# An Improved Image Steganography Scheme Based on Partial Preservation Embedding Algorithm for Wireless Visual Sensor Networks

Authors: Qian Shen; Tao Jiang; Yongjun Zhu; Yin Wu
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

With the continuous improvement of encryption algorithms, some applications based on the architecture of wireless visual sensor networks have gradually shifted their attention to the imperceptibility and antijamming performance of secret images. To reduce the probability of secret images being detected, the current research focuses on hiding secret data in the least-significant bit of the cover image in the spatial domain or embedding data into the coefficients of the high-frequency band in the transformational domain, which usually leads to poor performance in a hostile environment. Therefore, some researchers proposed to substitute the coefficients of the medium-frequency band in the transformational domain with secret information to enhance the anti-interference performance. However, this idea would severely affect the imperceptibility of secret images. As a result, an improved version based on the partial preservation embedding algorithm was designed in this paper. Theory analysis and simulation results indicate that the proposed scheme performs better than the existing methods by directly substituting the coefficients of the medium-frequency band in the transformational domain, especially in the case of strong noise interference.


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## Body

## 1. Introduction

Because of the convenience in networking, low cost in maintenance, and strong resistance to natural disasters, Wireless Visual Sensor Networks (WVSN) are suitable for various applications such as traffic management and intelligent monitoring. Recently, continuous progress has been made in the security and compressibility of image encryption systems owing to the development of chaos and compressive sensing (CS) technology [1–4]. However, some applications might have specific requirements. For example, most of the tactical reconnaissance missions in battlefields need to transmit scenes obtained by visual acquisition nodes through the wireless channels, during which the corresponding electromagnetic signals exposed in the air are easy to be accessed by enemies. The most common solution is to use various encryption algorithms to improve the security of data before transmitting. To get satisfactory security performance, systems designed for this kind of applications are also required that secret images must be imperceptible [5]. As a result, confidential information is generally transmitted by means of hiding in unrelated images. In this case, the hidden data should be safely transmitted in the channel and accurately reconstructed at the receiving terminals, while there are no strict requirements on the reconstruction accuracy of cover images. To delve into these questions, researchers combined information security theory with signal processing technology and then proposed the basic concept and specific scheme of information hiding [6–12].Nowadays, image hiding has become a hotspot of relevant areas. Since images are naturally redundant, they are quite suitable for embedding confidential information. According to the basic architecture of image hiding systems, the key indicators include not only the security and anti-interference performance but also the maximum information embedding capacity and imperceptibility [5]. Traditional image steganography schemes focused on hiding secret data to the least significant bit (LSB) of cover images in the spatial domain or replacing the coefficients of the high-frequency band in the transformational domain with secret images [13–15]. These methods are simple and feasible to be utilized. Moreover, the desired imperceptibility could be obtained because the human visual system is insensitive to changes in the low-significant bits of pixel values. Nevertheless, even basic image processing operations (compression, filtering, etc.) would cause serious distortion to secret information [16]. More importantly, the propagation in a wireless channel is likely to be affected by various kinds of interference, which is unqualified to WVSN applications.To address this problem, Li et al. [17] designed a reversible image steganography scheme based on block compressive sensing (BCS). In the front node, each element of bit-serialized pixels in the secret image would be hidden into one nonoverlapping block. When secret information was being extracted, a priori knowledge of the strong correlation between adjacent pixels on the boundary of each block could be utilized to recognize hidden information from each block of the stego image. However, this method requires the terminal users to take the correlation between adjacent pixels on the blocks’ boundary as an evaluation function for extracting secret images, which results in low maximum embedding capacity because for that size of blocks must be big enough to ensure the accuracy of judgment. For example, the maximum embedding rate would be less than 0.05% if employing 16×16 blocks. Furthermore, for special cover images, such as images with flat texture in the vertical or horizontal direction, it is likely to have misjudgement in the process of extracting hidden information by the weak correlation between adjacent pixels on some boundaries. It would definitely reduce the accuracy of the extracted information. In conclusion, the BCS-based steganography method exhibits low practical value because of its low embedding rate and poor universality. Later, some other research studies were proposed to hide secret images in the space of the medium-frequency band to boost the maximum embedding capacity and antijamming performance [18, 19]. However, it would lead to a sharp decrease in the similarity between the stego image and cover image, which affected the imperceptibility of the secret image.To improve the imperceptibility of secret images without reducing the antijamming performance and the maximum embedding capacity, this paper designed an optimized image steganography scheme based on the partial preservation embedding algorithm (ISS-PPEA). The rest of this paper would be organized as follows. First, the preliminary knowledge would be briefly introduced in the next section. Then, in Section3, the framework of the proposed system and the detailed steps are explained in detail. In addition, the simulation results and the corresponding analysis are illustrated in Section 4. Lastly, all the work in this paper would be summarized in Section 5.


## 2. Preliminary Knowledge

Due to the characteristics of deterministic randomness, extreme sensitivity to initial states, etc., chaotic systems are widely used as the generator of encryption sequences in image encryption systems. In addition, CS has been considered as an optimal technique to counter threats caused by open channel, big data, and harsh communication circumstances in WVSN. Since the image encryption algorithm based on CS and nonuniform quantization (IEA-CS-NQ) has been proved to be safe enough for WVSN [20], this paper takes it directly as part of the proposed scheme. To make the designed system easier to be understood, the main steps of the encryption part in IEA-CS-NQ would be reviewed in this section as follows.


### 2.1. Measurement

In sensor nodes, scenes are directly acquired by a micromirror array controlled by the measurement matrices. Therefore, the core problem in this step is the construction of it. Considering the Restricted Isometry Property (RIP), building the Gaussian random matrix and Bernoulli random matrix are the preferable solutions. However, due to the security requirements, the measurement matrix is generally generated indirectly by the secret key transferred, which makes this plan inappropriate. As a result, IEA-CS-NQ employs the chaotic sequence to construct a cyclic matrix to boost the generation efficiency of the measurement matrix. More importantly, it has been proved that this Toeplitz-structured matrix provides better performance in irrelevant measurements. The circulant matrix is as follows:(1)Φ=1m⋅S1nS1n−1⋯S11S11S1n⋯S12⋮⋮⋱⋮S1m−1S1m−2…S1m,which would be employed to measure the original scene, whose elements S11 and S12,…,S1n are pseudorandom sequences generated by specific chaotic systems. Here, the symbol n represents the length of the serialized original image, while m stands for the sequence length obtained by compressive measurement. Thus, the compression ratio (CR) could be defined as m/n. Besides, the coefficient 1/m is the scale factor to realize the column normalization. Then, the process of measuring could be represented as follows:(2)y=Φ⋅x,where x represents the serialized scene and y stands for the measurement result.


### 2.2. Quantization

As we know, the calculation result should be quantized to match the data type of pixel values in the digital image. However, the traditional uniform quantization (UQ) method would lead to significant loss of data accuracy because of the uneven distribution of quantization resources. Moreover, it is vulnerable against CPA based on differential analysis algorithms. Therefore, IEA-CS-NQ designed a nonuniform quantization (NQ) method by adding a nonlinear pretreatment function with adaptive parameters to solve these problems. This function,(3)z=11+e−ay−os,contains two parameters regulated by the measurement result y. The parameter a determines the convergence rate, while the parameter os determines the convergence centre of the result z.


### 2.3. Confusion and Substitution

The last step of encryption in IEA-CS-NQ is the process of confusion and substitution. To be specific, the confusion is controlled by an index sequenceI ranging from 1 to m, which is generated by a chaotic system. Substitution is operated by the following formula:(4)Ci=Qrci⊕Bi,with the help of chaotic sequence B. Here, C is the cipher image to be sent, and i represents the index of the sequence. In addition, Qrc stands for the result of confusion.After all steps mentioned above have been completed, the corresponding cipher image could be obtained. Theory analysis and simulation experiments have proved that IEA-CS-NQ performs better in terms of security and antijamming.


