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In most of the digital steganography methods provided for natural digital images, the embedding of the confidential message is based on the minimisation of the defined distortion functions. It is often done based on choosing the most optimal criterion of distortion. Although the distortion functions are designed innovatively, steganography algorithms will be optimal. In such approaches, embedding interactions are often overlooked. Unlike usual images that have areas with a variety of tissue features, there are many smooth areas in medical images that will make the changes more visible if they are manipulated. Therefore, this study presents an adaptive approach that comes from the interactions between the changes made during the embedding algorithm to reduce the probability of recognising the message embedded in medical images and reducing the distortion caused by embedding in a discrete cosine transform space and based on the imperialist competitive algorithm for joint photographic experts group images, especially in medical images due to the importance of information steganography in them. The results obtained show the high efficiency of the proposed algorithm in comparison with the state‐of‐the‐art methods that are presented in this area.
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Received: 16 January 2020 Revised: 13 September 2020 Accepted: 8 October 2020 IET Image Processing
DOI: 10.1049/ipr2.12055
ORIGINAL RESEARCH PAPER
Medical JPEG image steganography method according to the
distortion reduction criterion based on an imperialist
competitive algorithm
Hamidreza Damghani1Farshid Babapour Mofrad2Leila Damghani3
1Department of Electrical and Computer
Engineering, Science and Research Branch, Islamic
Azad University, Tehran, Iran
2Department of Medical Radiation Engineering,
Science and Research Branch, Islamic Azad
University, Tehran, Iran
3Department of Computer Sciences, Kharazmi
University, Tehran, Iran
Correspondence
Hamidreza Damghani, Department of Electrical
and Computer Engineering, Science and Research
Branch, Islamic Azad University, Tehran, Iran.
Email: hamidreza.damghani@gmail.com
Abstract
In most of the digital steganography methods provided for natural digital images, the
embedding of the confidential message is based on the minimisation of the defined distor-
tion functions. It is often done based on choosing the most optimal criterion of distortion.
Although the distortion functions are designed innovatively, steganography algorithms will
be optimal. In such approaches, embedding interactions are often overlooked. Unlike usual
images that have areas with a variety of tissue features, there are many smooth areas in med-
ical images that will make the changes more visible if they are manipulated. Therefore, this
study presents an adaptive approach that comes from the interactions between the changes
made during the embedding algorithm to reduce the probability of recognising the message
embedded in medical images and reducing the distortion caused by embedding in a discrete
cosine transform space and based on the imperialist competitive algorithm for joint pho-
tographic experts group images, especially in medical images due to the importance of
information steganography in them. The results obtained show the high efficiency of the
proposed algorithm in comparison with the state-of-the-art methods that are presented in
this area.
1 INTRODUCTION
Modern steganography is the science and art of hidden
communications that create intangible changes in digital
media to conceal confidential information without creating
suspicion of the information existence [1, 2]. At present,
most professional steganography methods are based on the
distortion minimisation framework, which defines distor-
tion as the total cost of embedding each of the cover
media elements. Syndrome-trellis codes provides a generic
and effective coding method that can theoretically optimise
the average embedded distortion based on cost function
[3].
With rapid reforms and the development of a biometric sys-
tem, digital medical images have become increasingly important
in recent years [4]. Medical images can be easily transferred to
the internet to research, training, and counsel. Since medical
images have information such as personal information of
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properly cited.
© 2021 The Authors. IET Image Processing published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology
patients, the security protection of the private information and
privacy of patients is also important in the transmission of med-
ical images [5]. Ambika [6] has proposed a method for medical
image steganography using the elephant herding-monarch but-
terfly optimisation algorithm for effective selection of pixels for
embedding the secret message. Senapati [7] combines discrete
Tchebichef transform with a singular value decomposition
scheme and overcomes the false positive and diagonal line
problems.
JPEG images have been very common on the internet to
reduce bandwidth and improve storage space. Thus, over the
last few years, these types of images have become a major
objective in the field of steganography in images and many
researchers have investigated the methods of images steganog-
raphy in JPEG format and suggested ways to hide a variety of
messages in JPEG images including Jsteg [8], Outguess [9], F5
[10], J-UNIWARD [11], uniform embedding distortion (UED)
[12].
