
the total number for classes for the specific image.
• Kappa Coefficient (κ): Kappa (κ) is a degree of agreement between predicted
class accuracy and reality. Generally, it is considered more robust than OA and
AA.
A detailed definition of each evaluation measure is presented in Fig.2.13.

Fig. 2.13 Definition and evaluation measures for classification performance
2.5 Literature Review
Deep Learning (DL) based algorithms extract discriminative and representative fea-
tures from the complex data recently outperformed many typical algorithms in many
areas including audio, video, speech, and image analysis. DL has recently been intro-
duced in Remote Sensing and has demonstrated convincing results. By feeding the
DL network with the spectral data, the features from the top layer of the network
are fed into a classifier for pixel-wise classification. Moreover, by addressing the
HSI-related issues and carefully adjusting the input–output parameters, we observed
that DL can perform significantly better in HSI analysis.
In this section, the overall framework of DL for HSI classification is presented,
along with the advanced DL-based deep networks and tuning tricks. How useful
features can be extracted from such an increased volume of data. Traditional feature
extraction approaches extracts the feature through models [7]. Substantial develop-
ment has been attained in recent years, in HSI classification such as handcrafted
feature [8–10], discriminative feature learning [11–13], and classifier designing [14,
15]. However, most of the existing techniques can extract only shallow features,
which is not strong enough for the classification task. Moreover, these approaches
are unable to extract the deep discriminative and representative feature due to the
requirement of handcrafted features [11, 16]. Even these handcrafted features don’t
contain the details of the complex data. The problem even worsens due to the great
variability of the HSI data. Detailed description of the existing approaches is depicted
inFig.2.14[4].Thankstodeeplearningarchitectures[17],whichprovidesdeep,shal-
low, discriminative, and representative features for HSI classification. Even though
deep learning contains complex and diverse hierarchical architectures, DL meth-
ods for HSI classification can be integrated into one broad framework. A general
framework of DL methods for HSI analysis is presented in Fig.2.15.
It comprises three main phases, preprocessed input data, hierarchical multi-layer
core deep model, and the extracted output features and classification. In the first

2.5 Literature Review 27
Fig. 2.14 Summary of classification approaches [4]
phase, the input vector comprises of either spectral feature vector, spatial feature
vector, or spectral-spatial feature vector combined.
2.5.1 HSI Noise/Redundancy Detection
Increased volume of HSI data cubes frequently covers a large amount of redundancy
and noise that has some undesirable statistical and geometrical characteristics. This

Fig. 2.15 A general framework for the pixel classification of hyperspectral images using DL meth-
ods [18]
drawback is due to a number of reasons such as sensor or instrumental noise, environ-
mental effects. Sensor noise comprises thermal noise, quantization noise, and shot
Noise, which is the basis of degrading and corrupting the spectral data.
Thecapabilitytoevaluatethenoisefeaturesofhyperspectralremotesensingimage
is a vital stage in creating its abilities and limitations in an operative and scientific
perspective. Many efforts have been made to detect and remove noise and redundant
data. Noise in HSI can be grouped into two main classes [19]: random noise and
fixed-pattern noise. Random noise, due to its stochastic nature, cannot be removed
easily. HSI-processing algorithms are usually based on specific noise models, and
their performance may reasonably degrade if the model does not properly address
the noise characteristics. A widely used random noise model in HSI is the additive
model [20, 21]. Most of the hyperspectral processing literature does not address any
atmospheric effects that were not mitigated through other methods within their noise
models. HIS-processing encounters noise contamination before the radiance enters
the sensor similar to water-vapor absorption.
Existingnoise-estimationmethodscanmainlybeclassifiedintothreetypes:block-
based, filter-based, and their combination. Block-based approaches first divide an
image into dense blocks, followed by the discovery of blocks with the least structure
and texture, then estimation of noise variance based on these blocks. Commonly,
these approaches use variance, spatial homogeneity or spatiotemporal homogeneity
[22, 23], local-uniformity analyzers [24], and gradient-covariance matrices [25] as
a measurement of structure.
Band Selection (BS) work can be grouped into two categories [26]: (1) Maxi-
mum Information or Minimum Correlation (MIMC)-based techniques and (2) Max-

imum Interband Separability (MIS)-based techniques. MIMC techniques typically
use intraband-correlation and cluster criterion. The intraband-correlation criterion-
based algorithm gathers suitable subsets of bands by maximizing the overall amount
of information using entropy-like measurements [27, 28]. MIS-based algorithms
select the suitable set of bands having minimum intraband correlations. For exam-
ple, [29, 30] included a mutual information-based algorithm and a Constrained
Band Selection algorithm based on Constrained-Energy Minimization (CBS-CEM),
respectively.
2.5.2 Deep Learning Based Algorithms
In recent years, several DL-based algorithms have been presented [31] and have
outperformed existing techniques in many fields such as audio identification [32],
natural language processing [33], image classification [34, 35]. The motivation for
such an idea is inspired by multiple levels of abstraction human brain for the process-
ing of tasks such as objection identification [36]. Motivated by the multiple levels
of abstraction and depth of the human brain, researchers have established innovative
deep architectures as an alternative to traditional shallow architectures.
2.5.2.1 Auto-encoder
It is a feed-forward neural network, much like a typical neural network for classifica-
tion but the main difference is its objective to replicate the input onto the output layer
unlike feed-forward, where the objective is to characterize a sharing of a particular
class at the output layer. Figure2.16 shows an auto-encoder with a single hidden
layer. Input and output layers in auto-encoder have the same size. During training,
we compare the values at the output produced by the auto-encoder with the input data
and encourage the auto-encoder to reproduce as perfectly as possible, at the output
layer, the values which are at the input layer. Other than this, it is a regular neural
network. In auto-encoder, the part of the model that computes the hidden layer is
called encoder, which encodes the input into latent representation:
l = f (wl x + bl), m = f (wm y + bm) (2.1)
The major aim is to reduce the disparity among the input and the output:
arg min
wl ,wm .bl ,bm
[error(l, m)] (2.2)
For encoding, a typical sigmoid of the linear transformation is utilized. On the
other hand, decoder, which is going to take the latent representation h(x), i.e., output
of the encoder, linear transform it, and pass it through nonlinearity. So the output is

(a) Basic Auto-encoder (b) Stacked auto-encoder
Fig. 2.16 General SAE model. It learns a hidden feature from input
the decoded output based on the latent representation extracted by the auto-encoder.
Wa, Wb are the weights between the hidden layer and the reconstruction layer. Each
hidden unit extracts a particular feature and during reconstruction that feature is
fed back into the decoder. We train the model such that the hidden representation
maintains all the information about the input. For instance, if we use the hidden
layer that is much smaller than the input layer, it means auto-encoder is going to
compress the information, ignore the part of input that is not useful for reconstructing
it and focuses on the part of the input that is more important to extract from it, for
subsequent reconstruction. Therefore, it could be used to extract meaning full feature
for classification.
C(x, z) = −
1
m
d

k=1

(xk − zk)2
+ (1 − xik) +
β
2
W2

(2.3)
Where x and z are the input and reconstructed data respectively.
2.5.2.2 Deep Belief Network
At the origin of the recent advances in DL, Deep Belief Network (DBN) is one of
the major parts. It is considered as the origin of the unsupervised layer-wise training
procedure. DBN is based on a lot of important concepts in training deep neural
networks that are probabilistic in nature. DBN is a generative model that mixes
undirected and directed interactions between the variables that constitute either the
input or visible layer or all the hidden layers. As shown in Fig.2.17 as an example.
Here we have undirected connections in the start from input to hidden layer but the
directed connection from hidden to hidden and hidden to output layer. In DBN, the
top 2 layers always form an RBM. In Fig.6.15, distribution over h2
and h3
is an
RBM with undirected connections. While other layers are going to form Bayesian
Network with directed interactions.

