Secure OMP Based Pattern Recognition that Supports Image Compression

SECURE OMP BASED PATTERN RECOGNITION
THAT SUPPORTS IMAGE COMPRESSION
Takayuki Nakachi1
and Hitoshi Kiya2
1
Nippon Telegraph and Telephone Corporation,Kanagawa, Japan
2
Tokyo Metropolitan University, Tokyo, Japan
ABSTRACT
In this paper, we propose a secure Orthogonal Matching Pursuit (OMP) based pattern recognition scheme
that well supports image compression. The secure OMP is a sparse coding algorithm that chooses atoms
sequentially and calculates sparse coefficients from encrypted images. The encryption is carried out by
using a random unitary transform. The proposed scheme offers two prominent features. 1) It is capable of
pattern recognition that works in the encrypted image domain. Even if data leaks, privacy can be main-
tained because data remains encrypted. 2) It realizes Encryption-then-Compression (EtC) systems, where
image encryption is conducted prior to compression. The pattern recognition can be carried out using a
few sparse coefficients. On the basis of the pattern recognition results, the scheme can compress selected
images with high quality by estimating a sufficient number of sparse coefficients. We use the INRIA dataset
to demonstrate its performance in detecting humans in images. The proposal is shown to realize human de-
tection with encrypted images and efficiently compress the images selected in the image recognition stage.
KEYWORDS
Surveillance Camera, Pattern Recognition, Secure Computation, Sparse Coding, Random Unitary Trans-
form
1. INTRODUCTION
With the increase in threats and criminal activity, security is seen as a major public concern.
Image/video surveillance is one approach to addressing this issue. Many image/video surveillance
systems are now widely deployed in many public spaces such as airports, banks, shopping streets,
and public streets, and they are recording huge amounts of image/video every day. Fortunately,
edge/cloud computing offers an efficient way of handling and analyzing the huge amounts of
image/video data. However, edge/cloud computing poses some serious issues for end users, such
as unauthorized use, data leaks, and privacy failures due to the unreliability of providers and
accidents [1].
Many studies have examined the processing of encrypted data; most proposals use homomorphic
encryption (HE) and secure multiparty computation (MPC) [2]-[7]. Even though service providers
cannot directly access the native content of encrypted signals, they can still apply HE and MPC.
In particular, fully homomorphic encryption (FHE) allows arbitrary computation on encrypted
data [6][7]. However, these methods impose high communication costs, high computational com-
plexity, or large cipher text sizes, so further advances are needed for attractive applications such
as big data analysis and advanced image/video processing. We take a random unitary transform
approach, which has much lower communication, lower computational complexity, and a smaller
ciphertext size than either FHE or MPC has. Secure computation methods based on the random
unitary transform have been reported for biometric template protection [8]-[11].
Signal & Image Processing: An International Journal (SIPIJ) Vol.11, No.2, April 2020
DOI: 10.5121/sipij.2020.11202 23