IET Image Process. 2021;15:705–714. wileyonlinelibrary.com/iet-ipr 705
706 DAMG HA NI ET AL.
As mentioned earlier, the JPEG format has recently been
increasingly used to store and transfer medical images. Because
it can increase not only the higher compression speed but also
the visual quality of the image. Hence, JPEG format can be
used to embed a patient’s personal information into medical
images.
The Jsteg method rewrites the least significant bit (LSB) of
the quantised discrete cosine transform (DCT) coefficients with
the hidden message and changes the statistical properties of
histogram coefficients to recognisable methods [6, 13]. The
outguess method maintains almost half of the existing coeffi-
cients to correct statistical deviations in the total histogram of
the coefficients that are due to the change in LSBs in other
coefficients (remains unchanged). Therefore, its embedding
capacity is almost halved [7]. The classic F5 method embeds
only messages into the non-zero alternating current (AC) DCT
coefficients but also introduces the shrinkage effect so that
the coefficient becomes zero after embedding. The F5 method
without shrinkage is an improved version of the F5 method
that allocates infinite costs to some DCT coefficients and thus
reduces the negative effect of the usual method [14]. The
authors in [15] have presented the cost function and JPEG
images steganography method by designing and optimising a
multi-parameter model with the preservation of specific statis-
tical features. They recently proposed universal wavelet relative
distortion (UNIWARD) in [9] that evaluates the cost of embed-
ding DCT coefficients in the field of location using an inverse
DCT transform and executes embedding operations in the
JPEG domain. The J-UNIWARD embedding distortion is cal-
culated as the sum of coefficient variations in the decomposition
process with the directional filtre banks on the uncompressed
image [16]. Based on the concept of spread-spectrum commu-
nication, UED [12] and uniform embedding revisited distor-
tion (UERD) [17] with low computational complexity extend
the embedding changes in DCT coefficients from all possible
values. Improved UERD (IUERD) works well by exploring the
correlation among adjacent DCT blocks between the smooth
andtexturedareas[18]. The introduced methods are adaptive
steganography methods that are based on a shrinking distor-
tion model in which changes in cover media elements are per-
formed independently so that minimisation of the overall dis-
tortion equals the minimisation of the total cost of modified
elements.
In JPEG images, DCT coefficients show two complex cor-
relations called intra- and inter-block correlations. Intra-block
correlations refer to the relationship between coefficients with
similar frequencies in a block, while inter-block correlations
describe the relationship between coefficients in correspond-
ing positions in different DCT blocks; inter-block correla-
tions have been ignored in recent JPEG-based embedding
methods.
In this study, we design an adaptive JPEG image stegano-
graphic scheme to minimise the defined distortion. A novel
scheme based on imperialist competitive algorithm (ICA) is
proposed, and it preserves the correlation among inter-block
adjacent coefficients by adjusting cost values in the embed-
ding process. We divided the original JPEG image into several
non-overlapping sub-images. The initial cost of DCT coeffi-
cients is calculated by the cost function. The cost values of the
coefficients in sub-images (according to the embedding algo-
rithm) are updated to the change in the inter-block neighbour-
ing values. Cross-distortion does not change as much as possi-
ble by changing the effect of DCT coefficients in the process of
allocating cost values to maintain the difference of inter-block
neighbourhood. Experimental results show that the proposed
method can obtain better performance on the distortion reduc-
tion criterion.
The rest of the study is organised as follows. A basic con-
cept is introduced in Section 2. In Section 3, we describe a cost
function based on the wavelet transform in detail. The strategy
of the proposed method is presented in Section 4. In Section 5,
we describe the procedures of embedding and extraction algo-
rithms. The results of the simulation are presented in Section 6.
Discussion and comparisons are presented in Section 7. Finally,
the conclusion is given in Section 8.
2BASIC CONCEPTS
Without losing the totality, X=(xi, j )∈{£}
n1×n2denotes
n1×n2 the pixel of the cover image, Y=(yi, j )
{£}n1×n2also shows the stego image after the embedding
operation in the cover image Xand m=(mi)∈{0,1}krep-
resents the embedded message. £is pixel or DCT coefficient
of dynamic image range. For example, £={0,,255}is for
the 8-bit grayscale image, and £={1024,,1023}is for
the JPEG image. Therefore, xi, j is a pixel or DCT coefficient in
the (i, j ) position. When embedding the input and output of the
steganography system, LSBs are the cover and stego images.