## 2.1. Measurement

In sensor nodes, scenes are directly acquired by a micromirror array controlled by the measurement matrices. Therefore, the core problem in this step is the construction of it. Considering the Restricted Isometry Property (RIP), building the Gaussian random matrix and Bernoulli random matrix are the preferable solutions. However, due to the security requirements, the measurement matrix is generally generated indirectly by the secret key transferred, which makes this plan inappropriate. As a result, IEA-CS-NQ employs the chaotic sequence to construct a cyclic matrix to boost the generation efficiency of the measurement matrix. More importantly, it has been proved that this Toeplitz-structured matrix provides better performance in irrelevant measurements. The circulant matrix is as follows:(1)Φ=1m⋅S1nS1n−1⋯S11S11S1n⋯S12⋮⋮⋱⋮S1m−1S1m−2…S1m,which would be employed to measure the original scene, whose elements S11 and S12,…,S1n are pseudorandom sequences generated by specific chaotic systems. Here, the symbol n represents the length of the serialized original image, while m stands for the sequence length obtained by compressive measurement. Thus, the compression ratio (CR) could be defined as m/n. Besides, the coefficient 1/m is the scale factor to realize the column normalization. Then, the process of measuring could be represented as follows:(2)y=Φ⋅x,where x represents the serialized scene and y stands for the measurement result.


## 2.2. Quantization

As we know, the calculation result should be quantized to match the data type of pixel values in the digital image. However, the traditional uniform quantization (UQ) method would lead to significant loss of data accuracy because of the uneven distribution of quantization resources. Moreover, it is vulnerable against CPA based on differential analysis algorithms. Therefore, IEA-CS-NQ designed a nonuniform quantization (NQ) method by adding a nonlinear pretreatment function with adaptive parameters to solve these problems. This function,(3)z=11+e−ay−os,contains two parameters regulated by the measurement result y. The parameter a determines the convergence rate, while the parameter os determines the convergence centre of the result z.


## 2.3. Confusion and Substitution

The last step of encryption in IEA-CS-NQ is the process of confusion and substitution. To be specific, the confusion is controlled by an index sequenceI ranging from 1 to m, which is generated by a chaotic system. Substitution is operated by the following formula:(4)Ci=Qrci⊕Bi,with the help of chaotic sequence B. Here, C is the cipher image to be sent, and i represents the index of the sequence. In addition, Qrc stands for the result of confusion.After all steps mentioned above have been completed, the corresponding cipher image could be obtained. Theory analysis and simulation experiments have proved that IEA-CS-NQ performs better in terms of security and antijamming.


## 3. The Proposed Scheme

The structure of the image steganography scheme proposed by this paper is illustrated in Figure1. It could be divided into two parts: the encryption-hiding process in sensor nodes and the extraction-decryption process in terminal user nodes.Figure 1
The framework of the proposed scheme.For sensor nodes, the information which is being necessary to generate chaotic sequences is extracted from the secret key allocated in a safe way firstly. Then, the construction of the measurement matrix, generation of the confusion sequence, substitution sequence, and embedding position are completed based on the generated sequences. After that, the secret image containing information about the current scene captured by a sensor node could be obtained by executing the encryption process of IEA-CS-NQ. And, it would be embedded into the medium-frequency band in the Discrete Cosine Transformation (DCT) coefficients of a cover image bit by bit with the proposed partial preservation embedding algorithm (PPEA) afterwards. Finally, Inverse Discrete Cosine Transformation (IDCT) would be performed to obtain the stego image that is visually similar to the cover image, and it would be sent to the database nodes or terminal user nodes through the wireless channel.After the stego image is captured by terminal users, DCT should be conducted to acquire coefficients containing secret information. Then, the secret image about the original scene captured by the sensor node could be extracted by the inverse scheme of PPEA used in the sensor node. Afterwards, the estimation of the original scene would be reconstructed by the decryption part in IEA-CS-NQ. In most applications, the terminal user just needs to precisely get the original scene, and there is no requirement for the quality of reconstruction for the cover image. However, as the cover image reconstructed in the terminal node is equivalent to the stego image transmitted in the wireless channel, the accurate reestablishment of the cover image is beneficial to the improvement in the imperceptibility of secret images.Without loss of generality, this paper assumes that the size of the cover image in the sensor node isN1×N1, and the size of the scene in front of the sensor isN2×N2. Besides, all images are eight-bit grey-scale, whose elements range from 0 to 255. The Orthogonal Matching Pursuit (OMP) is taken as the reconstruction algorithm of CS for the reason that this paper does not concern the corresponding design. The workflow of the designed system would be introduced in the following steps by taking the hiding process as an example.


### 3.1. IEA-CS-NQ

According to Figure1, the scene at the sensor node would be captured and encrypted by IEA-CS-NQ. The necessary information such as parameter values and initial values used by chaotic systems are extracted from the key sequence allocated in a safe way. After all steps in the encryption part of IEA-CS-NQ are accomplished, the secret image containing information about the original scene could be obtained, which is clearly the object to be hidden. On the basis of equation (1), its size should be m×N2 if the measurement matrix Φ has m rows. In this situation, the number of bits that need to be hidden is 8m×N2.


### 3.2. DCT Transformation

As described earlier in this article, the hiding method designed is executed in the medium-frequency band in the transformational domain of the cover image. For the sake of convenience, DCT was selected to convert the cover image from the spatial domain to the frequency domain by the following formula:(5)Fu,v=αuαv∑k=0N1−1∑l=0N1−1fk,lcos2k+1uπ2N1cos2l+1vπ2N1,where fk,l stands for the kth row and the lth column element in the cover image. In addition, αu and αv are the normalization coefficients defined by(6)αu,αv=1N1,u,v=0,2N1,u,v=1,2,…,N1−1.In the practical image processing operation, for reducing the complexity of DCT, the cover image is usually divided into nonoverlapping image blocks with equal size before transmitting. Thus, the final results calculated by equation (5) are generally DCT coefficient blocks. Current research has proven that, in the process of image segmentation, the accuracy of the reconstructed image would be reduced, and the segmentation effect would be obvious if the block size is too small. However, if the size of the block is oversize, the complexity of the transformation would increase dramatically. Therefore, most researchers chose a compromise that the block size was set to 16×16.This paper also assumes that the block size of the cover image and the corresponding DCT coefficient matrix are both16×16, by which N1 could be divisible. Research studies have proved that most elements in the DCT coefficient matrix block are close to zero, for the reason that digital images usually contain a large amount of redundant data. Besides, the upper left to lower right elements in the coefficient block are generally considered as the low-frequency to high-frequency DCT coefficients. That is to say, the major information is concentrated in the upper left corner of the DCT coefficient block, while the minor information is concentrated in the lower right corner. If all coefficients in a block are serialized with the zigzag order, the elements of the obtained vector could be considered as a coefficient sequence ordered by importance, and the specific process is drawn in Figure 2. It can be found that the coefficient matrix arranges its elements in the order indicated by the dotted line from the top left corner to the lower right corner. As a result, the importance of elements in this sequence is gradually descending. For facilitating subsequent theoretical analysis and simulation experiments, the low-frequency, medium-frequency, and high-frequency bands in the DCT coefficient matrix of an image block sizing 16×16 are defined as the elements whose indexes are 1∼15, 16∼143, and 144∼256 in the zigzag sequence, respectively.Figure 2
The diagram of the zigzag structure in the DCT coefficient matrix.