We proposed secure sparse coding based on the random unitary transform for pattern recognition
[12]-[15], and Encryption-then-Compression (EtC) methods [16]-[18]. Early work on sparse cod-
ing was based on the efficient coding hypothesis, which states that the goal of visual coding is to
faithfully reproduce visual input while minimizing neural effort [20][21]. It effectively represents
observed signals as the linear combination of a small number of atoms. Sparse dictionary learning
has been successfully applied to various image/video and audio processing applications [22]-[30].
The effectiveness of sparse coding has been reported for pattern recognition/image classification
[24]-[26] and image compression [27]-[30]. For example, the experiments of Ref. [30] show that
rate-distortion based sparse coding outperforms JPEG and JPEG2000 by up to 6+ dB and 2+ dB,
respectively.
In this paper, we propose a secure pattern recognition scheme that extends the previously proposed
EtC methods. The secure pattern recognition methods and EtC systems mentioned above were
proposed separately. The current proposal offers not only image pattern recognition but also
image compression. The integrated system is realized by performing pattern recognition in the
compressed signal domain. 1) It is capable of efficient pattern recognition in the encrypted image
domain. Even if data leaks, privacy is maintained because the data remains encrypted. 2) It works
as an EtC system. Pattern recognition and image compression can be carried out seamlessly in the
same compressed signal domain. In the proposed scheme, Orthogonal Matching Pursuit (OMP)
[19] is executed in the compressed signal domain. OMP is a sparse coding algorithm that chooses
the atoms of sparse coding sequentially and calculates the sparse coefficients. Pattern recognition
employs a few sparse coefficients. On the basis of the pattern recognition results, additional
enhancement atoms are chosen and used to compress the selected images. Finally, we employ the
INRIA person dataset [31] to evaluate the human detection performance of the proposed method.
Detecting humans in images is essential for not only image/video surveillance but also many
applications such as automatic driver assistance.
The organization of this paper is as follows. In Sec. 2, we explain related work. Section 3
describes sparse coding for image patches. In Sec. 4, we propose secure OMP based pattern
recognition that supports image compression. Section 5 shows experimental results. Conclusions
and future work are given in Sec. 6.
2. RELATED WORK
In this section, we review the conventional secure pattern recognition methods and EtC systems.
2.1. Secure Pattern Recognition
We previously proposed secure sparse coding for pattern recognition [12]-[15]. Feeding encrypted
images into the secure OMP computation yields sparse coefficients used for pattern recognition.
We verified that by adopting the random unitary transform, the pattern recognition performance is
not degraded, which proves that this proposed framework operates securely with no performance
degradation. Furthermore, compared with deep-learning based methods such as Stacked PCA
network (SPCANet) [32], our sparse coding based method has several prominent advantages such
as 1) low computational complexity and less data needed for training and 2) transparent machine
learning; the algorithm is interpretable as the optimization problem is written in closed form.
Refs. [12]-[15] detail the experiments and results.
2.2. Encryption-then-Compression (EtC) Systems
Encryption-then-Compression (EtC) systems [16]-[18] [33]-[35] have been proposed to securely
transmit and compress images through an untrusted channel provider; the traditional technique is
24

Figure 1: Sparse coding for image patches.
to use Compression-then-Encryption (CtE) systems. EtC systems allow us to close non-encrypted
images to SNS providers because encrypted images can be directly compressed even when the
images are recompressed by SNS providers multiple times. Well-known EtC systems are block
scrambling-based encryption schemes that are compatible with international standards, e.g., JPEG
and JPEG2000 [33]-[35]. While sparse coding based EtC systems [16]-[18] are not compatible
with international compression standards, their coding performance is high because they form
dictionaries that fit the observed signals.
3. SPARSE CODING FOR IMAGE PATCHES
In this section, we overview sparse coding for image patches, which is the basis of secure pattern
recognition and EtC systems.
3.1. Basic Formulation
We consider image patches of size
√
n ×
√
n pixels that are ordered lexicographically as column
vectors yi = {y1, , ..., yn}T
∈ Rn
. The patches are extracted from image Y as shown in Fig. 1. We
assume that every image patch yi can be represented sparsely given the over-complete dictionary
D = {d1, ..., dK} ∈ Rn×K
whose columns contain K prototype atoms di:
yi = Dxi, (1)
where xi = {x1, ..., xK}T
∈ RK
are sparse coefficients, i = 1, · · · , N, and N is the total number of
patches. In advance, the dictionary D is designed for the images by training algorithms such as
MOD [36] and K-SVD [37].
If n < K and D is a full-rank matrix, an infinite number of solutions to the representation problem
are available. The solution with the least number of nonzero coefficients is certainly an appealing
representation. This sparsest representation is the solution given by
(P0) min
xi
||xi||0 subject to yi = Dxi, (2)
where ||·||0 is the l0-norm, counting the nonzero entries of the vector. Extraction of the sparsest
representation is, however, an NP-hard problem [38].
3.2. Selection of Dictionary Atoms
Dictionary atoms are typically estimated by a “pursuit algorithm” that finds the following approx-
imate solution:
xi = arg min
xi
!
!
!
!
!
!yi − Dxi
!
!
!
!
!
!
2
2
subject to ||xi||0 < ϵi. (3)
We assume that the dictionary D is fixed. Well-known pursuit algorithms include Orthogonal
Matching Pursuit (OMP) [19]. OMP is a greedy, step-wise regression algorithm. At each stage,
OMP chooses the dictionary atom having the maximal projection onto the residual signal. After
each selection, the representation coefficients w.r.t. the atoms selected so far are found via least-
squares search.
25