In this study, the binary vector LSB,Xb=(xb
i, j )(0,1)n1×n2
and Yb=(yb
i, j )(0,1)n1×n2, is used to display cover and
stego images.
To minimise the probability of statistical detection and dis-
tortion caused by the embedding of confidential messages, the
adaptive steganography process tries to design a distortion func-
tion well that is generally defined as
D(X, Y )=
(i, j )
𝜌i, j xb
i, j yb
i, j (1)
or
D(X, Y )=
(i, j )
𝜌i, j xb
i, j yb
i, j (2)
such that 𝜌i, j (xb
i, j yb
i, j )or𝜌i, j xb
i, j yb
i, j is the change cost of
the cover image xb
i, j to yb
i, j . When the message ‘m’ is embedded
based on the cost value of 𝜌i, j , the inverse probability criterion
is calculated as follows:
𝜋i, j =e−𝜆𝜌i, j
1+e−𝜆𝜌i, j (3)
DAMG HA NI ET AL.707
Therefore, the sender can send an average H(𝜋)bits
while the average distortion is E𝜋[D] and represented as
follows:
(𝜋)=−
i, j
𝜋i, j log2𝜋i, j (4)
and
E𝜋[D]=
i, j
𝜋i, j 𝜌i, j (5)
The following two conditions are considered in the sender:
1. Payload-limited sender (PLS): In this case, a certain number
of mbits are embedded, while the average distortion is min-
imised.
min
𝜋E𝜋[D]subject to H(𝜋)=m(6)
2. Distortion-limited sender: In this case, the embedding capac-
ity is maximised, while the embedding distortion stays con-
stant.
max
𝜋H(𝜋)(7)
PLS is the most common mode for the design of adap-
tive steganography methods, and the corresponding extraction
method can be shown as follows:
HYb=m(8)
In which, His the parity-check matrix for the coding scheme.
Besides, λin the above equations can be obtained based on the
states expressed.
The problem of minimising embedding distortion, as
described in the previous paragraph, is described in [19]and
entitled ‘syndrome coding’. In this study, the embedding and
extraction maps are as follows:
Emb :{0,1}n×{0,1}m→{0,1}n
Ext :{0,1}n→{0,1}m(9)
In which the following equation must be true:
Ext (Emb (X, m )) =m(10)
In particular, it is not possible to determine the distortion
profile 𝜌i, j in the receiver, but in practice, we are interested in
practical methods that can embed the one m-bit message into n
elements of the cover image, and it is expected that the amount
of distortion E[D(x, Emb(x, m ))], if possible, has a minimum
value.
In syndrome coding, embedding and extracting are obtained
using a linear binary code Cwith dimensions n-m:
Emb (X,m)=min
yC(m)D(X,Y)
Ext (Y)=HY (11)
Thus, H∈{0,1}m×nis a parity-check matrix of the binary
codes,C(m)={z∈{0,1}nHz =m}, all operations are done in
binary. The most important challenge in this section is the opti-
mal implementation of the binary code to achieve the binary
vector z.
In this study, a solution to obtain the z-vector, taking into
account the relationship and correlation between the DCT coef-
ficients in the neighbouring blocks and creating the possible
minimum distortion in the stego image, is presented based on
an ICA and the cost function used in the J-UNIWARD method
[11]. In [20], the clustering modification directions (CMD) strat-
egy is presented that mainly focuses on maintaining the corre-
lation between pixels in a neighbourhood in the sphere of loca-
tion. As a result, it can synchronise the embedding paths and
increase the performance evaluated by steganalysis.
In this study, by inspiration from CMD, an image steganog-
raphy scheme compatible with JPEG is proposed in which the
correlation of the adjacent coefficients between the blocks is
maintained by adjusting the cost values in the embedding pro-
cess. The initial cost values of all coefficients are first calcu-
lated by the distortion function. The original JPEG image is
divided into several sub-images that are not overlapped. For a
given DCT coefficient, there are four corresponding points in
the same place in the four adjacent DCT blocks (we call them
neighbours between the blocks). The cost of each coefficient is
dynamically adjusted according to the changes of its neighbours.
3A COST FUNCTION BASED ON THE
WAVELET TRANSFORM
As previously mentioned, in this study we use the cost function
used in [11], which we will discuss as follow.