### 3.3. Secret Information Embedding

As we all know, the physiological structure of the human eyes determines that the human visual system is only sensitive to the information expressed by the high-significant bits in the pixel values of an image, and it is rather difficult for them to distinguish changes in the low-significant bits. In other words, the information contained in different significant bits could be considered to have different weights. As for DCT, this characteristic is directly reflected by the fact that different frequency coefficients are of different importance.To intuitively perceive the different importances of coefficients in different bands, the standard Baboon image with size256×256 was taken as an example to conduct experiments. Suppose that fifteen low-frequency DCT coefficients, thirty medium-frequency DCT coefficients, or sixty high-frequency DCT coefficients were lost, the peak signal-to-noise ratio (PSNR) values of the corresponding reconstructed images were 26.97, 38.67, and 41.80, respectively. They are plotted in Figure 3. Surely, the extent of information loss in the reconstructed image is not positively correlated with the number of lost coefficients, but closely related to the frequency band of the lost coefficients. Specifically, the number of coefficients lost in the low-frequency band is the least, but the information loss in the reconstructed image is the most severe. The degree of loss in high-frequency coefficients is the worst, while the information loss is slightest. It means that the low-frequency coefficients are definitely essential during image reconstruction. Besides, even if the medium- and high-frequency coefficients are severely lost, the reconstruction would not be significantly affected.Figure 3
Reconstruction results of the Baboon image in different coefficient-loss situations. (a) No loss. (b) Fifteen low-frequency DCT coefficient losses. (c) Thirty medium-frequency DCT coefficient losses. (d) Sixty high-frequency DCT coefficient losses.
(a)(b)(c)(d)Based on the conclusion mentioned above, this paper proposed to embed secret information into the medium-frequency band in the DCT coefficient matrix of the cover image to improve the antijamming performance of the image steganography system without significant influence on the reconstruction accuracy. Without loss of generality, it is assumed that the size of the cover image is512×512, and the size of the original scene at the sensor node is 128×128. In addition, the value of CR utilized in IEA-CS-NQ is marked with cr. Clearly, the cover image could be transformed into 1024 groups of DCT coefficient block sizing 16×16, while the measurement result acquired by the sensor node could be converted into 1024 groups of bit sequence with 128∈cr elements. According to the condition that cr∈0,1, the lengths of the bit sequence in each group assembled by the measurement results are certainly less than 128, which ensures that each group of the bit sequence could be embedded into the medium-frequency coefficients of one DCT coefficient block.It is necessary to specify the embedding positions and the specific hiding method in the hiding process. As shown in Figure1, the positions are determined by the sequence generated by a specific chaotic system. Before the lth group of operation, a total of 128 elements from 128⋅l−1+1th to 128⋅lth in the chaotic sequence are indexed by values to get a sequence correlated to the embedding positions. Then, the elements indexed from 1 to 128⋅cr in this sequence would add 15 to be taken as the embedding positions of the current group. The process of hiding the ith bit Bi for the lth group of operation into the jth element Aj in the corresponding DCT coefficient sequence A would be taken as an example to demonstrate PPEA. Suppose that Bi=0, the embedding operation designed by(7)A′j=Aj,Aj≤−α⋅Amid¯,−α⋅Amid¯,−α⋅Amid¯<Aj,would be applied to hide the bit sequence in the medium-frequency band of the DCT coefficient matrix orderly. Otherwise, the embedding operation would be(8)A′j=Aj,α⋅Amid¯≤Aj,α⋅Amid¯,Aj<α⋅Amid¯.Here, the conditionsl∈1,2,…,1024, i∈1,2,…,128⋅cr, and j∈16,17,…,143 should be met. Besides, the symbol Amid¯ represents the absolute value of the average for all 128 medium-frequency coefficients A16∼A143. In addition, the parameter α is utilized to regularize the region size, whose value could be increased to enhance the antijamming performance of the steganography system or be reduced properly to improve the imperceptibility for secret information. Sign A′j is the result of the embedding operation for the medium-frequency band coefficient Aj chosen from one group of DCT coefficients.According to equations (7) and (8), the designed PPEA could improve the imperceptibility of secret information for the reason that it preserves most elements in the process of steganography. In other words, it only affects the elements valued between −α⋅Amid¯ and α⋅Amid¯ in the medium-frequency band of DCT coefficients for the cover image. Besides, the result of the embedding operation is constrained outside the interval −α⋅Amid¯,α⋅Amid¯, which could guarantee the antijamming performance of the steganography system. Indeed, the result of the embedding operation is not only determined by the absolute value of the average for all medium-frequency band coefficients but also by the region regulation parameter α.


### 3.4. IDCT Transformation

Before data is transmitted through the wireless channel, the modified coefficient blocks obtained by the embedding operation should be converted to the stego image by applying IDCT. The obtained stego image would be visually safe but contains confidential information, which means the entire steganography is completed.According to the structure shown in Figure1, the extraction-decryption process in terminal user nodes is the inverse operation corresponding to the encryption-hiding process in sensor nodes. It is worth mentioning that each bit extracted is determined by the sign of the corresponding coefficient. After the extraction process is completed, the reconstructed scene could be obtained by directly applying the decryption part in IEA-CS-NQ.


## 3.1. IEA-CS-NQ

According to Figure1, the scene at the sensor node would be captured and encrypted by IEA-CS-NQ. The necessary information such as parameter values and initial values used by chaotic systems are extracted from the key sequence allocated in a safe way. After all steps in the encryption part of IEA-CS-NQ are accomplished, the secret image containing information about the original scene could be obtained, which is clearly the object to be hidden. On the basis of equation (1), its size should be m×N2 if the measurement matrix Φ has m rows. In this situation, the number of bits that need to be hidden is 8m×N2.


## 3.2. DCT Transformation

As described earlier in this article, the hiding method designed is executed in the medium-frequency band in the transformational domain of the cover image. For the sake of convenience, DCT was selected to convert the cover image from the spatial domain to the frequency domain by the following formula:(5)Fu,v=αuαv∑k=0N1−1∑l=0N1−1fk,lcos2k+1uπ2N1cos2l+1vπ2N1,where fk,l stands for the kth row and the lth column element in the cover image. In addition, αu and αv are the normalization coefficients defined by(6)αu,αv=1N1,u,v=0,2N1,u,v=1,2,…,N1−1.In the practical image processing operation, for reducing the complexity of DCT, the cover image is usually divided into nonoverlapping image blocks with equal size before transmitting. Thus, the final results calculated by equation (5) are generally DCT coefficient blocks. Current research has proven that, in the process of image segmentation, the accuracy of the reconstructed image would be reduced, and the segmentation effect would be obvious if the block size is too small. However, if the size of the block is oversize, the complexity of the transformation would increase dramatically. Therefore, most researchers chose a compromise that the block size was set to 16×16.This paper also assumes that the block size of the cover image and the corresponding DCT coefficient matrix are both16×16, by which N1 could be divisible. Research studies have proved that most elements in the DCT coefficient matrix block are close to zero, for the reason that digital images usually contain a large amount of redundant data. Besides, the upper left to lower right elements in the coefficient block are generally considered as the low-frequency to high-frequency DCT coefficients. That is to say, the major information is concentrated in the upper left corner of the DCT coefficient block, while the minor information is concentrated in the lower right corner. If all coefficients in a block are serialized with the zigzag order, the elements of the obtained vector could be considered as a coefficient sequence ordered by importance, and the specific process is drawn in Figure 2. It can be found that the coefficient matrix arranges its elements in the order indicated by the dotted line from the top left corner to the lower right corner. As a result, the importance of elements in this sequence is gradually descending. For facilitating subsequent theoretical analysis and simulation experiments, the low-frequency, medium-frequency, and high-frequency bands in the DCT coefficient matrix of an image block sizing 16×16 are defined as the elements whose indexes are 1∼15, 16∼143, and 144∼256 in the zigzag sequence, respectively.Figure 2
The diagram of the zigzag structure in the DCT coefficient matrix.