(a) Basic RBM (b) DBN
Fig. 2.17 General DBN model
This is going to correspond to the probabilistic model associated with the logistic
regression model. DBN is not a feed-forward network. Specifically, joint distribution
over the input layer and three hidden layers are going to be prior over h2 and h3.
Training a DBN is a hard problem. Good initialization can play a really crucial role in
the quality of results. The idea of the initialization procedure is that in order to train,
for instance, 3 hidden unit DBN, we take parameters of the first RBM as an input
to the second RBM and so on. After this, there is a fine-tuning procedure that is not
backpropagation. The algorithm for fine-tuning is known as the up-down algorithm.
2.5.2.3 Convolutional Neural Networks
Convolutional Neural networks or Conv nets or CNNs is an artificial neural network
so far has been popularly used for analyzing images. Although image analysis is
the most widespread use of CNNs, they can also be used for other data analysis
such as classification problems. CNNs are designed from biologically driven mod-
els. Researchers found that human beings are perceiving the visual information in
structured layers. Most generally we can take CNN as an artificial neural network
that has some specialization for being able to detect patterns and make sense of them.
This pattern detection is what makes CNN useful for image analysis. It is a trainable
multi-layer architecture comprising of an input layer, a set of hidden convolutional
layers, and an output layer as Fig.2.18 presents. Generally, CNN consists of several
feature extraction phases. Each phase comprises three layers, hidden Convolutional
layer, pooling layer, and nonlinear layer. A typical CNN comprises of two or three
such phases for deep feature extraction, and then one or more typical fully connected
layers and then a classifier at the top, to classify the learned features. CNN can extract
the deep representation but the main bottleneck in HSI classification is the limited
label data as CNN requires a lot of training data to learn the parameters. Each phase
is briefly explained in the following section.

Fig. 2.18 General framework of deep CNN [37]
Convolutional Layer
Convolutional layer is a set of filters that are applied to a given input data. In case
of HSI, the input to convolutional layer is a three-dimensional data with n two-
dimensional features each of size r × c. The output of the convolutional layer is also
a three-dimensional data of size rl × cl × l. Where l is the size of features each of
size rl × cl. Convolutional comprises of filter banks which connects the input to the
output.
Nonlinear Layer
Nonlinear layer is a CNN that comprises an activation function that takes the features
generated as an output by convolutional layer and generates the activation map as
an output. Activation function comprises element-wise operation so the size of input
and output is the same.
Pooling Layer
It is a kind of nonlinear downsampling layer, responsible for decreasing the spatial
dimensional of activation maps. Generally, they are used after convolutional and
nonlinear layers to reduce the computational burden.
2.5.2.4 Sparse Coding Model
Sparse coding is a model in the context of unsupervised learning. In the context where
we have training data that is not labeled, i.e., set of x vectors in the training set. It
helps us to extract meaningful features from the unlabeled training set and allows
us to leverage the accessibility of unlabeled data. A great number of sparse-based
techniques have been proposed for HSI classification.
Any input x, seek the latent representation h that is sparse that means h consists of
many zeros and only a few none zero elements. We also want the latent representation
to contain meaning full information about x to be able to reconstruct the original
input. The objective function for these conditions can be formulated as
min
D
1
M
M

k=1
min
h(k)
1
2

[(xk
− Dhk
)

2
2
+ β

h(k)

1
(2.4)

Where the first part of the equation represents the reconstruction error that we
want to minimize. Matrix D refers to a dictionary matrix. The next term is sparsity
penalty as we want latent representation to be sparse, for this we will penalize the l1
norm. While β term controls to what extent we wish to get a good reconstruction error
compared to achieving high sparsity. So that is the objective we want to optimize for
each training example x(t)
.
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Chapter 3
Unsupervised Hyperspectral Image Noise
Reduction and Band Categorization
This chapter presents a thorough study and development of the algorithm for the
first step toward HSI classification, i.e., noise/redundancy detection as shown in
Fig.3.1. A complete description of all the HSI classification phases is depicted in
Chap.1, Fig.1.3. This phase aims at the detection of noise and redundancy for the
classification of remote sensing hyperspectral images by addressing a number of
issues.
As discussed earlier, the hyperspectral image consists of hundreds of spectral
channels with a significant amount of redundancy and noise that not only makes
the subsequent analysis of HSI, really challenging and difficult but also degrades
the performance of subsequent classification algorithms. Over the most two recent
decades, progression has been witnessed in hyperspectral sensors. In the area of
remote sensing, analysis of the hyperspectral image is observed as one of the rapidly
developing innovations. There are hundreds of thin adjoining spectral bands included
in hyperspectral data. In the widespread area of applications, this kind of rich data
becomes remarkably important. These applications include environmental surveil-
lance, mineral detection, environmental monitoring, precision farming, environmen-
tal management, and urban planning. Although there is a substantial value of noise
and redundancy involved in the hyperspectral images, that causes geometric and
statistical properties that result in the problematic and reduces effectiveness for the
successive Hyperspectral image data applications and analysis. This includes spec-
tral unmixing, data display, data storage, data transmission, identification of the data,
categorization of the data, and data processing. From the scientific and operational
point of view, while creating its abilities and limitations it is an important step that
it can assess the hyperspectral band properties. On the basis of data included in
every band and band quality, an adaptive boundary band characterization has been
suggested in this study for the first time. This makes bands to be available for all
consequent applications. Bands with dissimilar possessions and features are required
35

36 3 Unsupervised Hyperspectral Image Noise Reduction …
for different applications. From these classified bands on the basis of characteristics,
it is possible to select the subsets of bands. As an example, the bands with dissimilar
features are required for object detection, classification, denoising, noise estimation,
and band selection. On the basis of the movement of boundary movement or bound-
ary adjustment tri-factor criteria with the utilization of local structural regularity and
self-similarity, the suggested approach, allows the classification of bands based on the
level of information contained in each band. For the consequent applications, issues
can also be solved with efficient band characterization. This comprises of Hughes
phenomenon without making causing any issues to the original spectral meaning
of a raw dataset of hyperspectral image. By implementing the proposed method to
the hyperspectral image classification and noise estimation, the application of this
framework is demonstrated. On the basis of the segmented regions obtained from the
adaptive boundary adjustment and movement execution of noise estimation is done.
On the basis of the new suggested segmented regions and noise model, the classi-
fication and noise estimation provide comparable output. The hyperspectral images
originated from the hyperspectral sensors have reliability and quality that is sensitive
to noise [1]. The attained data consists of a substantial quantity of instrument noise,
bands that are noisy, and momentary externalities that are linked with regular water
absorption features, even due to the progression in the hyperspectral images. Image
with high Signal-to-Noise Ratio (SNR) is needed for many hyperspectral images
applications which includes, classification [2], signal-subspace identification [3],
spectral unmixing, information extraction, analysis, scene interpretation, etc. Not
only the precision of consequent applications is affected by this excess noise, but
also for subsequent applications [2]. Therefore, detection of noise is considered an
imperative job and altogether influences further HSI examination. For instance, in
airborne noticeable/infrared-imaging spectrometer (AVIRIS) and intelligent optics
framework imaging spectrometer-sensor (ROSIS) datasets [4], a considerable lot of
the phantom groups have a high SNR; in any case, as per analyst experience, a numer-
ous number of groups (up to 20%) are very loud. A few applications dispose of the
boisterous groups, despite the fact that this may bring about loss of valuable informa-
tion [5, 6]. The versatile limit based band arrangement (A3BC) calculation permits
estimation of the data/commotion level and recoups helpful data from uproarious
groups so as to make it accessible for further examination and application.
There are two main categories for hyperspectral images noise [7]. One is fixed
pattern noise and the other one is random noise. Random noise is stochastic in
nature, so it could not be eradicated easily. There are specific noise models for
the processing of hyperspectral image algorithms, due to which their performance
is remarkably degraded if these models did not address the characteristics of noise
properly. The additive model is mostly used as a random noise model in hyperspectral
images. The majority of literature addressing the processing of hyperspectral does not
cater for atmospheric effects. Other noise models did not reduce the effect of these
atmospheric effects. Before the rays enter the detector, for example, water vapor
absorption noise contamination is encountered by the hyperspectral images process.
During the literature review, we have observed the noise as a composition of detector
noise and scene noise. Scene noise is caused by interactions between radiance and the