Most of the existing JPEG steganographic schemes embed
messages by modifying DCT coefficients, but the dependencies
among DCT coefficients would be disrupted [21]. We preserve
the differences among DCT coefficients at the same position
in adjacent DCT blocks as much as possible and spread the
embedding modification to each DCT coefficient evenly and
designed a cost function for homogeneous embedding accord-
ing to the principles of the spread spectrum communication.
We evaluate its smoothness in multiple directions using the
Daubechies 8-tap wavelet directional filter bank. According to
a pair of the cover and stego images, Xand Y,W(k)
(uv)(X)and
W(k)
(uv)(Y) are the wavelet coefficients of (uv)inthekth decom-
position obtained using below kernels:
K(1)=hgT,K
(2)=ghT,K
(3)=ggT(12)
708 DAMG HA NI ET AL.
We calculate the initial cost value matrix Dof all DCT
coefficients by applying cost functions. In this study, the ini-
tial cost value matrix D(X, Y ) is computed by the cost func-
tion in J-UNIWARD. If Xand Yare JPEG images, they are
first converted to the sphere of location, and then the wavelet
transform is applied. In other words, they are first decom-
pressed to the spatial domain, and then the wavelet transform is
applied:
D(X, Y )
3
k=1
(u,v)W(k)
(uv)(X)W(k)
(uv)(Y)
𝜀+W(k)
(uv)(X)
(13)
where the sum of the (uv) parameters is taken over all coeffi-
cients of the subband n1×n2, and 𝜀> 0 is a constant to avoid
dividing by zero. To do this, we consider εequal to 10 ×Eps
in MATLAB software, which means ε1015 that the secu-
rity of embedding using UNIWARD is relatively sensitive to the
precise amount of parameter. To further understand the logic
behind this function, we should state that when the ratio of the
indicated equation is small, a large wavelet coefficient has been
changed in the cover image, which in this case usually happened
in tissue or noise areas and near the edges in the image. On the
other hand, if the minimum coefficient, which is small, changes
to a relatively large value, the amount of distortion will also be
large. Therefore, the function in question prevents changes in
the smooth areas of the image.
The initial cost values of DCT coefficients are calculated
by one of the existing cost functions. The first sub-image is
embedded based on the initial cost values. The cost values of
coefficients in the other sub-images will be updated according
to the modifications of inter-block neighbours. The mutual
embedding impacts of DCT coefficients are taken into account
in the process of assigning cost values to maintain the differ-
ence of inter-block neighbours unchanged as much as possible.
Since the initial cost values can be computed by any of the
existing cost functions, the proposed method can be flexibly
implemented together with the state-of-the-art JPEG image
steganographic methods [22].
4THE STRATEGY OF THE PROPOSED
METHOD
JPEG image steganography method usually hides informa-
tion into an image by adding or subtracting the values of
DCT coefficients. In a specific framework, the coefficients may
be corrected by an increase or a decreasing unit. The sys-
tems of analysing the steganography methods always detect the
data by examining the fluctuations and distortions caused by
hiding.
When the inter-block correlation remains unchanged, the dis-
tortion may be reduced. To maintain inter-block correlation,
when calculating cost values, the effect of embedding adjacent
inter-block coefficients must also be taken into account, that is,
the coefficient changes must be consistent with its block neigh-
bours.
FIGURE 1 Eight neighbours for the discrete cosine transform (DCT)
coefficient in adjacent blocks
FIGURE 2 The process of dividing the cover image into sun-images
Based on the above analysis, a strategy to maintain inter-
block correlations is presented in Figure 2. The JPEG image
is divided into several sub-images n1×n2
8×8and the message ‘m
is also divided into several parts. Each part of the message is
embedded in the corresponding sub-image. The initial cost of
DCT coefficients is calculated by the cost function described
in Section 3. The first sub-image is embedded in terms of ini-
tial cost values. The cost values of the coefficients in sub-images
(according to the embedding order–Figure 3) are updated to the
change in the inter-block neighbouring values. Cross-distortion
does not change as much as possible by changing the effect
of DCT coefficients in the process of allocating cost values to
maintain the difference of inter-block neighbourhood [23].