## 3.3. Secret Information Embedding

As we all know, the physiological structure of the human eyes determines that the human visual system is only sensitive to the information expressed by the high-significant bits in the pixel values of an image, and it is rather difficult for them to distinguish changes in the low-significant bits. In other words, the information contained in different significant bits could be considered to have different weights. As for DCT, this characteristic is directly reflected by the fact that different frequency coefficients are of different importance.To intuitively perceive the different importances of coefficients in different bands, the standard Baboon image with size256×256 was taken as an example to conduct experiments. Suppose that fifteen low-frequency DCT coefficients, thirty medium-frequency DCT coefficients, or sixty high-frequency DCT coefficients were lost, the peak signal-to-noise ratio (PSNR) values of the corresponding reconstructed images were 26.97, 38.67, and 41.80, respectively. They are plotted in Figure 3. Surely, the extent of information loss in the reconstructed image is not positively correlated with the number of lost coefficients, but closely related to the frequency band of the lost coefficients. Specifically, the number of coefficients lost in the low-frequency band is the least, but the information loss in the reconstructed image is the most severe. The degree of loss in high-frequency coefficients is the worst, while the information loss is slightest. It means that the low-frequency coefficients are definitely essential during image reconstruction. Besides, even if the medium- and high-frequency coefficients are severely lost, the reconstruction would not be significantly affected.Figure 3
Reconstruction results of the Baboon image in different coefficient-loss situations. (a) No loss. (b) Fifteen low-frequency DCT coefficient losses. (c) Thirty medium-frequency DCT coefficient losses. (d) Sixty high-frequency DCT coefficient losses.
(a)(b)(c)(d)Based on the conclusion mentioned above, this paper proposed to embed secret information into the medium-frequency band in the DCT coefficient matrix of the cover image to improve the antijamming performance of the image steganography system without significant influence on the reconstruction accuracy. Without loss of generality, it is assumed that the size of the cover image is512×512, and the size of the original scene at the sensor node is 128×128. In addition, the value of CR utilized in IEA-CS-NQ is marked with cr. Clearly, the cover image could be transformed into 1024 groups of DCT coefficient block sizing 16×16, while the measurement result acquired by the sensor node could be converted into 1024 groups of bit sequence with 128∈cr elements. According to the condition that cr∈0,1, the lengths of the bit sequence in each group assembled by the measurement results are certainly less than 128, which ensures that each group of the bit sequence could be embedded into the medium-frequency coefficients of one DCT coefficient block.It is necessary to specify the embedding positions and the specific hiding method in the hiding process. As shown in Figure1, the positions are determined by the sequence generated by a specific chaotic system. Before the lth group of operation, a total of 128 elements from 128⋅l−1+1th to 128⋅lth in the chaotic sequence are indexed by values to get a sequence correlated to the embedding positions. Then, the elements indexed from 1 to 128⋅cr in this sequence would add 15 to be taken as the embedding positions of the current group. The process of hiding the ith bit Bi for the lth group of operation into the jth element Aj in the corresponding DCT coefficient sequence A would be taken as an example to demonstrate PPEA. Suppose that Bi=0, the embedding operation designed by(7)A′j=Aj,Aj≤−α⋅Amid¯,−α⋅Amid¯,−α⋅Amid¯<Aj,would be applied to hide the bit sequence in the medium-frequency band of the DCT coefficient matrix orderly. Otherwise, the embedding operation would be(8)A′j=Aj,α⋅Amid¯≤Aj,α⋅Amid¯,Aj<α⋅Amid¯.Here, the conditionsl∈1,2,…,1024, i∈1,2,…,128⋅cr, and j∈16,17,…,143 should be met. Besides, the symbol Amid¯ represents the absolute value of the average for all 128 medium-frequency coefficients A16∼A143. In addition, the parameter α is utilized to regularize the region size, whose value could be increased to enhance the antijamming performance of the steganography system or be reduced properly to improve the imperceptibility for secret information. Sign A′j is the result of the embedding operation for the medium-frequency band coefficient Aj chosen from one group of DCT coefficients.According to equations (7) and (8), the designed PPEA could improve the imperceptibility of secret information for the reason that it preserves most elements in the process of steganography. In other words, it only affects the elements valued between −α⋅Amid¯ and α⋅Amid¯ in the medium-frequency band of DCT coefficients for the cover image. Besides, the result of the embedding operation is constrained outside the interval −α⋅Amid¯,α⋅Amid¯, which could guarantee the antijamming performance of the steganography system. Indeed, the result of the embedding operation is not only determined by the absolute value of the average for all medium-frequency band coefficients but also by the region regulation parameter α.


## 3.4. IDCT Transformation

Before data is transmitted through the wireless channel, the modified coefficient blocks obtained by the embedding operation should be converted to the stego image by applying IDCT. The obtained stego image would be visually safe but contains confidential information, which means the entire steganography is completed.According to the structure shown in Figure1, the extraction-decryption process in terminal user nodes is the inverse operation corresponding to the encryption-hiding process in sensor nodes. It is worth mentioning that each bit extracted is determined by the sign of the corresponding coefficient. After the extraction process is completed, the reconstructed scene could be obtained by directly applying the decryption part in IEA-CS-NQ.


## 4. Simulation and Analysis

For simplicity, simulation experiments were conducted with scenes of size128×128 and cover images of size 512×512. According to the definition of the medium-frequency band and the designed embedding scheme introduced above, the maximum number of bits embedded is half of the number of elements in the DCT coefficient block for the cover image. Therefore, one secret image of size no more than 128×128 could be embedded in a cover image. The security performance of ISS-PPEA could be obtained by analysing the experimental results. Moreover, the imperceptibility of the secret information, the anti-interference performance, and the operating efficiency of the system were also evaluated.Some standard images were taken as examples to verify the effectiveness of the proposed scheme in conditions of zero-mean additive white Gaussian noise (AWGN) with standard deviations of2% or 6.25% occlusion by rectangular shape in the corresponding stego images. Assuming that CR was set to 0.7, the results shown in Figure 4 indicated that ISS-PPEA had satisfactory imperceptibility and robustness.Figure 4
Experimental results of standard images in different interference situations. (a) The cover images of (i) Baboon, (ii) Barbara, and (iii) Pepper. (b) The scenes of (i) Bridge, (ii) Couple, and (iii) Lena. (c) The stego images of (i) Baboon, (ii) Barbara, and (iii) Pepper with AWGN. (d) The reconstruction results of (i) Bridge, (ii) Couple, and (iii) Lena by stego images with AWGN. (e) The stego images of (i) Baboon, (ii) Barbara, and (iii) Pepper with occlusion. (f) The reconstruction results of (i) Bridge, (ii) Couple, and (iii) Lena by stego images with occlusion.


### 4.1. Security Performance

#### 4.1.1. Ability of Resisting CPA

According to the conclusion that IEA-CS-NQ is invulnerable to various kinds of attacks [20], ISS-PPEA could also be safe enough to resist common attacks including CPA because IEA-CS-NQ is directly utilized by the image steganography scheme proposed in this paper.


