TY - JOUR
AU - R S, Vinod Kumar
AB - Abstract Securing the privacy of the medical information through the image steganography process has gained more research interest nowadays to protect the privacy of the patient. In the existing works, least significant bit (LSB) replacement strategy was most popularly used to hide the sensitive contents. Here, every pixel was replaced for achieving higher privacy, but it increased the complexity. This work introduces a novel pixel prediction scheme-based image steganography to overcome the complexity issues prevailing in the existing works. In the proposed pixel prediction scheme, the support vector neural network (SVNN) classifier is utilized for the construction of a prediction map, which identifies the suitable pixels for the embedding process. Then, in the embedding phase, wavelet coefficients are extracted from the medical image based on discrete wavelet transform (DWT) and embedding strength, and the secret message is embedded into the HL wavelet band. Finally, the secret message is extracted from the medical image on applying the DWT. The experimentation of the proposed pixel prediction scheme is done by utilizing the medical images from the BRATS database. The proposed pixel prediction scheme has achieved high performance with the values of 48.558 dB, 0.50009 and 0.9879 for the peak signal to noise ratio (PSNR), Structural Similarity Index (SSIM) and correlation factor, respectively. 1. INTRODUCTION Steganography [10,11,17] has gained popularity over the years since it helps in covert communication. In the image steganography, the secret message formulated as an image is embedded into the ordinary image and helps in maintaining the secrecy of the information. Several streams have concentrated on maintaining the confidentiality of the messages, and the techniques fall under two streams, cryptography and steganography. Recent researchers have contributed to these streams, but have failed to achieve significant results due to the challenges prevailing in the process [6]. Steganography can be applied to several streams, such as low bit-rate speech streams [12] [14], speech applications [13] and text-based applications [15]. Image steganography scheme uses the image represented as the cover image for embedding the secret image, and the embedded image having the secret information is said to be the stego image. One of the major challenges faced by the embedding scheme is performing the embedding without distorting the information and the cover object. Thus, the steganography scheme needs to concentrate on a number of messages to be embedded in the cover object, and the distortion occurred by the secret message. The efficiency of the steganography process is measured based on embedding efficiency, which defines the number of bits per embedding change. Also, the technique of achieving high embedding efficiency is said to be optimal embedding [3]. Steganography techniques use various digital media sources such as image, video and audio for the embedding process. Hiding the sensitive information in the cover object should not alter the quality of the object, and also, it should not draw the attention of the unauthorized user to decode the information content [5]. Normally, the image steganography schemes fall into two major categories, such as reversible and irreversible image steganography [7]. In reversible image steganography [20], the payload present within the stego media is reconstructed efficiently with the use of the retrieval schemes, while in the irreversible image steganography scheme, the higher embedding capacity is achieved with minimal computation time. Several works have been opted for the optimal order embedding to hide the information content as it designs a cost function for estimating the suitable pixels for the prediction. Also, these schemes have aimed to reduce the distortion between the cover object and the stego media for increasing the embedding efficiency. It is done by assigning the cost function to each pixel element of the cover object [2]. One of the important criteria in the image steganography scheme is the identification of the suitable pixel for embedding the secret image. Commonly used embedding schemes are random order embedding and sequential order embedding, and they define the strategy for embedding the secret message in cover media. Literature has suggested various techniques for image steganography, and least significant bit (LSB) replacement is the commonly used schemes. The LSB replacement scheme allows the embedding process by replacing the LSB bit of cover object with the bits in the secret message. Since the scheme performs the embedding more easily; it remains to be a popular method for image steganography. It uses the pseudo-random generator for replacing the bit stream of the cover object. Besides its simplicity, replacing the LSB bit in the cover media may provoke distortion during the image retrieval phase. Also, it introduces the never decreasing even pixels and increasing odd pixels during the LSB replacement [18,19]. The high embedding capacity posed by the LSB replacement technique fails to avoid the distortion in the image [21]. Several works suggested the use of the artificial intelligence schemes, such as genetic algorithm (GA) [22], Lion Optimization algorithm [37], Whale Optimization algorithm [38] and particle swarm optimization (PSO) [23] for hiding the sensitive information [8] and these schemes achieved better performance when the image is affected due to noise. Optimization algorithms are used in various fields, such as image steganography, disease diagnosis [33], tumor detection [34], harmonic generation [35] and knowledge management [36]. Also, storing the digital media for a long period may result in noise induction, and using the noisy image for the steganography process may reduce the embedding efficiency. The content-adaptive spatial image steganography has significant results by embedding the secret information in the textured and noisy areas as it uses the distortion function [16]. The list of abbreviations used in this work is described in Table 1. TABLE 1. List of abbreviations. Abbreviation/acronym . Description . LSB Least significant bit SVNN Support vector neural network DWT Discrete wavelet transform GA Genetic algorithm