Figure 2: One atom dk and corresponding sparse coefficient vector xk
T .
3.3. Dictionary Learning
An over-complete dictionary D is designed by adapting its content to fit a given set of images.
Given the set Y={yi}N
i=1, we assume that there exists a dictionary, D, that can recreate the given
images via sparse combinations. The overall mean square error of a representation is given by
E = ||Y − DX||2
2 . (4)
Method of Optimal Direction (MOD) [36] and K-Singular Value Decomposition (K-SVD) [37]
are well-known dictionary learning algorithms. Assuming that X={xi}N
i=1 is fixed, the MOD al-
gorithm allows us to seek an update to D such that the above error is minimized. Taking the
derivative of (4) with respect to D yields
D = arg min
D
||Y − DX||2
F = YXT
(XXT
)−1
. (5)
K-SVD is an iterative method that uses singular value decomposition; it alternates between sparse
coding based on the current dictionary and the process of updating the dictionary atoms to better
fit the data. It has been shown to perform very well for image processing tasks. Here, we use K-
SVD for pattern recognition and image compression because of its ability to extract the features
of image data. Unlike MOD, K-SVD updates atoms sequentially. Figure 2 shows the k-th atom
dk and the corresponding sparse coefficient vector xk
T . For each atom dk (k = 1, 2, · · · , K in D),
update it with the following steps.
1) Compute the overall representation error matrix Ek with
Ek = Y −
K
"
j!k
djxj
T . (6)
2) Define the group of indexes that satisfy:
ωk = {i | 1 ≤ i ≤ K, xk
T (i) ! 0}. (7)
Define Ωk as a matrix of size N × |ωk| with ones on the (ωk(i), i)th entries and zeros elsewhere.
Multiplication ER
k = EkΩk creates a matrix that includes a selection of error columns that use the
atom dk.
3) Apply Singular Value Decomposition (SVD) to ER
k :
ER
k = U∆VT
=
n
"
i=1
ui · σivT
i . (8)
Choose the updated dictionary atom dk to be the first column u1. Update coefficient vector xk
R to
be the first column multiplied by the first eigenvalue σ1vT
1 .
26

Figure 3: Architecture of training process.
(a) Overall system
(b) Encryption process
Figure 4: Architecture of running process: pattern recognition that supports image compression.
4. SECURE OMP BASED PATTERN RECOGNITION THAT SUPPORTS
IMAGE COMPRESSION
In this section, we propose a secure pattern recognition method that offers image compression as
an integrated component. The integrated system is realized by performing pattern recognition in
the compressed signal domain.
4.1. Secure Computation Architecture
Figure 3 shows the training step. The dictionary D is designed by the K-SVD algorithm at the
local site. Feeding the training images to the learning algorithm yields the dictionary D. Next,
we apply random unitary transform function T(·) to the dictionary D to generate an encrypted
dictionary D̂. The encrypted dictionary D̂ is sent to the appropriate edge/cloud site and stored in
a database.
Figure 4 illustrates the running step. Figure shows (a) the overall system and (b) its encryption
process. The local site applies the same random unitary transform function T(·) to test image
27

Figure 5: Flow chart of secure OMP computation.
Y to generate encrypted image Ŷ. Then, encrypted image Ŷ is sent to the edge/cloud site. The
edge/cloud site uses encrypted image Ŷ and the encrypted dictionary D̂ to perform secure OMP
computation. Secure OMP chooses the atoms sequentially and calculates the sparse coefficients
X̂ from the encrypted Ŷ and D̂.
Figure 5 shows a flow chart of secure OMP computation. First, secure OMP chooses a few base
atoms and estimates a corresponding set of a few sparse coefficients x̂KB
for pattern recognition.
The pattern recognition is carried out in the compressed signal domain using a set of the sparse
coefficients x̂KB
. Then, on the basis of the pattern recognition results, only the selected images
are compressed. For example, if a user wants to store images of humans, image compression is
performed only for those images. Secure OMP chooses additional enhancement atoms in order
to store images in high quality. Then, a set of sparse coefficients x̂KBE
corresponding to both the
base and the enhancement atoms are calculated. x̂KBE
is used for compression.
4.2. Random Unitary Transform
The encrypted images and dictionary are generated by using the random unitary transform ap-
proach. A vector fi (i = 1, · · · , L) ∈ RN
is encrypted by a random unitary matrix Qp ∈ CN×N
with
a private key p:
ˆ
fi = T(fi, p) = Qp fi, (9)
where f̂i is an encrypted vector; L is the number of vectors. Note that the random unitary matrix
Qp satisfies
Q∗
pQp = I, (10)
where [·]∗
and I mean the Hermitian transpose operation and the identity matrix, respectively.
In addition to unitarity, Qp must have randomness for generating the encrypted signal. Gram-
Schmidt orthogonalization is a typical method for generating Qp. Security analyses on using
28