#### 4.1.2. Key Space and Key Sensitivity

Current research suggests that the key space in a safe cryptosystem should be larger than2112 when confronting brute-force attacks [21]. Actually, it depends on the complexity of the chaotic system utilized in the designed steganography scheme. Due to the Optimized Coupled Map Lattice (OCML) model applied, the IEA-CS-NQ and specified embedding positions in ISS-PPEA require a key stream of more than 240 bits if the data precision is 16 bit, which is enough to satisfy the demand for key space. Moreover, users could tailor the size of the key space on the basis of realistic situation and system requirements. In other words, the size of the key space in the designed scheme could easily meet the needs of different applications.Key sensitivity is also an important characteristic of cryptosystems. Generally speaking, it requires that the cipher images encrypted with different secret keys should be totally different, and that the decrypted images obtained by incorrect keys would lose all useful information about the original image. However, due to the imperceptibility demanded of secret information in steganography systems, the corresponding requirements in the encryption part should be removed. To be specific, the stego images obtained with different secret keys might be visually similar. It was assumed that there existed a slight difference between the two groups of keysk1 and k2, which resulted in a 0.001 deviation of the parameters in the corresponding chaotic system for generating the confusion sequence. Then, hiding the confidential Bridge scene into the Baboon cover image was taken as an example to verify the key sensitivity of ISS-PPEA. As shown in Figure 5, the difference between stego image A obtained with key k1 and stego image B obtained with key k2 is visually hard to be discovered, and it reflects the admirable imperceptibility in the steganography system. However, in the extraction-decryption process, the reconstructed images obtained from stego image A with different secret keys would be completely different according to Figure 6. It means that, even if there exists a tiny deviation in the secret key during the extraction-decryption process, the information in the original scene would be unrecoverable. Moreover, it is believed that the secret image annotated in Figure 1 is still extremely sensitive to key variations due to IEA-CS-NQ utilized in the designed scheme. In summary, the key sensitivity of ISS-PPEA conforms to the requirements in image steganography systems.Figure 5
The key sensitivity in the encryption-hiding process for ISS-PPEA. (a) The cover image of Baboon. (b) The confidential scene of Bridge. (c) The stego image A obtained with keyk1. (d) The stego image B obtained with key k2. (e) The difference between stego images A and B.
(a)(b)(c)(d)(e)Figure 6
The key sensitivity in the extraction-decryption process for ISS-PPEA. (a) The cover image of Baboon. (b) The confidential scene of Bridge. (c) The reconstructed image A obtained from stego image A with keyk1. (d) The reconstructed image B obtained from stego image A with key k2. (e) The difference between two reconstructed images A and B.
(a)(b)(c)(d)(e)


#### 4.1.3. Statistical Histogram

By analysing the statistical histograms of the cover image and stego image, the change rule of the pixel values’ distribution could be revealed, and then, some features of the corresponding steganography system might be leaked [22]. However, as shown in Figure 7, the stego images obtained mostly retained the statistical features of the original cover images, making it difficult for attackers to extract the information about the system from the statistical features of the stego images.Figure 7
The statistical histograms for ISS-PPEA. (a) Histogram of the cover image for (i) Baboon, (ii) Barbara, or (iii) Pepper. (b) Histogram of the stego image using the cover image for (i) Baboon, (ii) Barbara, or (iii) Pepper.


#### 4.1.4. Correlation Coefficients

Generally speaking, the cipher images obtained by a cryptosystem could effectively eliminate the correlation between adjacent pixels of the scene image acquired by the sensor node. However, to optimize the imperceptibility of the secret information contained in the stego image, it is necessary for the stego image to maintain the characteristics of correlation similar to that of the corresponding cover image. An example of embedding the scene of Bridge into the cover image of Baboon is conducted to evaluate the characteristics of correlation in ISS-PPEA. The relationship of 1024 groups of adjacent pixel pairs in horizontal, vertical, and diagonal directions in the cover image and the corresponding stego image are drawn in Figure8. Owing to the similar distribution of correlation, it could be considered that exploring system characteristics from adjacent pixel values is difficult for attackers. In addition, the correlation coefficients listed in Table 1 further provided evidence for the above conclusion.Figure 8
The correlation of adjacent pixel pairs for ISS-PPEA. (a) The correlation in the cover image of Baboon by (i) horizontal direction, (ii) vertical direction, or (iii) diagonal direction. (b) The correlation in the stego image using the cover image of Baboon by (i) horizontal direction, (ii) vertical direction, or (iii) diagonal direction.Table 1
The correlation coefficients of adjacent pixel pairs in the cover image and stego image for ISS-PPEA.
Cover image/SceneHorizontal directionVertical directionDiagonal directionBaboon/Bridge0.7317/0.75980.8578/0.86980.7093/0.7304Barbara/Couple0.9621/0.96430.9098/0.91970.8897/0.9052Pepper/Lena0.9828/0.98260.9861/0.98570.9768/0.9766Average value0.8922/0.90220.9179/0.92510.8586/0.8707


#### 4.1.5. Randomness Analysis

Information entropyHs is usually used to estimate the statistical measure of uncertainty. It could be defined as(9)Hs=∑i=0255Psilog21Psi.Here, the symbols is a discrete random variable, and Psi represents the probability density function of the appearance of si. If all values have the same probability, that is, Psi=1/28, then the value of Hs should be 8. The information entropy of a meaningful image must be less than that. For an image steganography system, the information entropy of the stego image should be close to that of the corresponding cover image to improve the imperceptibility of the secret information. Some scene images embedded to cover images were taken as examples to evaluate this performance in ISS-PPEA. According to the results listed in Table 2, the characteristics of randomness in the cover images could be well preserved in the corresponding stego images. Therefore, the random characteristics of ISS-PPEA are believed to meet the design requirements.Table 2
The information entropies in cover images and stego images for ISS-PPEA.
Cover image/SceneCover imageStego imageBaboon/Bridge7.15607.1235Barbara/Couple7.63327.6752Pepper/Lena7.63967.6644Average value7.47637.4877


## 4.1. Security Performance

### 4.1.1. Ability of Resisting CPA

According to the conclusion that IEA-CS-NQ is invulnerable to various kinds of attacks [20], ISS-PPEA could also be safe enough to resist common attacks including CPA because IEA-CS-NQ is directly utilized by the image steganography scheme proposed in this paper.


### 4.1.2. Key Space and Key Sensitivity

Current research suggests that the key space in a safe cryptosystem should be larger than2112 when confronting brute-force attacks [21]. Actually, it depends on the complexity of the chaotic system utilized in the designed steganography scheme. Due to the Optimized Coupled Map Lattice (OCML) model applied, the IEA-CS-NQ and specified embedding positions in ISS-PPEA require a key stream of more than 240 bits if the data precision is 16 bit, which is enough to satisfy the demand for key space. Moreover, users could tailor the size of the key space on the basis of realistic situation and system requirements. In other words, the size of the key space in the designed scheme could easily meet the needs of different applications.Key sensitivity is also an important characteristic of cryptosystems. Generally speaking, it requires that the cipher images encrypted with different secret keys should be totally different, and that the decrypted images obtained by incorrect keys would lose all useful information about the original image. However, due to the imperceptibility demanded of secret information in steganography systems, the corresponding requirements in the encryption part should be removed. To be specific, the stego images obtained with different secret keys might be visually similar. It was assumed that there existed a slight difference between the two groups of keysk1 and k2, which resulted in a 0.001 deviation of the parameters in the corresponding chaotic system for generating the confusion sequence. Then, hiding the confidential Bridge scene into the Baboon cover image was taken as an example to verify the key sensitivity of ISS-PPEA. As shown in Figure 5, the difference between stego image A obtained with key k1 and stego image B obtained with key k2 is visually hard to be discovered, and it reflects the admirable imperceptibility in the steganography system. However, in the extraction-decryption process, the reconstructed images obtained from stego image A with different secret keys would be completely different according to Figure 6. It means that, even if there exists a tiny deviation in the secret key during the extraction-decryption process, the information in the original scene would be unrecoverable. Moreover, it is believed that the secret image annotated in Figure 1 is still extremely sensitive to key variations due to IEA-CS-NQ utilized in the designed scheme. In summary, the key sensitivity of ISS-PPEA conforms to the requirements in image steganography systems.Figure 5
The key sensitivity in the encryption-hiding process for ISS-PPEA. (a) The cover image of Baboon. (b) The confidential scene of Bridge. (c) The stego image A obtained with keyk1. (d) The stego image B obtained with key k2. (e) The difference between stego images A and B.
(a)(b)(c)(d)(e)Figure 6
The key sensitivity in the extraction-decryption process for ISS-PPEA. (a) The cover image of Baboon. (b) The confidential scene of Bridge. (c) The reconstructed image A obtained from stego image A with keyk1. (d) The reconstructed image B obtained from stego image A with key k2. (e) The difference between two reconstructed images A and B.
(a)(b)(c)(d)(e)


### 4.1.3. Statistical Histogram

By analysing the statistical histograms of the cover image and stego image, the change rule of the pixel values’ distribution could be revealed, and then, some features of the corresponding steganography system might be leaked [22]. However, as shown in Figure 7, the stego images obtained mostly retained the statistical features of the original cover images, making it difficult for attackers to extract the information about the system from the statistical features of the stego images.Figure 7
The statistical histograms for ISS-PPEA. (a) Histogram of the cover image for (i) Baboon, (ii) Barbara, or (iii) Pepper. (b) Histogram of the stego image using the cover image for (i) Baboon, (ii) Barbara, or (iii) Pepper.


