Medical image analysis and processing using a dual transform

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 03 Issue: 02 | Feb-2014, Available @ http://www.ijret.org 325
MEDICAL IMAGE ANALYSIS AND PROCESSING USING A DUAL
TRANSFORM
Shiby Angel K1
1
Assistant Professor, Karunya University, Coimbatore
Abstract
The demand for images in medical field has increased drastically over the years. The need for reducing the storage space has resulted
in image compression. This paper presents a dual transform for medical image compression algorithm. The experimental results
determines how the compression ratio (CR), peak signal to noise ratio (PSNR) and SNR (signal to noise ratio) of different
compression algorithms responds to dual transform algorithm.
Keywords: DCT, SPIHT, Haar Wavelet, Linear approximation transform, image compression, Singular Value
Decomposition (SVD).
----------------------------------------------------------------------***------------------------------------------------------------------------
1. INTRODUCTION
Image compression, an important area in the field of digital
image processing deals with techniques for reducing the
storage required for saving an image or the bandwidth
required for transmitting. The aim of image compression is to
reduce the number of bits required to represent an image and
is done by removing the redundancies. The degree of
redundancy determines how much compression can be
achieved.
The main classification of compression includes lossy and
lossless compression. Lossy compression compresses data by
discarding some of the data while lossless compression does
not change the content of the file. Lossless compression is
mainly preferred for archival purposes and medical imaging.
Medical images are of interest for a large number of
applications and it resulted in a constant growth in the
amounts of data that have to be transmitted, processed, and
stored efficiently [1].
The people in India, particularly in rural and remote areas are
found struggling to access timely medical treatment. The
region of the country is characterized by densely populated
communities spread over vast distances; there is a lack of
qualified personnel in certain sectors of the health service.
Telemedicine has come originally to serve rural populations,
or any people who are geographically dispersed, where time
and the cost of travel make access to the best medical care
difficult. In this paper an efficient method for compression of
medical images is compared and studied with different metrics
and algorithms.
2. BACKGROUNDS
SVD is one of the most useful tools of linear algebra [2]
compared to other linear approximation methods. SVD is a
factorization and approximation technique which effectively
reduces any matrix into a smaller invertible and square matrix.
The SVD matrix decomposition which is extensively used in
mathematics [3] appears in ﬁelds related directly with algebra,
such as least squares problems or the calculus of the matrix
rank. Its usefulness in applications concerning image
processing includes pattern recognition, secret communication
of digital images, movement estimation, quantization, and
compression of images and video sequences.
SVD is commonly used in face recognition, object detection,
field matching techniques and meteorological and
oceanographic data analysis. One of the main features that
made SVD to have application in image processing is that it is
a factorization and approximation technique which effectively
reduces any matrix into a smaller invertible and square matrix
[3]. SVD was also used in the area of face recognition which
proved some properties that the SVD approach is robust,
simple, easy and fast to implement [5]. SVD when compared
with wavelet compression, block truncating compression, and
discrete cosine transform compression provided evidence that
when singular value increases, the size and quality of
compressed image improves [6]. Similarly the performance
analysis of SVD Algorithm portrayed that using SVD
computation, an image matrix can be compressed to a
significantly smaller sized matrix and during decomposition
the image is almost identical to original image. This in turn
saves a lot of memory space [7].

__________________________________________________________________________________________
Haar transform, a simplest compression process of wavelet, is
a multi scale transformation [12]. Wavelets are functions
generated from a single function by its dilations and
translations [13]. Haar wavelet has special properties such as
robust, high compression ratios and provides good results in
terms of imperceptibility which makes it use mainly in
watermarking [14]. DCT transform introduces no loss to the
source image samples; it transforms them to a domain in
which they can be more efficiently encoded.
There are several encoding methods that provide high image
quality at high compression rates. The SPIHT image coding
algorithm developed in 1996 [15] is another more efficient
implementation of the embedded zero tree wavelet (EZW)
algorithm [16]. SPIHT provides even better performance [17]
than the other extensions of EZW. EBCOT [18] which is a
block based encoder is more complicated and also time-
consuming [24]. SPECK [19] also which uses recursive set-
partitioning procedure to sort subsets of wavelet coefficients
by maximum magnitude with respect to integer powers of two
thresholds. When compared to other encoders mentioned
above SPIHT provides salient features such as better quality,
visually superior, intensive progressive capability, SNR
scalability and, low computational complexity [20,21,22,23].
The computational speed of the SPIHT algorithm is also found
to be very good [23].
3. DUAL TRANSFORM
3.1Singular Value Decomposition & Haar-Wavelet
Transform
SVD, extensively used in mathematics is a factorization of a
real or complex matrix in linear algebra. One of the special
features of SVD is that it can be performed on any real m x n
matrix. It factorizes matrix A into three matrices U, S and V
where, U is a left singular matrix and V is the right singular
matrix and S is a diagonal matrix. U, S and V are obtained by
calculating rank, eigen values and eigen vectors of the matrix
A. The process of SVD begins by selecting the matrix A(m x
n) which has m rows and n columns. Now, matrix A is
factorized into three matrices U, S and VT
.
A = USVT
(1)
Wavelet transform or wavelet analysis is a very efficient
approach developed as a mathematical tool for signal analysis.
The Haar Transform technique widely used in wavelet
analysis is the simplest wavelet. Haar wavelet transform has
been used as an earliest example for orthonormal wavelet
transform with compact support. The haar transform (HT) is
one of the simplest and basic transformations from a space
domain are a local frequency domain and it reduces the
calculation work [27]. HT decomposes the linear
approximated image as approximation components and detail
components.
3.2 Encoding Process
Once the linear approximated image is transformed using haar
wavelet, the coefficients are further decomposed using the
SPIHT encoder. Salient features of SPIHT makes it visually
superior and of better quality. After the haar wavelet transform
is applied to an image, the SPIHT algorithm works by
partitioning the wavelet decomposed image into significant
and insignificant partitions based on the following function:



 

otherwise
C
Us
n
ji
n
,0
2||max,1
)( , ….……..
(2)
Where )(Usn is the significance of a set of co-ordinates T,
and jic , is the coefficient value at co-ordinate  ji, . The
block diagram of dual transform and SPIHT encoder is seen in
Fig.1.
Algorithm: Dual Transform based Image Compression
Step1: Data-Input image A(m,n) of size 256x256 which is a
matrix A(m x n)
Step2: Apply dual transform:
a) Compute its transpose AT
and AT
A.
b) Determine the eigen values of AT
A and sort these in
descending order, in the absolute sense. Square roots these to
obtain the singular values of A.
c) Construct diagonal matrix S by placing singular values in
descending order along its diagonal. Compute its inverse, S-1
.
d) Use the ordered eigen values from step b and compute the
eigenvectors of AT
A. Place these eigenvectors along the
columns of V and compute its transpose, VT
.
e) Compute U as U = AVS-1
. Now, compute the full SVD
using A = USVT
.
f) Decompose the linearly approximated image using haar
wavelet transform.
Step 3: Encode the resultant coefficients using SPIHT
encoder.
Step 4:Calculate the resulting image quality of the compressed
images using different metrics such as Peak Signal to Noise
Ratio (PSNR), Mean Square Error (MSE), Bits Per Pixel
(BPP), Compression ratio (CR) and Computational time (CT).
4. PERFORMANCE EVALUATION
To evaluate the performance of dual transform with other
transforms, three medical images of size 256 x 256 with 8 bits
per pixel are used. The efficiency is compared with Haar
Wavelet–SPIHT [28] and DCT-SPIHT [29] for different
metrics such as PSNR, MSE, CR, CT and BPP. Table 1-3
shows the performance of different methods using the 3

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medical images. Fig. 4-6 shows the rate vs. PSNR
performance of the 3 different medical images. Bit rate is the
average bits required to represent a single pixel in the
compressed image. It’s obviously clear from the graphs that
the PSNR value increases with increase in bits per pixel.
Fig-1: The block diagram of the proposed compression
method
a) b)
c)
a) T1WIAnkle b) T2WI-Axial-1 c) T2WI-Axial -2
Fig-2: Original Images
Table-1: MSE values attained by dual transform and Existing
methods at 0.4bpp
Compressi
on
Methods
T1WIAnkl
e
T2WIAxia
l-1
T2WI-Axial
-2
Haar-
SPIHT
1.77 2.3 1.4
DCT-
SPIHT
1.73 2.9 3.35
Proposed
1.43 1.95 1.08
Table-2: CR values attained by dual transform and Existing
methods at 0.4bpp
Compressi
on
Methods
T1WIAn
kle
T2WI-
Axial-1
T2WI-Axial
-2
Haar-
SPIHT
12.02 11.0
13.44
DCT-
SPIHT
8.87 7.84
10.46
Proposed 16.92 13.75 16.15
Table-3: PSNR values attained by dual transform and
Existing methods at 0.4bpp
Compressi
on
Methods
T1WIAn
kle
T2WI-
Axial-1
T2WI-Axial
-2
Haar-
SPIHT
45.65 44.51 46.68
DCT-
SPIHT
45.74 43.51 42.88
Proposed 46.59 45.23 47.81
Fig-4: Rate-PSNR performance of T1W1Ankle image
obtained using dual transform and existing methods

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Fig-5: Rate-PSNR performance of T2W1-Axial-1 image
Fig.6 Rate-PSNR performance of T2W1-Axial-2 image
5. CONCLUSIONS
Thus a dual transform for medical image compression was
studied. This dual transform method highly preserves quality
of images with high compression ratio and bits per pixel. The
quality of the image is also improved in terms of PSNR.
In the case of medical images there is a great need to have no
deterioration in image quality. The results proved that with no
image quality loss, it can be used in the applications of
medical purposes. It can also be used to compress images used
in telemedicine applications.
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