the random unitary matrix have been considered in terms of brute-force attack, diversity, and
irreversibility [8]-[10]. Furthermore, the encrypted vector has the following properties.
· Property 1: Conservation of Euclidean distances.
!
!
!
!
!
!fi − f j
!
!
!
!
!
!
2
2
=
!
!
!
!
!
! ˆ
fi − ˆ
f j
!
!
!
!
!
!
2
2
(11)
· Property 2: Norm isometry.
!
!
!
!
!
! ˆ
fi
!
!
!
!
!
!
2
2
=
!
!
!
!
!
!fi
!
!
!
!
!
!
2
2
(12)
· Property 3: Conservation of inner products.
f∗
i f j = ˆ
f
∗
i
ˆ
f j (13)
The proposed secure sparse coding computation generates encrypted signal ŷi and dictionary D̂
with two transforms:
ŷi = T(yi, p) = Qpyi (14)
D̂ = T(D, p) = Qp D. (15)
Then, the encrypted image patches ŷi (i = 1, 2, · · · , N) are randomly permuted using a random
integer generated by a private key q. Finally, the permuted patches are combined to form an
encrypted image Ŷ, which is fed to the OMP computation.
4.3. Secure OMP Computation
The sparse coefficient x̂i is estimated for each image patch ŷi. Instead of Eq. (3), we consider the
following optimization problem in which ŷ and D̂ are assumed to be given:
x̂i = arg min
x
∥ ŷi − D̂xi ∥2
2 sub ject to ||xi||0 < ϵ. (16)
The sparse coefficient x̂i yielded by secure OMP computation is the same result as that created by
the non-encrypted version [16]. The algorithm is shown below (prefix i of x̂i and ŷi is omitted for
notation simplicity):
Secure OMP computation for pattern recognition that supports image compression
Initialization: k = 0, and set
· The initial solution x0
= 0
· The initial residual r̂0
= ŷ − D̂x0
= ŷ
· The initial solution supports S0
= ∅.
Main Iteration:
Increment k by 1 and perform the following steps:
· Sweep: Compute the errors
ϵ̂(i) =
!
!
!
!
!
!r̂k−1
!
!
!
!
!
!
2
2
−
(d̂i · r̂k−1
)2
!
!
!
!
!
!d̂i
!
!
!
!
!
!
2
2
. (17)
Here, we define an atom d̂i as
d̂i = D̂δi, (18)
29