3 Unsupervised Hyperspectral Image Noise Reduction … 37
Fig. 3.1 First phase aligned with the framework toward the classification of hyperspectral remote
sensing images
atmosphere and is mainly composed of path-scattered effects and absorption effects.
Scene noise is significant at certain wavelengths, whereas sensor noise is mainly
derived from thermal energy and shot noise. There are signal-dependent elements in
both detector noise and scene noise.
Recently there are three main categories in which noise can be classified. These
are filter-based, block-based, and it could be a combination of both. Images in the
block-based approach are first divided into a number of dense blocks, after this
block is sorted out with minimal texture and structure. Based upon these blocks
noise variance is estimated. Usually, the structure measurement in these approaches
is made by spatiotemporal homogeneity, variance, spatial homogeneity, and gradient
covariance matrices.
Recent methods that are being used for noise estimation are segmentation based
and pixel growing. To define the same object segments for estimation of covariance-
matrix based on extremely non-uniform optically shallow environment for image-
based segmentation is used by Sagar et al. Likewise, the method described in ref
21, that is, kernel-based method is an edition of pixel growing approach which is
basically developed by Dekker and patters. Similar methods were adopted in remote
sensing scenarios for studies of optically shallow water.
There are a number of disadvantages we have to face whenever we are using these
approaches. Firstly during processing, we have to treat special and spectral dimen-
sional equally but in actual hyperspectral images, spatial correlation is much lesser

38 3 Unsupervised Hyperspectral Image Noise Reduction …
as compared to spectral correlations. Along with this, mixed noises are induced by
hyperspectral sensors and the intensity of noise is different between most sensors.
Gaussian noise having uniform variance between bands could be handled by previ-
ously described techniques. Another unrealistic assumption made is that noise is the
same in each band. Therefore, we are unable to achieve the desired result using the
actual data of these approaches. Keeping in view these drawbacks, we need to use a
specific band estimation strategy for noise. So, our focus is to develop this kind of
band-specific strategy for estimation of noise.
In this research, we additionally considered the (Band Selection) BS classifica-
tion of low dimensionality, however, permitted the adaptability of isolating all groups
into various classifications without wiping out any groups, making our methodol-
ogy not the same as BS. We can categorize BS work into two categories [8]: (1)
maximum information or minimum correlation (MIMC)-based techniques and (2)
maximum interband separability (MIS)-based techniques. MIMC techniques typi-
cally use intraband-correlation and cluster criterion. Cluster model and Intra band
correlation are used by MIMC methods. The intraband-connection model based cal-
culation assembles reasonable subsets of groups by amplifying the general measure
of data utilizing entropy like measurements. In 24, 25 MIS-based calculations select
the appropriate arrangement of groups having the least intraband relationships. For
instance, Refs. 26, 27 incorporated a shared data-based calculation and a compelled
band-choice calculation dependent on obliged vitality minimization, individually.
In this investigation, we proposed a ghostly spatial, versatile limit-based band
arrangement (AB3C) system, where contrasts in clamor power between adjoining
groups and spatial attributes are both considered. AB3C could likewise be con-
sidered as an underlying advance for hyperspectral images commotion estimation,
denoising, BS, characterization among others. In this examination, hyperspectral
images’ commotion estimation and arrangement are likewise executed as an appli-
cation dependent on AB3C. In hyperspectral images, neighborhood force varieties
are because of reflectivity, illumination from the picture itself, or from noise. Uti-
lizing picture fluctuation as an estimation of commotion level is probably going to
result in overestimation; in this way, we sectioned the hyperspectral images into
bunches and doled out certainty scores to the groups dependent on the degree to
which the variety was brought about by clamor. Rather than utilizing the credulous
mean of the middle to gauge commotion level, we fit a clamor level capacity with the
majority of the groups weighted by certainty scores. Since clamor levels differ with
groups, we had the option to gauge commotion levels on each band, individually. A
noise model is proposed for the estimation of noise, which combines different factors
like instrument-based SNR estimation, variation of environment that affect the scene
explicitly, interference of air and water, and diffused refractions of daylight and direct
sky. The images are divided into three bands based on the cluster in the proposed
philosophy (28–30). Strategies based on clusters are surprisingly delicate to noise, as
certain groups may comprise totally of boisterous information that can be evaluated
utilizing limit alteration-based criteria autonomously. The clamor level of each band
would then be able to be determined dependent on different limit change factors. The
primary commitments of the proposed system are outlined as follows: The proposed

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walking a little way with your mother, I hope? Mr. Inspector, have
you any opinion----
Don't ask me for opinions, interrupted Inspector Robson.
Pardon my indiscretion, but one's natural curiosity, you know.
There will be an inquest?
Of course there will be an inquest.
Of course--of course. Good day, Mr. Inspector, I am greatly
obliged to you. Now, my dear madam.
They walked out of Deadman's Court, Mrs. Death and Dr. Vinsen
in front, Dick and Gracie in the rear, at whom now and then the
doctor, his head over his shoulder, cast an encouraging smile.
Do you like him, Dick? asked Gracie.
No, I don't, he replied, and I don't know why.
I do, said Gracie. He's so slimy.
CHAPTER XXIX.
A MODERN KNIGHT OF CHIVALRY.
Draper's Mews and its purlieus were on fire with excitement,
raised by a spark dropped by a vicious beetle-browed coster, whose
chronic state for years past had been too much beer, and liquor of a

worse kind. Mrs. Death's neighbours were by no means unfavourably
disposed towards her and her family. The kindness of the poor to the
poor is proverbial, and there is much less friction in the way of social
scandal among the lower classes than among those of higher rank.
This was exemplified in Draper's Mews, where the Death family had
long resided, and had fought life's bitter battle in amity with all
around them. Now and then, of course, small differences had
cropped up, but they were soon got over, and there was no serious
disturbance of friendly relations. To this happy state of things there
was, however, an exception. It happened in this way.
Two or three years ago, on a bright summer day, the beetle-
browed coster wheeled his barrow through the poor neighbourhood,
disposing of his stock of early cherries at fourpence the standard
pound. Children who had a halfpenny or a penny to spare, beggared
themselves incontinently, and walked about with cherry ear-rings
dangling in their ears, while some made teapots with fruit and
stalks, and refreshed themselves with imaginary cups of the finest
leaf of China. Abel Death stood by, and looking at the children
thought of his own, and fingered the few loose coppers in his
pocket. Strange that fruit so tempting and young--the cherries were
whitehearts, with the daintiest blush on their innocent cheeks--
should have been destined to bring sorrow to the hearts of those
who were dear to the poor clerk! But in this reflection we must not
forget the apple in the Garden of Eden.
Unable to resist the temptation Abel Death bought half a pound of
the pretty things, and had received and paid for them, when he
noticed an ugly piece of lead at the bottom of the scale in which the
fruit was weighed. What made the matter worse was that on the
coster's barrow was displayed an announcement in blazing letters of
vermilion, Come to the Honest Shop for Full Weight. Which
teaches a lesson as to the faith we should place in boisterous
professions. Abel Death remonstrated, the coster slanged and
bullied, there was a row and a growling crowd, some of whom had
been defrauded in like manner, and among the crowd an inspector of