### 4.1.4. Correlation Coefficients

Generally speaking, the cipher images obtained by a cryptosystem could effectively eliminate the correlation between adjacent pixels of the scene image acquired by the sensor node. However, to optimize the imperceptibility of the secret information contained in the stego image, it is necessary for the stego image to maintain the characteristics of correlation similar to that of the corresponding cover image. An example of embedding the scene of Bridge into the cover image of Baboon is conducted to evaluate the characteristics of correlation in ISS-PPEA. The relationship of 1024 groups of adjacent pixel pairs in horizontal, vertical, and diagonal directions in the cover image and the corresponding stego image are drawn in Figure8. Owing to the similar distribution of correlation, it could be considered that exploring system characteristics from adjacent pixel values is difficult for attackers. In addition, the correlation coefficients listed in Table 1 further provided evidence for the above conclusion.Figure 8
The correlation of adjacent pixel pairs for ISS-PPEA. (a) The correlation in the cover image of Baboon by (i) horizontal direction, (ii) vertical direction, or (iii) diagonal direction. (b) The correlation in the stego image using the cover image of Baboon by (i) horizontal direction, (ii) vertical direction, or (iii) diagonal direction.Table 1
The correlation coefficients of adjacent pixel pairs in the cover image and stego image for ISS-PPEA.
Cover image/SceneHorizontal directionVertical directionDiagonal directionBaboon/Bridge0.7317/0.75980.8578/0.86980.7093/0.7304Barbara/Couple0.9621/0.96430.9098/0.91970.8897/0.9052Pepper/Lena0.9828/0.98260.9861/0.98570.9768/0.9766Average value0.8922/0.90220.9179/0.92510.8586/0.8707


### 4.1.5. Randomness Analysis

Information entropyHs is usually used to estimate the statistical measure of uncertainty. It could be defined as(9)Hs=∑i=0255Psilog21Psi.Here, the symbols is a discrete random variable, and Psi represents the probability density function of the appearance of si. If all values have the same probability, that is, Psi=1/28, then the value of Hs should be 8. The information entropy of a meaningful image must be less than that. For an image steganography system, the information entropy of the stego image should be close to that of the corresponding cover image to improve the imperceptibility of the secret information. Some scene images embedded to cover images were taken as examples to evaluate this performance in ISS-PPEA. According to the results listed in Table 2, the characteristics of randomness in the cover images could be well preserved in the corresponding stego images. Therefore, the random characteristics of ISS-PPEA are believed to meet the design requirements.Table 2
The information entropies in cover images and stego images for ISS-PPEA.
Cover image/SceneCover imageStego imageBaboon/Bridge7.15607.1235Barbara/Couple7.63327.6752Pepper/Lena7.63967.6644Average value7.47637.4877


## 4.1.1. Ability of Resisting CPA

According to the conclusion that IEA-CS-NQ is invulnerable to various kinds of attacks [20], ISS-PPEA could also be safe enough to resist common attacks including CPA because IEA-CS-NQ is directly utilized by the image steganography scheme proposed in this paper.


## 4.1.2. Key Space and Key Sensitivity

Current research suggests that the key space in a safe cryptosystem should be larger than2112 when confronting brute-force attacks [21]. Actually, it depends on the complexity of the chaotic system utilized in the designed steganography scheme. Due to the Optimized Coupled Map Lattice (OCML) model applied, the IEA-CS-NQ and specified embedding positions in ISS-PPEA require a key stream of more than 240 bits if the data precision is 16 bit, which is enough to satisfy the demand for key space. Moreover, users could tailor the size of the key space on the basis of realistic situation and system requirements. In other words, the size of the key space in the designed scheme could easily meet the needs of different applications.Key sensitivity is also an important characteristic of cryptosystems. Generally speaking, it requires that the cipher images encrypted with different secret keys should be totally different, and that the decrypted images obtained by incorrect keys would lose all useful information about the original image. However, due to the imperceptibility demanded of secret information in steganography systems, the corresponding requirements in the encryption part should be removed. To be specific, the stego images obtained with different secret keys might be visually similar. It was assumed that there existed a slight difference between the two groups of keysk1 and k2, which resulted in a 0.001 deviation of the parameters in the corresponding chaotic system for generating the confusion sequence. Then, hiding the confidential Bridge scene into the Baboon cover image was taken as an example to verify the key sensitivity of ISS-PPEA. As shown in Figure 5, the difference between stego image A obtained with key k1 and stego image B obtained with key k2 is visually hard to be discovered, and it reflects the admirable imperceptibility in the steganography system. However, in the extraction-decryption process, the reconstructed images obtained from stego image A with different secret keys would be completely different according to Figure 6. It means that, even if there exists a tiny deviation in the secret key during the extraction-decryption process, the information in the original scene would be unrecoverable. Moreover, it is believed that the secret image annotated in Figure 1 is still extremely sensitive to key variations due to IEA-CS-NQ utilized in the designed scheme. In summary, the key sensitivity of ISS-PPEA conforms to the requirements in image steganography systems.Figure 5
The key sensitivity in the encryption-hiding process for ISS-PPEA. (a) The cover image of Baboon. (b) The confidential scene of Bridge. (c) The stego image A obtained with keyk1. (d) The stego image B obtained with key k2. (e) The difference between stego images A and B.
(a)(b)(c)(d)(e)Figure 6
The key sensitivity in the extraction-decryption process for ISS-PPEA. (a) The cover image of Baboon. (b) The confidential scene of Bridge. (c) The reconstructed image A obtained from stego image A with keyk1. (d) The reconstructed image B obtained from stego image A with key k2. (e) The difference between two reconstructed images A and B.
(a)(b)(c)(d)(e)


## 4.1.3. Statistical Histogram

By analysing the statistical histograms of the cover image and stego image, the change rule of the pixel values’ distribution could be revealed, and then, some features of the corresponding steganography system might be leaked [22]. However, as shown in Figure 7, the stego images obtained mostly retained the statistical features of the original cover images, making it difficult for attackers to extract the information about the system from the statistical features of the stego images.Figure 7
The statistical histograms for ISS-PPEA. (a) Histogram of the cover image for (i) Baboon, (ii) Barbara, or (iii) Pepper. (b) Histogram of the stego image using the cover image for (i) Baboon, (ii) Barbara, or (iii) Pepper.