where δi = [(0, · · · , 0, δ(i), 0, · · · , 0)]T
has all elements equal to 0 except one (i.e., the i-th element
is 1).
· Update Support: Find the minimizer
i0 = arg min
i"Sk−1
{ϵ̂(i)} , Sk
= Sk−1
∪ {i0} ,
where Sk
is a support that is the set of indexes corresponding to non-zero elements of the sparse
coefficient vector x at the k-th iteration.
· Update Provisional Solution: compute
x̂k
= {(D̂Sk )T
D̂Sk }−1
{(D̂Sk )T
ŷ}, (19)
where D̂Sk is a submatrix of D̂ consisting of the columns d̂i with i ∈ Sk
, and x̂k
is the set of
columns of x corresponding to the support Sk
.
· Update Residual: compute
r̂k
= ŷ − D̂Sk x̂k
. (20)
· Stopping Rule: For the pattern recognition,
k = KB, (21)
where KB is the number of a few specified atoms, e.g., KB = 1 or 2. Iteration is repeated until
the number of chosen atoms reaches KB. Then, by using a set of the estimated sparse coefficients
x̂k
= x̂KB
, the pattern recognition is performed with the processing steps described in Sec. 4.4.
On the basis of the pattern recognition results, further iteration is needed for image compression
of the selected image. For image compression,
k = KBE, (22)
where KBE(> KB) is the sufficient number of atoms that can be used to store images in high
quality. KBE is directly specified by the user. A set of the sparse coefficients x̂k
= x̂KBE
is used for
image compression. An alternative stopping rule is that if
||r̂k
||2 < ϵ, (23)
stop. Here, ϵ is a threshold specified by the user. The corresponding set of the sparse coefficients
x̂k
= x̂KBE
is used for image compression. k = KBE is indirectly controlled by ϵ, which is generally
a different value from Eq. (22). Until satisfaction is achieved, commence another iteration.
Output: The proposed solution x̂ is obtained after k iterations.
4.4. Pattern Recognition
The pattern recognition consists of two steps: feature extraction and classification. The secure
OMP algorithm chooses atoms sequentially and calculates the corresponding sparse coefficients
for each image patch. We use just a set of the few sparse coefficients x̂KB
(calculated using only
k = 1 or 2 iterations) for pattern recognition and classification.
1. Feature Extraction
Figure 6 shows the procedure of feature extraction and classification. The sparse coef-
ficients for each image patch are used for formatting the feature vector. To reduce the
30

Figure 6: Pattern recognition: feature extraction and classification.
dimension of the feature, we take the statistics of the spatially local sparse coefficients as
the feature, which corresponds to local spatial pooling. Multiple sparse coefficients x̂KB
i ,
which correspond to local B × B image patch yi, are grouped into the averaged sparse co-
efficient x̄j(j =, 1, 2, · · · , N/B2
), where B is block size. The averaged sparse coefficients x̄j
are vectorized to produce a feature vector ⃗
x.
2. Classification
Support Vector Machine (SVM) is a supervised machine learning algorithm that can be used
for both classification or regression tasks, but it is mostly used for the former. In SVM, we
input the feature vector ⃗
x to the discriminant function as
(⃗
x) = sign(ωT
⃗
x + b) (24)
with
sign(u) =
#
1(u > 1)
−1(u ≤ 1),
(25)
where ω is a weight parameter, and b is a bias. SVM also has a technique called the kernel
trick, which is a function that takes a low dimensional input space and transforms it into
a higher dimensional space. This can be used for non-linear classification. For the pattern
recognition task, classification is performed using a linear SVM. The SVM is trained using
task data from training subjects.
4.5. Image Compression
Feeding the encrypted dictionary D̂ and the encrypted image Ŷ into the secure OMP computation
yields a set of the sparse coefficients x̂KBE
i for each image patch yi. Then, quantization is applied to
a set of the sparse coefficients x̂KBE
i and entropy encoded. The rate-distortion tradeoff between the
compression ratio and decoded image quality of each image patch can be controlled by altering the
number of atoms KBE or the threshold ϵi without decoding the encrypted image. Rate-distortion
control can be done gracefully by adding atoms sequentially. To keep the image quality of each
image patch, the same threshold is set: ϵi = constant (i = 1, · · · , N).
The decompression and decryption processes are the reverse processes of compression and en-
cryption. The decoded image ẏi for each image patch can be obtained by ẏi = Q∗
p D̂x̂KBE
i . Only the
authorized user can decrypt the encrypted images.
5. EXPERIMENTAL RESULTS
We carried out experiments on detecting humans in images from the INRIA person dataset [31].
Here, we assume that we compress only those that include human(s) captured by surveillance
systems.
31