weights and measures, who, backed by a constable, forthwith
brought before the magistrate the cheat, the barrow (the coster
wheeling it), the innocent cherries, and the scales with the piece of
lead attached to the wrong balance. The moving scene, with its
animated audience laughing, babbling, explaining at the heels of the
principal actors in the drama, was almost as good a show as a Punch
and Judy. With tears in his eyes, which he wiped away with his cuff,
the coster declared that he'd take his oath he didn't know how the
piece of lead could have got on the bottom of the scale, all he could
say was that some one who had a down on him must have put it
there to get him in trouble, he'd like to find out the bloke, that he
would, he'd make it hot for him; and, despite this whining defence,
was fined, would not pay the fine, and went to prison for seven
days, whimpering as he was led from the court, Wot's the use of a
cove tryin' to git a honest livin'?
The result of this swift stroke of justice was a mortal enmity
against Abel Death. He proclaimed a vendetta, and waited for his
chance, meanwhile avenging himself by kicking and cuffing the
younger members of the Death family when he met them, and
encouraging his children to do the same. The chance came with the
disappearance of Abel Death and the discovery of the murder of
Samuel Boyd. Forthwith he set light to a fire which spread with
startling rapidity, and he went about instilling his poison into the ears
of Mrs. Death's neighbours. Hence her agony of mind.
Dick traced the rumours to their fountain head, found the man,
talked to him, argued with him--in vain. It was a public matter, and
the usual crowd collected.
Look 'ere, cried the coster, to Dick, we don't want none o' your
cheek, we don't. Who are you, I'd like to know, puttin' your spoke
in? A innercent man, is 'e? Looks like it, don't it? Wot's the innercent
man a-keepin' out of the way for? Why don't 'e come 'ome? Tell me
that? 'Ere, I'll wait till you've made up somethink, somethink tasty,
yer know. Take yer time. Wot! Ain't got a bloomin' word to say for

yerself? Wot do you think? Appealing to the people surrounding
them. 'E's a nice sort o' chap to come palaverin' to me, ain't 'e?
The listeners were not all of one mind, many of them, indeed,
being mindless. Some took one side, some took another, while Mrs.
Death and Gracie stood by, pitiful, white-faced spectators of the
scene.
Why, it's as clear as mud, continued the coster. The sneakin'
thief killed 'is master, and then laid 'ands on everythink 'e could
collar, and cut away. Put them things together, and there you are,
yer know.
I know where you'll be, said Dick, speaking in his best judicial
manner, if you're not careful. It won't be the first time you've got
yourself in trouble. The shot told, and the listeners wavered. We're
Englishmen, I believe, said Dick, following up his advantage. We
don't carry knives like the Italians, or fight with our legs like the
French, and we're not made in Germany. This cosmopolitan
reference was an immense hit, and two or three politicians said
Hear, hear! Dick went on. We fight with our fists, and we don't hit
a man when he's down. What we insist upon is fair play; that's what
we wave our flag for--fair play. Look at Mrs. Death, a hard-working,
respectable woman, that's lived among you all these years, and
never done one of you an ill turn. Look at her innocent children that
this great hulking brute is flinging stones at. It's cowardly, sneaking
work. Oh, I'm not afraid of you, my man; if you lift your hand
against me I'll give you something to remember me by. You haven't
the pluck to hit one of your own size; you only hit women and
children. I don't believe you've got a drop of English blood in your
cowardly carcase. With sparkling eyes and glowing face he turned
to the crowd. I appeal to a jury of English men and women. Is what
this brute is doing manly, is it fair, is it English--that's the point, is it
English?

There was no doubt now as to the sympathy. It went out full and
free to Mrs. Death and Gracie, who stood, as it were, in the dock,
with the beetle-browed, sodden-faced coster accusing them, and
this generous, bright-eyed, open-faced young fellow defending
them. A woman who had a good recollection of the cherry incident,
called out, Cherries! and they all began to laugh. This laughter
completely settled the matter; the victory was won. The coster slunk
off.
Dick was overwhelmed with congratulations, and Mrs. Death cast
grateful glances at him, and wistful glances at her old friends and
neighbours. They answered the mute appeal by thronging about her.
To her they said, Never you mind, my dear, we'll see you righted.
And to Dick, You spoke up like a man, sir, and we're proud of you.
Which he capped, rather vaguely, by retorting, I'm proud of you.
You're the sort of women that have made England what it is. Wives
and mothers, that's what you are. A shrill voice called out, Not all
of us, sir, amid shouts of laughter, which caused Dick to add, Then
I hope you soon will be. This happy rejoinder won him the admiring
glances of all the single women, many of whom (as yet unattached)
breathed silent aspirations that heaven would send them such a
man. At the worst of times Dick was a good-looking young fellow;
seen now at his best, glowing with fervour, and espousing the cause
of the weak, he was positively handsome. What wonder that maiden
hearts were fluttering! He could have picked and chosen.
Dr. Vinsen had been an amused witness of the encounter.
My young friend, he said, my dear young friend, victorious
again, always victorious; and in eloquence a Demosthenes. Accept
my congratulations. Mrs. Death, take your little girl home and put
her to bed, then apply a hot linseed poultice. I will call upon you to-
morrow morning. Mr. Dick Remington--pardon the familiarity, but
Dick is so appropriate--I salute you--sal-ute you.
Dick nodded good-day, and turned off with Gracie.

Oh, Dick, she said, fondling his hand, you're splendid,
splendid! No knight of chivalry in the good old times (which were
much worse than the present) ever inspired deeper admiration in the
breast of lady fair than Dick did in the breast of this poor little waif.
I told you, mother, it would be all right if we had Dick with us.
Yes, you did, dear.
Don't I wish I was old enough to walk out with you! said Gracie.
How do you know I'm not a married man, Gracie? he asked.
Go along! she replied, with a touch of scorn. As if I don't know
the married ones by only looking at 'em!
You mustn't mind her foolishness, sir, said Mrs. Death. She says
the silliest things! We're very grateful to you, sir.
Oh, nonsense, he said, anyone else would have done the
same.
They wouldn't, said Gracie. They couldn't.
With a kind pressure of their hands he turned in the direction of
Aunt Rob's house, where a very different task awaited him.
CHAPTER XXX.
REGINALD'S MAN OF BUSINESS.

As it was in Draper's Mews so was it in other parts of the
metropolis. The murder was talked of everywhere, and in some
mysterious way the disappearance of Abel Death was associated
with it. The wildest speculations were indulged in. He had gone to
Australia, he had gone to America, he had never left England at all,
he had taken with him an enormous sum of money which he had
found in the house in Catchpole Square, he had so disguised himself
that his own wife and children would not have known him, he had
been seen in various parts of London. He was generally condemned,
and had no defenders. Had his fate, if caught and in the clutches of
the law, depended upon the public vote, his doom would have been
sealed.
So was it with Mrs. Pond and Mrs. Applebee, who could talk upon
no other subject.
Applebee says that when Inspector Robson saw the body he
turned as white as a ghost.
Why should he? asked Mrs. Pond. It's not the first body he's
seen by many.
Why, don't you know, my dear, said Mrs. Applebee, that his
daughter's married to Mr. Boyd's son?
No, I never heard of it.
Mrs. Applebee bristled with importance. They were married only
a few weeks ago, and they do say it was a runaway match. Off they
went one morning, arm in arm, to the registrar's office, and she
comes home half an hour afterwards, and says, 'Mother, I'm married
to Mr. Reginald Boyd.' 'Married, Florence!' cries Mrs. Robson, and
bursts into tears.
Florence! said Mrs. Pond, in dismay, thinking of the
handkerchief.