## 4.1.4. Correlation Coefficients

Generally speaking, the cipher images obtained by a cryptosystem could effectively eliminate the correlation between adjacent pixels of the scene image acquired by the sensor node. However, to optimize the imperceptibility of the secret information contained in the stego image, it is necessary for the stego image to maintain the characteristics of correlation similar to that of the corresponding cover image. An example of embedding the scene of Bridge into the cover image of Baboon is conducted to evaluate the characteristics of correlation in ISS-PPEA. The relationship of 1024 groups of adjacent pixel pairs in horizontal, vertical, and diagonal directions in the cover image and the corresponding stego image are drawn in Figure8. Owing to the similar distribution of correlation, it could be considered that exploring system characteristics from adjacent pixel values is difficult for attackers. In addition, the correlation coefficients listed in Table 1 further provided evidence for the above conclusion.Figure 8
The correlation of adjacent pixel pairs for ISS-PPEA. (a) The correlation in the cover image of Baboon by (i) horizontal direction, (ii) vertical direction, or (iii) diagonal direction. (b) The correlation in the stego image using the cover image of Baboon by (i) horizontal direction, (ii) vertical direction, or (iii) diagonal direction.Table 1
The correlation coefficients of adjacent pixel pairs in the cover image and stego image for ISS-PPEA.
Cover image/SceneHorizontal directionVertical directionDiagonal directionBaboon/Bridge0.7317/0.75980.8578/0.86980.7093/0.7304Barbara/Couple0.9621/0.96430.9098/0.91970.8897/0.9052Pepper/Lena0.9828/0.98260.9861/0.98570.9768/0.9766Average value0.8922/0.90220.9179/0.92510.8586/0.8707


## 4.1.5. Randomness Analysis

Information entropyHs is usually used to estimate the statistical measure of uncertainty. It could be defined as(9)Hs=∑i=0255Psilog21Psi.Here, the symbols is a discrete random variable, and Psi represents the probability density function of the appearance of si. If all values have the same probability, that is, Psi=1/28, then the value of Hs should be 8. The information entropy of a meaningful image must be less than that. For an image steganography system, the information entropy of the stego image should be close to that of the corresponding cover image to improve the imperceptibility of the secret information. Some scene images embedded to cover images were taken as examples to evaluate this performance in ISS-PPEA. According to the results listed in Table 2, the characteristics of randomness in the cover images could be well preserved in the corresponding stego images. Therefore, the random characteristics of ISS-PPEA are believed to meet the design requirements.Table 2
The information entropies in cover images and stego images for ISS-PPEA.
Cover image/SceneCover imageStego imageBaboon/Bridge7.15607.1235Barbara/Couple7.63327.6752Pepper/Lena7.63967.6644Average value7.47637.4877


## 5. Imperceptibility

Existing research shows that when observing an image, the human visual system would be highly adaptive to extract its structure information. And, it judges the degree of distortion by comparing the differences in the image structure information. Thus, the image steganography system should minimize the visual difference between the stego image and the corresponding cover image to reduce the detectability of secret information. According to the diagram illustrated in Figure1, the imperceptibility of the secret information is primarily determined by the structural similarity between the stego image and the cover image and is positively correlated with it. Therefore, the Structural Similarity Index (SSIM) is utilized to evaluate the imperceptibility of secret information. It could be calculated with(10)SSIMx,y=lx,yα⋅cx,yβ⋅sx,yγ.Within this formula, there are definitions of(11)lx,y=2μxμy+C1μx2+μy2+C1,(12)cx,y=2σxσy+C2σx2+σy2+C2,(13)sx,y=σxy+C3σxσy+C3.Here, the symbolsx and y represent the pixel values of the stego image and the corresponding cover image. Signs μx and σx are the average and variance of the stego image, respectively. Symbol σxy stands for the covariance between the stego image and the cover image. Besides, C1, C2, and C3 are constants with small values, which are used to ensure the stability of the denominators for equations (11) to (13). Parameters α, β, and γ are conveyed to adjust the weight distribution of brightness (average), contrast (variance), and structural information in the model. Surely, from the perspective of image information composition, SSIM defines the structure information as a special property reflecting the scene structure independent of brightness and contrast and models the whole scene information as a combination of brightness, contrast, and structure. According to the definition of SSIM, the mean value of pixel values is taken as the estimation of brightness, while the standard deviation of pixel values is used as the estimation of contrast, and the covariance between two images acts as the estimation of the approximate degree of structure. In general, there are C1=k1⋅L2, C2=k2⋅L2, C3=C2/2, k1=0.01, k2=0.03, and L=255. Equation (10) could be simplified to(14)SSIMx,y=2μxμy+C12σxy+C2μx2+μy2+C1σx2+σy2+C2,when α=β=γ=1. On the basis of equations (7) and (8), the designed steganography scheme could modify the region adjustment parameter α to meet the requirements for different applications. Specifically, the smaller α would result in the smaller loss of the medium-frequency band of DCT coefficients in the encryption-hiding process. It means a larger SSIM of the stego image and the corresponding cover image, which optimizes the imperceptibility of the secret information. However, in this situation, the anti-interference performance would be influenced due to the smaller judgment threshold used for information extraction. On the contrary, if the value of the parameter α is enlarged, the loss of the medium-frequency band of DCT coefficients would increase. It means a smaller SSIM of the stego image and the corresponding cover image, which degrades the imperceptibility of the secret information. However, the antijamming performance would be optimized because of the larger judgment threshold used for information extraction. In general, it is necessary to balance the relationship between the imperceptibility and anti-interference performance according to the requirements for different applications. Then, the appropriate region adjustment parameter could be found out.Assuming that CR was set to 0.7 for measurement and zero-mean AWGN with standard deviation of 2/4/6 existed in the channel, experiments were conducted with different region adjustment parameters to verify the theoretical analysis mentioned above. As shown in Figure9, the larger parameter α correlated with better anti-interference performance and worse imperceptibility. Moreover, the environment with greater noise intensity would be related to the more obvious improvement in the anti-interference performance. Conversely, the smaller parameter α would result in worse anti-interference performance and better imperceptibility. And, greater AWGN strength correlates with the more obvious improvement in the imperceptibility.Figure 9
The reconstruction performance of ISS-PPEA with the channel containing AWGN. (a) The PSNR values of the reconstructed image with the channel containing zero-mean AWGN with standard deviations of (i) 2, (ii) 4, or (iii) 6. (b) The SSIM values of the stego image and the cover image with the channel containing zero-mean AWGN with standard deviations of (i) 2, (ii) 4, or (iii) 6. (c) The SSIM values of the reconstructed image and the original scene with the channel containing zero-mean AWGN with standard deviations of (i) 2, (ii) 4, or (iii) 6.