(a) Human images
(b) Non-human images
Figure 7: Several samples of 480 × 640-pixel human and non-human images in INRIA person
datasets [31].
5.1. INRIA Person Dataset and Parameters
The INRIA person dataset is one of the most popular and widely used pedestrian detection bench-
mark datasets. It contains images of various sizes with and without humans. We evaluated the
performance of the proposed method by challenging it with 480 × 640-pixel human and non-
human images. Several samples of the INRIA person dataset are shown in Fig. 7. The upper rows
are human images, and the lower rows are non-human ones. The parameter settings are:
1. Designing K-SVD: We applied K-SVD and trained a dictionary of size 64 × 256. The
training data consisted of a set of image patches of size 8 × 8 pixels, randomly taken from
20 human images.
2. Creating the random unitary transform: We generated a 64 × 64 random unitary transform
by using the Gram-Schmidt orthogonalization method.
3. Designing and running the SVM: Block size B=20 for local pooling of the sparse coeffi-
cients. For the human detection task, two-class classification was performed using a linear
SVM. In the training step, the SVM was trained using 100 images (50 human images and
50 non-human images).
In the evaluation, we used 10-fold cross-validation. One-hundred images were partitioned into 10
sub-samples (a single sub-sample contained 5 human and 5 non-human images). Of the 10 sub-
samples, a single sub-sample was retained as the validation data for testing, and the remaining 9
subsamples were used as training data. The cross-validation process was then repeated 10 times,
with each of the 10 subsamples used exactly once as the validation data. The 10 results were then
averaged to produce a single estimate.
5.2. Results
The trained dictionary D and corresponding encrypted dictionary D̂ are shown in Fig. 8. Figures
9 and 10 show the original Y and corresponding encrypted images Ŷ for a sample of human and
non-human images, respectively. It can be seen that the encrypted dictionary and the encrypted
images provided no visible information. Feeding the encrypted dictionary D̂ and the encrypted
images Ŷ, the secure OMP computation was performed.
A. Pattern Recognition
The detection rate of the proposed privacy-preserving pattern recognition method is shown in
Table 1. We evaluated two cases: the number of atoms KB = 1 and KB = 5. The detection rate is
32

(a) Dictionary D (b) Encrypted dictionary D̂
Figure 8: Trained dictionary and corresponding encrypted dictionary for human images.
(a) Original Y (b) Encrypted image Ŷ
Figure 9: Sample of original and encrypted human images.
(a) Original Y (b) Encrypted image Ŷ
Figure 10: Sample of original and encrypted non-human images.
calculated by
Detection rate =
Number of images correctly detected
Total number o f test images
. (26)
Table 1 shows that the proposed method achieved a detection rate of around 80 [%]. Note that the
results were obtained from encrypted images. Setting the number of atoms to KB = 1 or KB = 5
yielded almost the same performance. This means that a small number of sparse coefficients was
enough for pattern recognition. Figures 11 and 12 show feature vectors (reshaped to matrix forms)
for the human image of Fig. 9 and the non-human image of Fig. 10, respectively. These figures
show that the feature vectors of the human image were more sparse than that of the non-human
image. Regarding the difference in the number of atoms (KB = 1 and KB = 5), the feature vector
was almost the same. This also supports the assumption that a small number of sparse coefficients
is sufficient for pattern recognition.
For comparison, we evaluated a pattern recognition method with the input being the non-encrypted
version of OMP. The detection rate of the non-encrypted version is shown in Table 2. The 10-
33

Table 1: Detection rate (DR) [%] of proposed method.
(a) Number of atoms: KB = 1
Test 1 2 3 4 5 6 7 8 9 10 Ave.
DR 100 70 80 70 90 90 80 60 90 70 80
(b) Number of atoms: KB = 5
Test 1 2 3 4 5 6 7 8 9 10 Ave.
DR 90 60 90 70 90 90 80 50 100 70 79
(a) Number of atoms: KB = 1 (b) Number of atoms: KB = 5
Figure 11: Feature vectors (reshape to matrix forms) for human image of Fig. 9.
(a) Number of atoms: KB = 1 (b) Number of atoms: KB = 5
Figure 12: Feature vectors (reshape to matrix forms) for non-human image of Fig. 10.
fold cross-validation used the same training and testing datasets as for the non-encrypted version
of OMP and the secure OMP. The results show that the proposal had exactly the same detection
performance as the non-encrypted version of the pattern recognition method.
B. Image Compression
Figure 13 plots the coding efficiency (number of atoms KBE vs. decoded image quality PSNR
[dB]) for the selected human images. We controlled the image quality of the human images for
each patch by setting the number of atoms KBE = {1, 2, 3, 4, 5}. For practical use, we set the
number of atoms according to the condition KBE > KB. Here, KBE was set without following
this condition in order to evaluate the coding efficiency. This figure shows that the proposed
method increased the decoded image quality by adding atoms sequentially. It can be seen that
when the number of atoms was 5, high quality images were obtained. Note that there is no need
to decompress and decrypt images when running the secure OMP algorithm.
34