That's her name, my dear, and a pretty girl I'm told. She's a
lucky one. Applebee says if Mr. Boyd hasn't made a will her
husband'll come in for everything. Mr. Boyd must have been worth
piles of money. Let's hope it'll do somebody good; it never did while
he was alive. It's curious that your lodger, Mr. Remington, is mixed
up in it, too. He's Inspector Robson's nephew, you know; him and
Miss Florence was brought up together. He's been hanging about
Catchpole Square a good deal the last week or two; in the dead of
night, too. Applebee says he'd like to get hold of that woman that
slipped through his hands on the night of the fog. He's got an idea
that she must have something to do with the murder.
But doesn't he think Abel Death did it? asked Mrs. Pond, faintly.
Oh, yes, he thinks that, as everybody does, but the woman
might be mixed up with it somehow. Just listen to those boys
shouting out another edition. What are they calling out? Fresh
discoveries! I must get a paper; that'll be the third I've bought to-
day. Perhaps they've caught Abel Death. The man on 'The Illustrated
Afternoon' took Applebee's portrait, and I'm dying to see it. I
wouldn't miss it for anything.
There was, of course, but one subject in Aunt Rob's mind when
Dick presented himself. She told him that Reginald was in a terrible
state.
I couldn't stop the boys coming into the street, she said, and
Reginald heard them. Florence ran down to me all in a flutter, and
asked if I didn't hear them calling out something about a murder in
Catchpole Square, and what was it? Then she caught sight of the
paper that I was trying to hide, and when she looked at it she was
frightened out of her life. We did all we could to keep it from
Reginald, but he couldn't help seeing from our faces that there was
something serious the matter. At last there was nothing for it but to
tell him, and we did it as gently as we could. But the shock was
dreadful; he sobbed like a little child. Then he cried that he must go

to the house, and we had almost to use force to prevent him leaving
his bed. Florence threw her arms round him, and begged and
implored so that he had to give in. We tried to comfort him by
saying that it mightn't be true, that it might be another man who
was murdered, and that you and Uncle Rob had gone to see about
it. I'm afraid to ask you if it's true, Dick.
It is too true, he replied, and rapidly related all that had passed
since he and Uncle Rob had left her. She listened horror-struck, and
when he finished could hardly find voice to ask who he thought was
the murderer.
I don't know what to think, he said.
There can be only one man, she said, but he stopped her from
proceeding.
Don't let's talk about it just now, aunt. There are a dozen men
who would rather see Samuel Boyd dead than alive. He had plenty
of enemies, and he deserved to have. If Reginald knew I was here
he would want to see me.
He made me promise the moment either of you came back to
bring you up to him.
We'll go at once. There must be no further concealment.
Reginald was sitting up in bed, very white and haggard.
I thought I heard voices, he said when they entered the room.
Have you been there?
Yes, I have been there, said Dick.
Did you see him? Speak--speak!
I saw him.

You saw him! Well--well?
He is dead.
My God! My God! My father!--Dead! And he died at enmity with
me! groaned Reginald, sinking down in bed, and turning his face to
the wall. They did not disturb him--did not dare to speak. Is it
certain that he was murdered, he said presently in a broken voice,
that he did not die a natural death?
I fear there is no doubt.
Strangled, the paper says--strangled! Dick was silent. Strangled
in his sleep! Without having time to think, to pray! Oh, Florence,
what shame, what misery I have brought upon you!
It is an awful misfortune, Reginald, dear, said Florence, her
arms round his neck, her face nestled close to his, and it makes us
all very unhappy. But there is no shame in it, dearest.
There is, there is, he moaned. Shame, shame--misery and
disgrace!
Dick, observing him closely, strove to arrive at some conclusion,
apart from the evidence in his possession, with respect to his
complicity in the terrible deed. Innocent or guilty, the shock of the
news could have produced no other effect than was shown in the
white face, the shaking body, the sobbing voice. There was another
interval of silence, which, again, Reginald was the first to break. Tell
me everything.
You know the worst, said Dick, let us wait till you are stronger.
No, cried Reginald, I cannot wait. You must tell me everything-
-now, here! Wait? With those cries ringing in my ears? Don't you
hear them? Hark! They listened, and heard nothing. It was the
spiritual echo of the ominous sounds that was in Reginald's ears. Is

anyone suspected? Is there any clue? Are not the people speaking
about it in the streets?
There are all sorts of rumours, said Dick, reluctantly. When
Uncle Rob and I went into the house we found everything as the
papers describe. Nothing seems to have been taken away, but of
course we can't be positive on that point yet. There were no signs of
a struggle.
The paper speaks of bloody footprints, said Reginald, a white
fear in his eyes.
There are signs of them, said Dick, with a guilty tremor.
And no blood on my--my father's body, nor in the bed?
None.
The house has been broken into?
Yes.
The man who broke into it did the deed, said Reginald, in a low,
musing tone; then, after a pause, But the blood--the blood! How to
account for that? How did you get into the house?
Through the front door.
But--the key! exclaimed Reginald, and Dick fancied he detected
signs of confusion. Where did you get the key from?
A policeman scaled the wall at the back of the house, and
entered through the broken window. He found the key in your
father's room, and he came down and let us in.
He had to draw the bolts?
The door was not bolted, and the chain was not up.

Then my father couldn't----, said Reginald, and suddenly
checked himself. Go on.
When Uncle Rob and I left the house Mrs. Death and her little
girl were in the square; she had tried to force herself into the house,
but the policeman kept her back. You know from the papers that her
husband has not been seen since Friday week.
Until I read it in this paper an hour ago, said Reginald, pointing
to the copy of The Little Busy Bee that lay on the bed, I was in
ignorance of it. I cannot understand his disappearance; it is a
mystery. The last I saw of him was on the afternoon of that very
Friday, when I went to see my father in Catchpole Square.
Yes? said Dick, eagerly, greatly relieved at this candid
confession. It was a gleam of comfort.
My father was not at home, and I came away. He pressed his
hand upon his eyes, and a long silence ensued. They looked at him
anxiously, and Florence, her finger at her lips, warned them not to
speak. Removing his hand, he proceeded: I ought to tell you now
why I went to see my father. Had I been well I should have spoken
of it before. Even you, Florence, have not heard what I am about to
say. Dick, I can trust you not to speak of this to any one.
You may trust me thoroughly, Reginald.
I know, I know. In my dear wife's eyes you are the soul of
honour and faithfulness, and in my eyes, also, Dick. It is my hope
that we shall always be firm friends.
With but one thought in his mind, the peace and happiness of the
woman he loved, Dick answered, And mine.
Thank you, said Reginald, gravely. What I wish to tell you
commences with my child-life. My mother, when she married my
father, brought him a small fortune, and she had money, also, in her

own right. Young as I was, I knew that she was not happy, and that
there were differences between her and my father, arising partly
from his endeavours to obtain the sole control of every shilling she
possessed. There were probably other causes, but they did not come
to my knowledge. My mother's refusal to comply with his demands
was prompted by her solicitude for my future. She was the best of
women, and never uttered one word of reproach against my father;
she suffered in silence, as only women can, and she found some
solace in the love she bore for me and in the love I bore for her. We
were inseparable, and, occupying the home with my father, we lived
a life apart from him. He had but one aim, the amassing of money,
and there was no sympathy between us. I hope there are not many
homes in which such estrangement exists. She died when I was ten,
and I lost the one dear friend I had in the world. In our last embrace
on her deathbed she said to me, in a whisper, 'Promise me that
when you are a man--a happy man, I fervently pray--you will not
become a money-lender.' I gave her the promise, and an abhorrence
of the trade my father practised took deep root in me, and has
grown stronger every year of my life. Over an open grave there
should be no bitterness, and though my heart is sore I will strive to
avoid it. My mother left me her little fortune, and appointed a
trustee over whom, by ill chance, my father subsequently obtained
great influence, and in the end had him completely in his power. This
trustee died when I was twenty-two, and before then my inheritance
was in my father's hands to deal with as he pleased. My mother's
will was very precise. A certain sum every year was to be expended
upon my education until I came of age, when the residue was to be
handed to me to make a practical start in life. She named the
schools and colleges in which I was to be educated, and when I was
nineteen I was to spend the next two years in France and Germany
and Italy, to perfect myself in the languages of those countries. It
was at my option whether I remained abroad after I came of age,
and, in point of fact, I did, returning home a year after the death of
my trustee. You will see by these provisions that I was cut off
entirely from the domestic and business life of my father, and I
understood and appreciated her reasons when I became intimately