The main idea of the proposed strategy is presented in
Figures 1and 2. For a JPEG image with the size of n1×n2,it
DAMG HA NI ET AL.709
FIGURE 3 The order of embedding the message ‘m’ in sub-images
consists of blocks with size n1×n2
64 created by DCT conversion.
And each DCT block contains 64 quantised DCT coefficients.
The X-character pointer represents the JPEG image after the
DCT conversion, and xi, j represents the position of the DCT
coefficient in the JPEG cover image. The stego image is repre-
sented by a matrix Y=(yi, j )(0,1)n1×n2.ForagivenDCT
coefficient xi, j , interblock neighbours are defined as follows
and their details are shown in Figure 1.
Zinter =xi8,j8,x
i8,j
,x
i8,j+8,x
i, j8,x
i, j+8,x
i+8,j8,
xi+8,j
,x
i+8,j+8(14)
To correct, xi, j must be compatible with most of the ele-
ments in the Zinter set, which can be expressed as
Pxi, j +1>Pxi, j 1if
N{x+1xZinter }>N{x1xZinter }
−−−−−−−−−−−
Pxi, j +1<Pxi, j 1if
N{x+1xZinter }<N{x1xZinter }
(15)
Here, P() denotes the probability of a change, and N{Q}
also indicates the number of elements in the ‘Q’ set. This equa-
tion states that if the number of neighbouring coefficients xi, j
in adjacent blocks of 8, that change with ‘+1’ is greater
than the number of neighbouring coefficients xi, j in adjacent
blocks of 8 with ‘–1’ change, then the probability that 1 unit
is added to xi, j is more than 1 unit is subtracted and vice
versa.
5THE EMBEDDING AND
EXTRACTION PROCEDURES
Considering the contents mentioned in the previous sections,
to maintain a correlation between the coefficients in adjacent
blocks, the most important challenge is to update the cost val-
ues. The allocation of cost values completely reduces the inter-
actions of embedding inter-block coefficients. The exact steps
of embedding and extraction algorithms are fully reviewed as
follows.
5.1 Embedding algorithm
Step 1: The JPEG cover image is divided into 8 ×8
blocks. So that blocks are considered in groups of four
and arranged to embed the message ‘m’inazigzag
form.
Step 2: We consider the number of non-zero AC coeffi-
cients PnzAC in each block.
Step 3: We obtain C=(ci, j )n1×n2the initial cost values
using the defined cost function for DCT coefficients
(all DCT coefficients by applying cost functions) in all
blocks.
Step4:Toembedmbits based on our ICA, we go through
the following steps:
Step 4.1: We formulate the following matrix equation based
on the coding logic:
Ḣ
Yb=m(16)
where ̇
Yb, is the embedded LSB of non-zero AC coefficients
in block 1 from Figure 2,andHis also the parity-check matrix.
For example, if we want to embed 4 bits of the message ‘m’in
eight non-zero coefficients of block 1, we will have
100000
11100000
00111000
00001110
̇y1
1
̇y1
2
̇y1
3
̇y1
4
̇y1
5
̇y1
6
̇y1
7
̇y1
8
=
m1
m2
m3
m4
(17)
where the parity-check sub-matrix ̂
H=10
11
has been used to
develop the Hmatrix.
Step 4.2: In this section, the purpose is to find the LSB ̇
Yb
such that the following equation holds:
̇y1
1=m1
̇y1
1y1
2y1
3=m1
̇y1
3y1
4y1
5=m2
̇y1
5y1
6y1
7=m3
(18)
Step 4.3: ICA which includes the following steps:
710 DAMG HA NI ET AL.
Step 4.3.1: Initialisation of ICA by a random method based
on non-zero AC coefficients
Country =
̇y1
1
̇y1
2
̇y1
3
̇y1
4
̇y1
5
̇y1
6
̇y1
7
̇y1
8
(19)
Variable values in one country represent the corresponding
index in the LSB in which the values of ̇y1
rare randomly deter-
mined.