Table 2: Detection rate (DR) [%] of the non-encrypted method.
(a) Number of atoms: KB = 1
Test 1 2 3 4 5 6 7 8 9 10 Ave.
DR 100 70 80 70 90 90 80 60 90 70 80
(b) Number of atoms: KB = 5
Test 1 2 3 4 5 6 7 8 9 10 Ave.
DR 90 60 90 70 90 90 80 50 100 70 79
Figure 13: Coding efficiency (Number of atoms KBE vs. decoded image quality).
C. Security Evaluation
Finally, we evaluated the security of secure OMP from the viewpoint of objective image quality
(PSNR) and the visibility of decoded images. We considered both (a) access by an authorized user
and (b) access by an unauthorized user. Tables 3 shows the decoded image quality obtained by the
authorized and unauthorized users for the encrypted human image of Fig. 9. From this table, we
can see that the decoded image quality obtained by the unauthorized user was very low regardless
of the number of atoms KEB. Figures 14 and 15 show decoded image examples obtained by the
authorized and unauthorized users for the encrypted human image of Fig. 9. These results show
that encrypted images cannot be decrypted by an unauthorized user.
6. CONCLUSION AND FUTURE WORK
In this paper, we proposed an OMP based pattern recognition scheme that well supports image
compression. Pattern recognition and image compression can be carried out seamlessly in the
same compressed signal domain. The proposed scheme offers two prominent features. 1) It is ca-
pable of pattern recognition that works in the encrypted image domain. Even if data leaks, privacy
can be maintained because data remains encrypted. 2) It also realizes EtC systems, where image
encryption is conducted prior to compression. We confirmed its performance by detecting humans
in the INRIA dataset. In terms of estimation accuracy for pattern recognition, these experiments
are merely the first step. Further study is required to enhance the proposal’s performance.
7. REFERENCES
[1] C. T. Huang, L. Huang, Z. Qin, H. Yuan, L. Zhou, V. Varad-harajan, and C-C. J. Kuo, “Sur-
vey on securing data storage in the cloud,” APSIPA Transactions on Signal and Information
Processing, vol. 3, e7, 2014.
EFERENCES
R
35

Table 3: Decoded image quality obtained by authorized and unauthorized users for encrypted
human image of Fig. 9.
(a) Authorized user
Number of atoms KBE 1 2 3 4 5
PSNR [dB] 31.24 33.72 35.47 36.78 37.84
(b) Unauthorized user
Number of atoms KBE 1 2 3 4 5
PSNR [dB] 13.24 13.21 13.20 13.19 13.19
(a) Number of atoms: KBE = 1 (b) Number of atoms: KBE = 5
Figure 14: Images decoded by authorized user for encrypted human image of Fig. 9.
(a) Number of atoms: KBE = 1 (b) Number of atoms: KBE = 5
Figure 15: Images decoded by non-authorized user for encrypted human image of Fig. 9.
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38

Authors
Takayuki Nakachi received a Ph.D. degree in electrical engineer-
ing from Keio University, Tokyo, Japan, in 1997. Since joining the
Nippon Telegraph and Telephone Corporation (NTT) in 1997, he has
been engaged in research on super-high-definition image/video cod-
ing and media transport technologies. From 2006 to 2007, he was a
visiting scientist at Stanford University. Dr. Nakachi is a member of
the Institute of Electrical and Electronics Engineers (IEEE) and the
Institute of Electronics, Information and Communication Engineers
(IEICE) of Japan.
Hitoshi Kiya received his B.E and M.E. degrees from the Nagaoka
University of Technology in 1980 and 1982, respectively, and his Dr.
Eng. degree from Tokyo Metropolitan University in 1987. In 1982,
he joined Tokyo Metropolitan University, where he became a Full
Professor in 2000. From 1995 to 1996, he attended the University
of Sydney, Australia as a Visiting Fellow. He is a Fellow of IEEE,
IEICE, and ITE. He currently serves as President-Elect of APSIPA,
and he served as Inaugural Vice President (Technical Activities) of
APSIPA from 2009 to 2013 and as Regional Director-at-Large for
Region 10 of the IEEE Signal Processing Society from 2016 to 2017.
39

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