acquainted with it--as I did when, my education completed, I
returned to his home in Catchpole Square. I lived with him between
two and three years, and during that time his one endeavour was to
induce me to share the business with him, to obey his orders, to
carry out his directions, to initiate myself into a system which I
detested, into practices which I abhorred. We had numberless
discussions and quarrels; he argued, he stormed, he threatened, and
I steadily resisted him. At length matters came to a head, and I
finally convinced him that I would not go his way, but would carve
out a path for myself. 'Upon what kind of foundation will you carve
out this path?' he asked. 'You will want money to keep yourself in
idleness till you establish a position, and are able to pay for your
livelihood.' 'I have it,' I replied. 'Indeed,' he said, 'I was not aware of
it. Have you some secret hoard of wealth which you have hidden
from me?' 'I have my inheritance,' I said. He laughed in my face.
'Your inheritance!' he exclaimed. 'You haven't a shilling. Every penny
of it, and more, has been spent upon your education and riotous
living since your beautiful lady mother died.' The sneering reference
to my dear mother angered me more than his statement that I was
a beggar, and hot words passed between us, in the midst of which I
left the room. The next day I returned to the subject, and said I had
understood from my trustee that when I was twenty-one years of
age I should come into a fortune of eight thousand pounds. 'He lied,'
my father said. 'I have the papers and the calculations here in my
safe. You can look them over if you like. I deal fair by every man,
and I will deal fair by you, ungrateful as you have proved yourself to
be. I could refuse to produce the papers for your private inspection,
but I am honest and generous, and though all is at an end between
us unless you consent to assist me in my business, I will satisfy you
that your father is not a rogue. You are indebted to me a large sum
of money, and I shall be happy to hear how soon you intend to pay
it.' I replied that I would choose the humblest occupation rather than
remain with him, and he took from his safe a mass of documents
and said I must examine them in his presence. I did examine them,
but could make nothing of them, the figures were so confusing.
There were records of transactions into which my trustee had

entered on my behalf, losses upon speculations, of charges for my
education, of sums of money which had been sent to me from time
to time for my personal expenses, of interest upon those advances,
of interest upon other sums, of the cost of my board and lodging
during the time I had lived at home with my father, of the small
sums he had given me during the last two or three years, and of
interest upon those sums. At the end of these documents there was
a debit upon the total amount of twelve hundred pounds, which my
father said I owed him. All this I saw as in a mist, but cunning as the
figures were, there was no doubt in my mind that I had been
defrauded, and by the last man in the world who should have
inflicted this wrong upon me. What could I do but protest? I did
protest. My father, putting the papers back in his safe, retorted that I
was reflecting upon his honesty, that I was his enemy and had
better go to law, and that he renounced me as his son. We had a
bitter quarrel, which ended in my leaving his house, a beggar, to
begin the world; and so strong were the feelings I entertained
towards him, and so sensitive was I to the opprobrium which, in the
minds of many people, was attached to the name of Boyd, that I
determined to renounce it, as he had renounced me. Thus it was
that you knew me only as Mr. Reginald; it caused me many a bitter
pang to deceive you, and I was oppressed with doubts as to the
wisdom of my resolve. All that is now at an end, however, and I ask
your pardon for the deceit. Perhaps you have heard from Florence of
the struggle I made to provide a home for her, and of my
disappointment and despair at not seeing the way to its
accomplishment. I thought much of the fraud of which I had been
the victim, and the more I thought the more was I convinced that
my father was retaining money which rightly belonged to me. At
length it seemed to me that it was my duty to see him again upon
the subject, and to make an earnest endeavour to obtain restitution.
For my own sake, no. Had I not my dear Florence I think I should
have left England, and have striven in another country to carve my
way; but having seen her I could not, could not leave her. It was in
pursuance of this resolution that I went to Catchpole Square last

Friday week, and saw Abel Death, who informed me that my father
was not at home. Now you know all.
It was with almost breathless interest that Dick listened to this
confession, and it was with a feeling of dismay that he heard the last
words, Now you know all. Did they know all? Not a word about the
key, not a word about the second visit to his father late on that fatal
Friday night!
Are people speaking about Abel Death? asked Reginald, turning
to Dick.
Yes. They are coupling his disappearance with the murder. A
strong suspicion is entertained. His poor wife is nearly mad with
grief.
Do you tell me he is suspected of the crime? cried Reginald, in
an excited tone.
Many suspect him.
What cruelty to defame an innocent man--what cruelty, what
cruelty!
Do you know for a certainty that he is innocent? asked Dick.
That is a strange question, Dick. How can I be certain? Until the
truth is known, how can any man be certain? I speak from my
knowledge of his character. A drudge, working from hand to mouth.
Alas! what misery and injustice this dreadful deed brings in its train!
Reginald, dear, said Florence, gently, you are exhausted. Do
not talk any more. Rest a little. Dick will remain here, and will come
up when you want him.
Yes, I am tired. You are a true friend, Dick. You will assist us, I
know. Do all you can to avert suspicion from Abel Death. I must rest

and think. There are so many things to think of--so many things!
He held out his hand to Dick, and then sank back in his bed and
closed his eyes. There was nothing more to be said at present, and
Dick and Aunt Rob stole softly to the room below.
Now, Dick, she said, I am going to open my mind to you.
Do, aunt.
Has it occurred to you that in this trouble that has fallen upon
Reginald he needs a man of business to act for him. Dick looked at
her for an explanation. A man of business, she repeated, and a
devoted friend, rolled into one. I am a practical woman as you know,
Dick, and we mustn't lose sight of Reginald's interests--because his
interests are Florence's now, and ours. He stands to-day in a very
different position from what he did when he married Florence
without our knowledge. Mr. Boyd's death is very shocking, and it will
be a long time before we get over it; but after all it's not like losing
one we loved. He's dead and gone, and the Lord have mercy upon
him. The longer he lived the more mischief he'd have done, and the
more poor people he'd have made miserable. It sounds hard, but it's
the honest truth. I'm looking the thing straight in the face, and I feel
that something ought to be done without delay.
What ought to be done, aunt?
Well, Reginald is Mr. Boyd's only child, and there's that house in
Catchpole Square, with any amount of valuable property in it, and no
one to look after it. It mustn't be left to the mercy of strangers.
It ought not to be.
Reginald won't be able to stir out of the house for at least three
or four days. Now, who's to attend to his interests? You. Who's to
search for the will, supposing one was made--which with all my
heart and soul I hope wasn't? You. Even if there is a will, leaving the

money away from him, he can lay claim to the fortune his mother
left him, for there isn't a shadow of doubt that he has been robbed
of it. There's no one else with time on their hands that will act fair
by him. You must be Reginald's man of business, Dick.
Some person certainly should represent him, said Dick,
thoughtfully, and I shall have no objection if he wishes it. But it
must be done legally.
Of course it must. Do you know a solicitor?
Not one.
And I don't, but I think I can put you on the scent of a
gentleman that will do for us. In High Street, about a dozen doors
down on the left hand side from here, there's a brass plate with 'Mr.
Lamb, Solicitor,' on it. Just step round, and ask Mr. Lamb if he'll be
kind enough to come and see me on very particular business. While
you're gone I'll say just three words to Reginald; I'll answer for it
he'll not object.
You are a practical woman, aunt, said Dick, putting on his hat.
Have you lived with us all these years without finding it out? Cut
away, Dick.
Away he went, and soon returned with Mr. Lamb, a very large
gentleman with a very small practice; and being a gentleman with a
very small practice he brought with him a capacious blue bag.
This is professional, Mr. Lamb, said Aunt Rob.
So I judge, madam, from your message, he answered, taking a
seat, and pulling the strings of his blue bag with the air of a
gentleman who could instantly produce any legal document she
required.

Aunt Rob then explained matters, and asked what Reginald's
position was.
If there is no will, madam, he is heir at law, said Mr. Lamb.
Until a will is found can he enter into possession of the house?
Undoubtedly.
And being too ill to leave his bed, can he appoint some one to
act for him?
He has an indisputable right to appoint any person he pleases.
Then please draw up at once a paper to that effect, in as few
words as possible.
At once, madam! exclaimed Mr. Lamb, with a professional
objection to a course so prompt and straightforward.
At once, said Aunt Rob, with decision. This is an unusual case.
There is the house with no one to take care of it, and here is my
son-in-law upstairs, unable to leave his bed. If you cannot do what
you want I must consult----
Madam, said Mr. Lamb, hastily, there is no occasion for you to
consult another solicitor. I will draw out such an authority as you
require, and it can be stamped on Monday. Favour me with the
name of the attorney.
The attorney? she said, in a tone of inquiry.
The gentleman whom Mr. Reginald Boyd appoints to act for
him?
Oh, Mr. Dick Remington. My nephew.