̇y1
r{0,1}1r8 (20)
Step 4.3.2: We place Yb
rYb
r
Step 4.3.3: The fitness of a country is obtained by evaluating
the following criteria on the variables
̇y1
1
̇y1
2
̇y1
3
̇y1
4
̇y1
5
̇y1
6
̇y1
7
̇y1
8
.
fitness npopulation=
8min
YrbXrbrYrbXrb
max
YrbXrbri,j 𝜌r
i, j 𝛿YrbXrb
(21)
where
𝛿(k1,k2)=
1if k1=k2
0if k1k2
(22)
Step 4.3.4: In this step, the highest value of fitness and the
best place to embed the ‘m’ message is obtained when
fitness (i)<fitness (k)
1,kNpo pulation (23)
Step 4.3.5: ‘N’, which has powerful states, is considered to
form an empire, and the rest of the ‘N’ is placed as colonies
within each empire; so there will be two types of countries,
colonisers and colonies.
Step 4.3.6: To initialise the empires, the colonies are placed
based on the power of each empire within the empires, and
the number of colonies in each empire must be directly pro-
portional to the power of that empire.
To divide the colonies among the proper empires, the nor-
malised fitness of an empire is defined as follows:
Cn=max
i{ci}−cn(24)
So that cnis the fitness (cost) of the nth empire and Cnis
normalised fitness (cost).
Step 4.3.7: Moving colonies toward coloniser in an empire:
At this step, colonial countries are beginning to improve their
colonies. This fact, as shown in Figure 4, is modelled by the
movement of all colonies towards the coloniser.
Step 4.3.8: Changing the position of coloniser and colony:
When moving towards a coloniser, a colony may reach a posi-
tion with higher fitness than that of the coloniser. In such a
case, the coloniser moves to the position of the colony and vice
versa.
Step 4.3.9: Removal and convergence of empires:
The weak empires are dissolved in the imperial rivalries and
their colonies are transferred to other colonisers.
Step 4.3.10: Go to step 4.3.7 and repeat the process.
v The above steps can be summarised in other words like the
below: (Pseudocode)
(0) Define objective function: f(x),x=(x1,x
2,…,xd);
1. Initialisation of the algorithm. Generate some random solu-
tion in the search space and create initial empires.
2. Assimilation: Colonies move towards imperialist states in dif-
ferent directions.
3. Revolution: Random changes occur in the characteristics of
some countries.
4. Position exchange between a colony and imperialist. A
colony with a better position than the imperialist has the
chance to take the control of empire by replacing the existing
imperialist.
5. Imperialistic competition: All imperialists compete to take
possession of colonies of each other.
6. Eliminate the powerless empires. Weak empires lose their
power gradually and they will finally be eliminated.
7. If the stop condition is satisfied, stop, if not go to 2.
8. End.
Step 4.4: In the end, we will have only one empire in which
the rest of the states will be colonised by a powerful coloniser
whose values, among the colonisers, are the best position in Yrb
to embed the message ‘m, which is most similar to Yrb,and the
correlation between the coefficients is satisfied.
DAMG HA NI ET AL.711
FIGURE 4 The process of moving colonies towards colonisers in an empire
Step 5: We calculate the difference between the embedded
and the original bits in the coefficients.
D=XrbYrb=di,j n1×n2(25)
Step 6: The values 𝜌+and 𝜌are, respectively, defined
as positive and negative correction cost values and we
have
ci, j =𝜌
+
i, j =𝜌
i, j (26)
Otherwise 𝜌+and 𝜌should be set as follows:
𝜌+
i, j =ci, j
𝛼if N+
i, j >N
i, j
𝜌
i, j =ci, j
𝛼if N+
i, j <N
i, j
(27)
where the parameter 𝛼>1 is considered as the adjustment
parameter [24].
Step 7: The algorithm continues from step 4 for blocks num-
bers 2, 3, and 4.
Step 8: Then for the rest of the block groups, the algorithm
continues from step 2 until all bits of the messages ‘m’are
embedded in the cover image.
5.2 Extraction algorithm
To extract, the receiver can extract the message ‘m’ without hav-
ing the original JPEG image. The stego image, like the embed-
ding algorithm, is divided into sub-images, and the receiver
extracts each sub-message ‘m’ from the sub-images and finally
combines all the sub-messages. The extraction steps of ‘m’mes-
sage are as follows:
Step 1: The image Y(stego image) is divided into four sub-
images based on blocks of 8 ×8, similar to those embedded in
the algorithm.
Step 2: Sub-message ‘m’ is extracted from each sub-image
using the decoding method and the following equation.
Ḣ
Yb=m(28)
in which ̇
Ybis the embedded LSB of non-zero AC coeffi-
cients that are obtained optimally at the embedding algorithm,
and His also the parity-check matrix.