## 6. Anti-Interference Performance

In the steganography applications based on the WVSN structure, the data transmitted in the wireless channel is not only easy to be affected by various kinds of interference but also easy to be attacked by hackers artificially. To obtain most of the scene information captured by the sensor node, the requirements for anti-interference performance of the system must be taken seriously. Most current schemes hid secret information into the LSB of the cover images in the spatial domain or into the coefficients of the high-frequency band of the cover images in the transformational domain. These methods are unable to meet the specific requirements of WVSN. Therefore, this paper proposed to hide the measurement results of the scenes into the medium-frequency DCT coefficients of the cover image bitwise randomly, which is surely beneficial to reduce the influence of AWGN and improve the anti-interference performance of the system. Because ISS-PPEA involves the entire structure of IEA-CS-NQ, the reconstruction accuracy in front of occlusion would not be worse than that in the existing literatures. Since the designed embedding algorithm has little effect on the image reconstruction ability in the case of data loss, this section would merely evaluate the system performance under AWGN interference.By comparing ISS-PPEA with the similar embedding method proposed by Poljicak et al. [19], it could be found that(1)
In the scheme proposed by Poljicak, the binarization treatment for the coefficients selected by the embedding operation was carried out on the basis of the average of the medium-frequency DCT coefficient, which significantly affected the SSIM for the stego image and the cover image. In ISS-PPEA, the coefficients chosen by the embedding operation are modified by the partial preservation treatment method described in equations (7) and (8) based on the region adjustment parameter according to specific requirements for applications. It could sharply reduce the number of DCT coefficients that have to be changed in the hiding process. Indeed, ISS-PPEA could help to improve the SSIM and imperceptibility.(2)
According to the embedding method described in equations (7) and (8), the proposed scheme could make the revised coefficients have regional distribution. That is to say, compared with the binarization treatment method designed in [19], the absolute value of stego coefficients in ISS-PPEA is larger, and the probability of misjudgement in the process of extracting sign is surely lower for the same AWGN. In other words, ISS-PPEA could improve the accuracy of information reconstruction.Several groups of standard images were applied to verify the theoretical analysis mentioned above. The designed steganography scheme based on the partial preservation treatment was compared with the available scheme based on the binarization treatment by assuming that zero-mean AWGN with standard deviations of 2/4/6 existed in the channel. The results are drawn in Figures10–12. It is worth mentioning that the symbols PM and BT are taken as the abbreviations for the proposed partial preservation treatment method and the available binarization treatment method, respectively. As shown in Figure 10, with AWGN interference of different intensities, the reconstruction result of the proposed scheme is more accurate. Moreover, the higher the noise intensity is, the more obvious the improvement of PSNR would be. According to Figure 11, the designed scheme significantly boosts the SSIM value for the stego image and the cover image. It means that the imperceptibility of secret information has been improved by the proposed method. Figure 12 shows that ISS-PPEA contributes to enhance the structural similarity of the reconstructed image and scene information. It should be noted that although the PSNR and SSIM values shown in Figures 10–12 were quite small, this would not affect the correctness of the experimental results and conclusions. In practice, it is easy to choose a better reconstruction algorithm to improve the performance of the reconstruction.Figure 10
The PSNR values of the reconstructed image under AWGN interference of different intensities for PM and BT. (a) The cover image is Baboon, and the scene is Bridge. (b) The cover image is Barbara, and the scene is Couple. (c) The cover image is Pepper, and the scene is Lena.
(a)(b)(c)Figure 11
The SSIM values of the stego image and cover image under AWGN interference of different intensities for PM and BT. (a) The cover image is Baboon, and the scene is Bridge. (b) The cover image is Barbara, and the scene is Couple. (c) The cover image is Pepper, and the scene is Lena.
(a)(b)(c)Figure 12
The SSIM values of the reconstructed image and scene under AWGN interference of different intensities for PM and BT. (a) The cover image is Baboon, and the scene is Bridge. (b) The cover image is Barbara, and the scene is Couple. (c) The cover image is Pepper, and the scene is Lena.
(a)(b)(c)As mentioned above, the ISS-PPEA designed by this paper could improve the reconstruction precision for the scene information under noisy environment, comparing with current schemes based on hiding secret data in the LSB of the cover image in the spatial domain or embedding data into the coefficients of the high-frequency band in the transformational domain. When comparing with the binarization embedding treatment method designed in the literature [19], the partial preservation scheme is better at improving the imperceptibility and reconstruction accuracy of scene information, which is equivalent to improving the anti-interference performance.


## 7. Efficiency

The operating efficiency of the image steganography system based on the partial preservation embedding algorithm would be evaluated from the aspects of time complexity, space complexity, information embedding rate, communication efficiency, and system consumption in this part.


### 7.1. Time and Space Complexity

Suppose the size of the cover image isn1×n1. According to the system framework shown in Figure 1, the size of objects and results of DCT/IDCT operation is still n1×n1. Therefore, the time and space complexity of the proposed system are both On1, equal to the existing schemes.


### 7.2. Information Embedding Rate and Communication Efficiency

For image steganography systems, the information embedding rate is defined as the ratio of the information amount in the confidential scene to the cover image. And, the communication efficiency could be considered as the ratio of the data volume in the scene to be hidden and the stego image transmitted in the channel.Indeed, the information embedding rate of the system is closely related to the information embedding method, while the communication efficiency is connected with the compression ratio during the measurement operation in CS. Suppose the size of the cover image isn1×n1, the size of the scene is n2×n2, and the compression ratio during measurement is 1. According to the definition that the medium-frequency DCT coefficients occupy 50% space of the cover image, the proposed system could work normally as long as the condition n1/16≥n2 is met. Therefore, the maximum embedding capacity of the steganography system is n1/2 bits, and the maximum embedding rate of information is 6.25%n1/16/n1. Since the communication efficiency is n2/n1, the communication efficiency would be the maximum value of 6.25% if n2=n1/16. In addition, if the compression ratio is less than 1, the communication efficiency of the system would be improved accordingly.


### 7.3. System Consumption

According to the scheme designed in Figure1, a sensor node only needs to complete the work of scene information acquisition, encryption, and embedding, which corresponds with limited consumption requirements. Reconstruction is confined to the terminal user node with powerful hardware for its difficulty. Therefore, it can be considered that the image steganography scheme designed by this paper is very suitable for the applications with WVSN architecture.


## 7.1. Time and Space Complexity

Suppose the size of the cover image isn1×n1. According to the system framework shown in Figure 1, the size of objects and results of DCT/IDCT operation is still n1×n1. Therefore, the time and space complexity of the proposed system are both On1, equal to the existing schemes.


## 7.2. Information Embedding Rate and Communication Efficiency

For image steganography systems, the information embedding rate is defined as the ratio of the information amount in the confidential scene to the cover image. And, the communication efficiency could be considered as the ratio of the data volume in the scene to be hidden and the stego image transmitted in the channel.Indeed, the information embedding rate of the system is closely related to the information embedding method, while the communication efficiency is connected with the compression ratio during the measurement operation in CS. Suppose the size of the cover image isn1×n1, the size of the scene is n2×n2, and the compression ratio during measurement is 1. According to the definition that the medium-frequency DCT coefficients occupy 50% space of the cover image, the proposed system could work normally as long as the condition n1/16≥n2 is met. Therefore, the maximum embedding capacity of the steganography system is n1/2 bits, and the maximum embedding rate of information is 6.25%n1/16/n1. Since the communication efficiency is n2/n1, the communication efficiency would be the maximum value of 6.25% if n2=n1/16. In addition, if the compression ratio is less than 1, the communication efficiency of the system would be improved accordingly.


## 7.3. System Consumption

According to the scheme designed in Figure1, a sensor node only needs to complete the work of scene information acquisition, encryption, and embedding, which corresponds with limited consumption requirements. Reconstruction is confined to the terminal user node with powerful hardware for its difficulty. Therefore, it can be considered that the image steganography scheme designed by this paper is very suitable for the applications with WVSN architecture.


## 8. Conclusions

The key technical problems of available image steganography schemes employed by applications with the structure of WVSN were firstly analysed in this paper. It was found that the performance of existing systems in the hostile environment was unsatisfactory. Besides, the current solutions based on the medium-frequency band in the transformational domain of the cover image have greatly affected the SSIM of the stego image and cover image. Thus, to settle these problems, an image steganography scheme based on PPEA is proposed in this paper. Theoretical analysis and simulation results have proved that the designed scheme possesses the following advantages:(1)
Due to IEA-CS-NQ being taken as part of the proposed scheme, it could be considered that the proposed ISS-PPEA inherits its advantages of high-level encryption efficiency and the ability to resist all kinds of attacks including CPA(2)
Comparing with existing schemes of embedding scene information into LSB in the spatial domain or hiding it to the high-frequency band in the transformational domain, the proposed scheme has better performance in the hostile communication environment(3)
The designed PPEA performs better in terms of optimizing the imperceptibility and boosting the reconstruction accuracy of the original scene information, when making a comparison with the existing method proposed by Poljicak et al. [19](4)
The proposed scheme could adapt to different performance requirements in various applications by setting region adjustment parameters, which ensures its practical value



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*Source: 6618134-2021-02-28.xml*