The solicitor, recognising that Aunt Rob was not a woman to be
trifled with, even by a solicitor, accepted the situation with a good
grace, and set to work.
I have spoken to Reginald, Dick, said Aunt Rob, and he
consented gladly. It is to be a matter of business, mind that. We
can't have you wasting your time for nothing.
In due time the solicitor announced that the document was ready,
and read it out to them, not quite to Aunt Rob's satisfaction, who
shook her head at the number of words, and was only reconciled
when Dick said it was all right.
It is in proper form and order, said Mr. Lamb, though shorter
than it should be.
The shorter the better, said Aunt Rob.
He smiled sadly. There is another thing Mr. Reginald Boyd should
do, madam. He should take out letters of administration.
Is that a long job? she asked.
No, madam, it is very simple, very simple.
Then let it be done immediately.
There are certain formalities, madam. With Mr. Reginald Boyd's
permission we will attend to it on Monday. To this present power of
attorney the signatures of two witnesses are necessary.
I'm one, and my nephew's another.
Your nephew, madam, being an interested party, is not available.
Your signature will be valid, and there is probably a servant in the
house.

Of course there is, said Aunt Rob, resentfully. The law seems to
me to be nothing but going round corners and taking wrong turnings
purposely. Such a fuss and to-do about a signature I never heard.
Mr. Lamb gave her a reproachful look. It is for the protection of
the individual, madam. The law is a thing to be thankful for.
Is it? she snapped.
Without law, madam, he said, in feeble protest, society could
not exist. We should be in a state of chaos.
The formalities were soon concluded. Reginald signed, Aunt Rob
signed, and the servant signed, though at the words, This is your
hand and seal, she trembled visibly. Then instructions were given
for the taking out of letters of administration, and Mr. Lamb took his
departure.
Your worthy aunt, he said, as Dick opened the street door for
him, is a very extraordinary woman. The manner in which she has
rushed this business through is quite unique, and I am not sure, in
the strict sense of the term, that it is exactly professional. I can only
trust it will not be accepted as a precedent.
CHAPTER XXXI.
SCENES IN CATCHPOLE SQUARE.

From time to time there had been murders committed in London
with details dismal and sordid enough to satisfy the most rabid
appetites, but it was generally admitted that the great Catchpole
Square Mystery outvied them all in just those elements of attraction
which render crime so weirdly fascinating to the British public. Men
and women in North Islington experienced a feeling akin to that
which the bestowal of an unexpected dignity confers, and when they
retired to bed were more than ordinarily careful about the fastening
of locks and bolts. Timid wives woke in the middle of the night, and
tremblingly asked their husbands whether they did not hear
somebody creeping in the passages, and many a single woman
shivered in her bed. Shopkeepers standing behind their counters
bristled with it; blue-aproned butchers, knife in hand, called out their
Buy, buy, buy! with a brisk and cheery ring; crossing sweepers
touched their hats smartly to their patrons, and preceding them with
the unnecessary broom as they swept nothing away, murmured the
latest rumour; the lamplighters, usually a sad race, lighted the street
lamps with unwonted alacrity; and the Saturday night beggars took
their stands below the kerb in hopeful anticipation of a spurt in
benevolence. Naturally it formed the staple news in the newspapers
on Sunday and Monday, and all agreed that the excitement it had
created was unparallelled in the records of the criminal calendar.
On Saturday evening, said The Little Busy Bee in its Monday's
editions, numbers of people wended their way to Catchpole Square
from every part of the metropolis. Up till late the usually quiet
streets resembled a Saturday night market, and there was an
extraordinary demand for the literature of crime, with which the
vendors of second-hand books had provided themselves. Towards
midnight the human tide slackened, but even during the early hours
of the morning there were many fresh arrivals. On Sunday the
excitement was renewed, and it is calculated that seven or eight
thousand persons must have visited the Square in the course of the
day, many of whom seemed to regard the occasion as a picnic.

In our columns will be found picturesque accounts of incidents
that came under the notice of our reporters, not the least amusing
of which is that of the mother and father who brought with them a
large family of children, and had come provided with food for a day's
outing. They arrived at eleven in the morning, and at eleven at night
were still there. They had been informed that when a murdered man
was lying in his own bed unburied on the Day of Rest he was
ordered to get up and dress himself when the church bells rang, and
go to church to pray for his sins. If he disobeyed his soul was lost,
and his ghost would appear on the roof at midnight, surrounded by
flames and accompanied by the Evil One. 'Did he go to church?'
asked our reporter, who, in a conversation with the woman late on
Sunday night, elicited this curious piece of information. 'No,' replied
the woman, 'and it's a bad day's work for him. I shouldn't like to be
in his shoes.' The woman furthermore said that she would give
anything to see the ghost at midnight on the roof, thus evincing
small regard for Samuel Boyd's salvation. 'It would be a better show,
wouldn't it?' she observed, with an eye to theatrical effect. 'I've
never seen the Devil.' It is deplorable that in this age such silly
superstitions should obtain credence, and that with numbers of
people in different parts of the country the belief in witchcraft and in
demoniacal demonstrations should still exist.
Secondary only in importance to the murder is the disappearance
of Samuel Boyd's clerk, Abel Death. To suggest anything in the
shape of complicity would be prejudging the case, but whatever may
be the fate of Abel Death his poor family are to be commiserated.
The theories and conjectures respecting the disappearance of this
man are perfectly bewildering, and many are the excited discussions
concerning it. Such licence of speech cannot be commended, and we
suggest to those persons indulging in it the advisability of
suspending their judgment.
A full report of the inquest held this morning appears in our
columns. In view of the burial of the body of the murdered man,
which will take place to-morrow, it was deemed necessary to open

the inquiry to-day, although it was anticipated that little progress
would be made; but although the Coroner stated that the
proceedings would be of a formal character, it will be seen that
matters were introduced the development of which will be followed
with the keenest interest. The appearance of an eminent barrister
for Lord and Lady Wharton, whose names have not hitherto been
associated with the mystery, aroused general curiosity, which was
intensified by the conduct of Lady Wharton herself. The Court was
crowded, and numbers of persons could not obtain admittance.
Among the audience we noticed several famous actors and
actresses.
CHAPTER XXXII.
THE LITTLE BUSY BEE'S REPORT OF THE INQUEST.
This morning, at the Coroner's Court, Bishop Street, Mr. John
Kent, the Coroner for the district, opened an inquiry into the death
of Mr. Samuel Boyd, of Catchpole Square, who was found dead in his
house on Saturday, the 9th inst., under circumstances which have
already been reported in the newspapers.
The coroner, addressing the jury, said the initial proceedings
would be chiefly formal. Their first duty would be to view the body
of the deceased; after that certain witnesses would be examined
who would testify to the finding of the body, and others who would
give evidence of identification. The inquiry would then be adjourned
till Wednesday, on which day medical and other evidence would be

forthcoming. He refrained from any comment on the case, and he
advised the jury to turn a deaf ear to the strange rumours and
reports which were in circulation; it was of the utmost importance
that they should keep an open mind, and be guided only by the
evidence which would be presented to them. Much mischief was
frequently done by the prejudice aroused by injudicious public
comment on a case presenting such singular features as the present.
Comments of this nature were greatly to be deplored; they
hampered, instead of assisting, the cause of justice.
The jury then proceeded to Catchpole Square to view the body,
and upon their return to court Mr. Finnis, Q.C., rose and stated that
he appeared for Lord and Lady Wharton, who had a close and
peculiar interest in the inquiry.
The Coroner said the inquiry would be conducted in the usual
manner, without the aid of counsel, whose assistance would be
available in another court, but not in this, where no accusation was
brought against any person, and where no person was on his trial.
Mr. Finnis: Our desire is to render material assistance to you and
the jury. Lady Wharton----
The Coroner: I cannot listen to you, Mr. Finnis.
Mr. Finnis: Lady Wharton has most important, I may say most
extraordinary evidence to give----
The Coroner: Her evidence will be received, but not to-day. Pray
be seated.
Mr. Finnis: Her ladyship is in attendance.
The Coroner: She is at liberty to remain; but I repeat, her
evidence cannot be received to-day. Only formal evidence will be
taken to enable the body to be buried.