Step 3: Depending on the order of the embedding operation
(Figure 3), all bits of sub-message ‘m’ are extracted and com-
bined.
6THE RESULTS OF THE
SIMULATION
The main idea of the proposed method is to maintain the cor-
relation of the coefficients in the neighbourhood of eight and
based on the ICA, which is carried out dynamically by setting
the cost values.
The JPEG cover image is divided into several sub-images so
that the DCT coefficients are placed in the different sub-images,
hence the mutual embedding distortion can be considered in
this way. For each coefficient, the values for positive correction
and negative correction are determined as 𝜌+
i, j and 𝜌
i, j .Both
of them are equal to the initial value of the coefficient cost in
the first sub-image. For other images, 𝜌+and 𝜌for the DCT
coefficients are adjusted according to the change in the intra-
block neighbours. If N+
i, j is greater than N
i, j , the probability of
increasing the coefficient as one unit to its reduction is more and
therefore its cost, 𝜌+
i, j , reduces. If N
i, j is greater, its cost 𝜌i,j
must be reduced simultaneously. Therefore, intra-block depen-
dencies can be maintained.
To find out if the proposed algorithm can optimally choose
the embedding paths, we will embed several sample images to
examine the changes. In this study, implementation functions
are used to randomly create binary sequences to embed in JPEG
images. Also, different types of text, audio, video and so forth
files can be embedded after converting to the binary sequence.
The most important thing about medical images that can be
considered and used in the embedding process is about the
patients and their illness information that can be embedded in
the image. Of course, it should be noted that for types of com-
pressed files, the debugging process will be required to reduce
the likelihood of a failure of compressed files after the extrac-
tion algorithm of the binary sequence.
To illustrate the performance of the proposed method, we
chose three brains magnetic resonance imaging images and sam-
ple cover images with dimensions of 512 ×512 pixels contain-
ing smooth areas, edges, and textures in Figures 5(a)–(c),andthe
results of embedding using the proposed algorithm are shown
in Figures 5(d)–(f). Also, for example, the changes in the sample
cover image shown in Figure 5(a) after applying the proposed
algorithm in the area of the location are shown in Figure 6(a),
and the difference between the cover and the stego images can
712 DAMG HA NI ET AL.
FIGURE 5 (a), (b), (c) Magnetic resonance imaging sample cover images. (d), (e), (f) The related stego images obtained using the proposed method with an
embedded amount of 0.2 bit per non-zero alternating current (AC) coefficient
FIGURE 6 (a)The changes in the sample cover image shown in Figure 5. (a) After applying the proposed algorithm in the area of the location, (b) the difference
between the image pixels and the stego image with an embedding rate of 0.2
be seen in Figure 6(b). As is clear, most changes have occurred
in the edges and border areas where the human eye system is
not sensitive to these changes.
Also, for example, the DCT coefficients that have been mod-
ified in Figure 5(a) and their numbers are shown in Figure 7(a),
and Figure 7(b) shows the coefficients that have been changed
in each DCT conversion block and their position in the DCT
blocks.
The evaluation of the ‘α’ adjustment parameter in the pro-
posed scheme is very important. The ‘α’ value may affect the
embedding locations and the displacement rate, and thus may
have different performances, which, according to Table 1,the
best value for ‘α’ equals to 1.5.
In the following, we examine the changes in the embedding
parameter among non-zero coefficients and its effect on the
coefficients changes rate for α=1.5, which is shown in Fig-
TAB L E 1 Percentage of changes in non-zero discrete cosine transform
(DCT) coefficients with increasing parameter ‘α’ for the embedding rate of 0.2
α
Percentage of changes in
non-zero DCT coefficients
1.5 3.06
23.84
2.5 4.483
3 4.701
DAMG HA NI ET AL.713
FIGURE 7 (a)The number of DCT
coefficients in the sample cover image (Figure 5(a))
that has been changed, and (b) their position in the
DCT blocks
FIGURE 8 The percentage of changes in non-zero DCT coefficients for
different embedding rates
TAB L E 2 Comparison of the proposed method with the two methods of
J-UNIWARD [11] and uniform embedding distortion (UED) [12]
Embedding rates 0.05 0.1 0.2 0.3 0.4 0.5
J-UNIWARD [11] 0.79 1.62 3.66 5.63 7.71 10.3
UED [12] 0.56 1.35 3.11 5.32 7.94 11.01
The proposed method 0.6 1.31 3.06 5.46 7.82 10.5
ure 8. As can be seen, by increasing the embedding rate in the
coefficients, more percentage of the coefficients are changed.