Mr. Finnis: Evidence of identification, I understand?
The Coroner: Yes.
Mr. Finnis: Lady Wharton's evidence bears expressly upon this
point.
The Coroner: It must be tendered at the proper time.
Mr. Finnis: With all respect, Mr. Coroner, I submit that this is the
proper time.
The Coroner: I am the judge of that. I ask you not to persist. I
shall conduct this inquiry in accordance with my duties as Coroner.
The first witness called was Mr. Robert Starr.
You are a reporter?
A special reporter and descriptive writer for 'The Little Busy
Bee.'
Were you the first person to enter the house in Catchpole Square
after the death of Mr. Samuel Boyd?
I cannot say. Some person or persons had been there before me,
as is proved by a broken window at the back of the house through
which I obtained entrance, but whether after or before the death of
Mr. Boyd is unknown to me.
It appears, however, to have been a recent entrance?
It appears so.
You have no knowledge of these persons?
None whatever.

Having obtained entrance into the house, what next did you do?
I went through a passage, and up a staircase to another passage
which leads to the street door. In this passage are doors opening
into various rooms. I looked into these rooms without making any
discovery, until I came to one which seems to have been used as an
office. There are two doors in this office, one opening into a small
room in which I saw nothing to arouse my suspicions, the other
opening into a larger room which I found was a sleeping apartment.
Examine this plan of the rooms, and tell us whether it is
accurate?
Quite accurate, so far as my memory serves.
The room on the right is the sleeping apartment?
Yes.
Mr. Samuel Boyd's bedroom?
I do not know. There was a bed in it, and the usual
appointments of a bedroom. I stepped up to the bed, and saw it was
occupied. Examining closer, I discovered that the person in it was
dead.
By the person you mean Mr. Samuel Boyd?
I do not. I have never seen Mr. Boyd in his lifetime, and I could
not therefore identify the body. But from the fact of the house being
his, and from certain rumours of foul play which had reached me, I
assumed that it was he.
You examined the body?
Yes, and I observed marks on the throat which favoured the
presumption that the man had been murdered.

In his sleep?
I cannot vouch for that.
Were there any signs of a struggle?
None. The limbs were composed, and what greatly surprised me
was the orderly condition of the bedclothes.
How long did you remain in the house?
About two hours.
During that time were you quite alone?
Quite alone.
Were there any indications of a robbery having been
committed?
I observed none. The clothes of the deceased were on a chair,
and there was no appearance of their having been rifled. There is a
safe fixed to the wall; it did not seem to have been tampered with.
Having completed your examination, what next did you do?
I left the house, and proceeded to the Bishop Street Police
Station to give information of my discovery.
And after that?
I went to the office of 'The Little Busy Bee,' and wrote an
account of what I had seen and done, which, being published, was
the first information the public received of the murder--if murder it
was.
Had any orders been given to you to take action in this matter?

None. I acted entirely on my own initiative.
What impelled you?
Well, there seemed to me to be a mystery which should be
unravelled in the public interests. I pieced three things together. The
disappearance of Mr. Boyd's clerk, as reported in our paper, the
silence of Mr. Boyd respecting that disappearance, upon which, had
he written or spoken, he could probably have thrown some light, and
the house in Catchpole Square sealed up, so to speak. These things
required to be explained, and I set about it.
Mr. Finnis, Q.C.: Now, Mr. Starr, at what time in the morning----
The Coroner: No, no, Mr. Finnis. I instruct the witness not to
answer any questions you put to him.
Mr. Finnis: Will you, then Mr. Coroner, ask him at what hour in
the morning he made the discovery? I assure you it is a most
important point.
The Coroner: At what hour in the morning did you enter the
house?
At a little after ten.
And you left it?
At a few minutes before twelve. I went straight to the police
station, where, no doubt, the time can be verified.
Have you any other information to give bearing on this inquiry?
One thing should be mentioned. In my printed narrative I state
that I noticed dark stains upon the floor of the office and the
bedroom, and that I traced these stains to the window at the back. I
scraped off a portion of the stains, which I gave to my chief, who

handed it to an analyst. His report is that they are the stains of
human blood.
Were they stains of old standing?
No. I scraped them off quite easily.
Did you observe any blood on the bedclothes?
None whatever.
The next witness was Constable Simmons, who stated that he
and Constable Filey were instructed by the day inspector at the
Bishop Street Police Station to enter the house for the purpose of
ascertaining whether there was any truth in the information given by
Mr. Starr.
At what time were those instructions issued?
Somewhere about three o'clock.
So that three hours elapsed before any action was taken?
I am under orders, sir.
The witness then gave an account of how he got into the house
by means of a ladder over the wall at the back, and through the
window. Corroborating in every particular the evidence of the
reporter, he went a step farther. In the bedroom of the deceased he
found the key of the street door, which he opened to admit
Constable Filey, who was keeping watch in the Square outside. The
street door was neither chained nor bolted. He did not see any
stains of blood on the floor; he did not look for them.
Constable Filey, who was next examined, gave evidence to the
same effect. Neither of these officers was acquainted with Mr.

Samuel Boyd, and could not therefore speak as to the identification
of the body.
Inspector Robson was then called. His appearance caused some
excitement, it being understood that his daughter was married to
the son of the deceased.
You are an inspector of police?
Yes. At present on night duty at the Bishop Street Station.
You were acquainted with Mr. Samuel Boyd?
Not personally. I have seen him several times, but have never
spoken to him.
You are sufficiently familiar with his features to identify him?
I am.
When did you first hear of his death?
On Saturday afternoon, when I was sitting at home with my wife
and my nephew, Mr. Richard Remington. The boys were calling out
news of a murder in Catchpole Square, and we went out and bought
a paper.
Before Saturday afternoon had your attention been directed in
any way to the house in which the deceased resided?
Yes. Last Tuesday night a woman was brought into the office
who made a statement respecting the disappearance of her
husband, who had been in the service of the deceased.
What is the name of the woman?
Mrs. Abel Death. I advised her to apply to the magistrate on the
following morning, in order that it might be made public.

After reading the news in the paper on Saturday afternoon what
did you do?
I went to the Bishop Street Station, and learned that constables
had been sent to enter the house, for the purpose of ascertaining if
the statement made by the reporter was correct.
And then?
I went to Catchpole Square, accompanied by Constable Applebee
and my nephew, Mr. Richard Remington--both of whom were
acquainted with the deceased--I entered the house and saw the
body. I identified it as the body of Mr. Samuel Boyd.
Is there any doubt in your mind on the point?
Not the slightest. I have seen him scores of times, and his
features were quite familiar to me.
You saw the marks on his throat?
Yes.
Have you any idea as to the cause of his death?
It appeared to me to have been caused by strangulation.
Now, Inspector Robson, I wish to ask you if you formed any idea
as to how long he had been dead. You cannot, of course, speak with
the authority of an expert, but we should like to hear what your
impression was?
My impression was that he had been dead several days.
At this answer considerable commotion was caused by a lady
exclaiming Impossible! Impossible!

CHAPTER XXXIII.
SCENES IN COURT.
The Coroner: I cannot allow the proceedings to be interrupted by
any of the spectators, and I must request the person who spoke to
preserve silence.
The Lady (rising): My name is Lady Wharton, and I know what I
am saying. It is not in the nature of things to be silent when so
monstrous a statement as that is made. I say again, it is impossible.
The Coroner: The witness has given his impression----
Lady Wharton: He cannot be in his right senses, or he must have
some motive----
The Coroner: You are impeaching the witness and delaying the
proceedings. Unless you resume your seat it will be my duty to have
you removed----
Lady Wharton (indignantly): Have me removed! Is this a court of
justice?
The Corner: I hope so. Kindly resume your seat.
Lady Wharton: I insist upon being heard.

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