For example, the embedding rate of 0.5 means that confidential
bits mhave been embedded in 50% of the DCT coefficients of
which 9.032% of the coefficients have been changed.
7DISCUSSION AND COMPARISONS
To evaluate the proposed method, Table 2compares the two
methods of J-UNIWARD [11]andUED[12] for the sample
cover image and different embedding rates.
According to the obtained values, the proposed method, for
the 37,240 non-zero DCT coefficients in the sample image iden-
FIGURE 9 Comparisons of detection errors Eoob by the proposed method
upon J-UNIWARD in against JSRM steganalysis
tified in implementation, has a lower percentage of change in
the coefficients than the compared methods. Specifically com-
pared to the J-UNIWARD method, our best performances were
in 0.05, 0.1, 0.2, 0.3 embedding rates, and to the UED method,
our best performances were in 0.1, 0.2, 0.4, and 0.5 embedding
rates.
About the security performance in digital images, it should
be noted that perfect security seems unachievable for empiri-
cal cover sources, and currently, the best the steganographer is
to minimise the detectability when embedding a required pay-
load [23, 25]. A way to approach this problem is to embed while
minimising the distortion function criteria. This converts the
problem of secure steganography to one that has been largely
resolved in terms of known bounds and general near-optimal
practical coding constructions. Since we have reduced the dis-
tortion function criteria, we can see the effect of the improve-
ment in security with five embedding payloads 0.1, 0.2, 0.3, 0.4,
0.5 bit per non-zero AC coefficient in Figure 9. All the 1000
images are JPEG with three quality factors 75, 85, 95, respec-
tively, and the percentage of incremental Eoob ratio (incremental
testing error ratio), that is, the ratio of difference of Eoob value
of ours proposed method and Eoob value of J-UNIWARD [26],
are obtained by the proposed scheme upon J-UNIWARD JSRM
714 DAMG HA NI ET AL.
steganalysis [26]. The proposed method could improve the
corresponding detection error and our best performance is in
0.5 embedding payload by about 7.2%.
8CONCLUSION
Today, the need to disseminate and share medical images is
rapidly increasing, and advanced medical information systems
have changed the way of changing the storage, access, and dis-
tribution of medical images. A large amount of patients’ per-
sonal information is presented and also available in medical
JPEG images, therefore the privacy of patients in JPEG medical
images has become an important issue. Also, medical images,
due to their smooth texture, are more likely to be exposed
to embedded distortions, and this problem has been accept-
ably resolved in the proposed method based on the distor-
tion reduction approach. Steganography is a useful tool to hide
patients’ information in medical images. Most existing JPEG
image steganography methods can eliminate interdependencies
of DCT blocks, thus the security performance is still not fully
satisfactory. More study on security parameters is one of the
aspects that should be considered more by researchers in this
field in future work. In this study, an adaptive strategy was first
considered to coordinate the correct paths for the same position
of adjacent DCT blocks based on the ICA, and then the cost val-
ues were dynamically adjusted using the inter-block neighbours’
changes in the embedding process. The process of adjusting
cost values, in turn, reduces the distortion caused by embed-
ding, which is a significant effect on not identifying images that
have embedded messages and patient confidential information.
Experimental results showed that the proposed method can sig-
nificantly improve performance on the distortion reduction cri-
terion, and subsequently the security of patient information is
improved in that it is not threatened by anti-steganalysis meth-
ods. Comparisons in medical images with different dimensions,
types of compression in medical images, and other types of dis-
tribution functions can also be considered in future works.
ORCID
Hamidreza Damghani https://orcid.org/0000-0001-9064-
4675
Farshid Babapour Mofrad https://orcid.org/0000-0002-5892-
7971
Leila Damghani https://orcid.org/0000-0003-0505-6778
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How to cite this article: Damghani H, Mofrad FB,
Damghani L. Medical JPEG image steganography
method according to the distortion reduction criterion
based on an imperialist competitive algorithm. IET
Image Process. 2021;15:705–714.
https://doi.org/10.1049/ipr2.12055
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