PSO Particle swarm optimization RM Reed–Muller JPEG Joint Photographic Experts Group DCT Discrete cosine transform PSNR Peak signal to noise ratio SNR Signal to noise ratio SSIM Structural Similarity Index MMED Modified median edge predictor HVS Human vision system PSPNR Peak signal to perceived noise ratio LBP Local binary pattern IDWT Inverse DWT CWSM Cost function using wavelet and edge transformation for medical image steganography Abbreviation/acronym . Description . LSB Least significant bit SVNN Support vector neural network DWT Discrete wavelet transform GA Genetic algorithm PSO Particle swarm optimization RM Reed–Muller JPEG Joint Photographic Experts Group DCT Discrete cosine transform PSNR Peak signal to noise ratio SNR Signal to noise ratio SSIM Structural Similarity Index MMED Modified median edge predictor HVS Human vision system PSPNR Peak signal to perceived noise ratio LBP Local binary pattern IDWT Inverse DWT CWSM Cost function using wavelet and edge transformation for medical image steganography Open in new tab TABLE 1. List of abbreviations. Abbreviation/acronym . Description . LSB Least significant bit SVNN Support vector neural network DWT Discrete wavelet transform GA Genetic algorithm PSO Particle swarm optimization RM Reed–Muller JPEG Joint Photographic Experts Group DCT Discrete cosine transform PSNR Peak signal to noise ratio SNR Signal to noise ratio SSIM Structural Similarity Index MMED Modified median edge predictor HVS Human vision system PSPNR Peak signal to perceived noise ratio LBP Local binary pattern IDWT Inverse DWT CWSM Cost function using wavelet and edge transformation for medical image steganography Abbreviation/acronym . Description . LSB Least significant bit SVNN Support vector neural network DWT Discrete wavelet transform GA Genetic algorithm PSO Particle swarm optimization RM Reed–Muller JPEG Joint Photographic Experts Group DCT Discrete cosine transform PSNR Peak signal to noise ratio SNR Signal to noise ratio SSIM Structural Similarity Index MMED Modified median edge predictor HVS Human vision system PSPNR Peak signal to perceived noise ratio LBP Local binary pattern IDWT Inverse DWT CWSM Cost function using wavelet and edge transformation for medical image steganography Open in new tab This paper aims to introduce a novel image steganography scheme by proposing the pixel-based prediction scheme. Here, the support vector neural network (SVNN) is used for constructing the prediction map for the input image. The steps involved in the proposed image steganography system are (i) identification phase, (ii) embedding phase and (iii) extraction phase. In the identification phase, various factors, such as wavelet energy, pixel coverage, edge information, scattering value, Gabor feature value and texture component based on LBP, are taken from the medical image to predict the pixels to be embedded. Here, the pixel prediction scheme is done on the SVNN classifier, which predicts whether the identified pixels are suitable for the embedding or not. Then, the patient’s information is embedded in the medical image using the embedding mechanism, which utilizes a DWT coefficient and the embedding strength. Finally, the extraction step extracts the secret message from the embedded image with the DWT-based extraction model. The major contribution of this scheme is the design and development of the DWT-based pixel prediction scheme with the SVNN, for image steganography in the medical data. The rest of this work is structured as follows: Section 1 presents the introduction to the image steganography technique and the various literary works related to the image steganography are explained in Section 2. Section 3 gives a brief description of the proposed pixel prediction based image steganography model with the SVNN classifier. Section 4 presents the simulation results achieved by the proposed pixel prediction scheme. Finally, Section 5 concludes this paper. 2. MOTIVATION 2.1. Literature survey This section presents various literature works contributed towards the image steganography. Abuadbba and Khalil [1] presented the image steganography model, which helped in hiding the sensitive information in the medical data, with the use of the Walsh–Hadamard transform. The model made use of less significant values of coefficients for reduced distortion, but this scheme is expensive. Zhou et al. [2] proposed the adaptive steganography model with the cost reassignment rule. It had achieved significant results in the spatial images, which have more distortion but cannot be applied to the Joint Photographic Experts Group (JPEG) image. T. Yang and H. Chen, [3] proposed the majority-logic decoding algorithm based on the Reed-Muller (RM) codes for image steganography. When the algorithm was used along with the bias propagation, the model had improved efficiency. The algorithm had better results only at higher iteration and hence, has increased complexity. Denemark and Fridrich [4] presented the steganography model for hiding the sensitive information in multiple JPEG images. The model had used the discrete cosine transform (DCT) for the embedding process and, hence, was suitable for the real-time applications. While performing the embedding process, the acquisition noise amplitude depends on luminance and hence has reduced efficiency. Sarmah and Kulkarni [5] proposed the Cohort Intelligence and Modified Multi-Random Start Local Search model for performing the steganography process in the JPEG images. The scheme had achieved improved balance between the security and quality. Besides, the PSNR of the secret image is not up to the standard after the retrieval stage. El-Bendary [6] proposed the LSB-based image steganography scheme for dealing with the security issues prevailing in the noisy images. The model also had used various encryption techniques for hiding the secured information content, and it had reduced the noise channel effects. However, the increase in the signal to noise ratio (SNR) limit in the embedding phase had limited the extraction process. Chakraborty et al. [7] proposed the Predictive Edge Adaptive image Steganography technique for the LSB replacement. The authors had also used the Modified Median Edge predictor (MMED) for identifying the suitable edge pixels in the image. The scheme had achieved improved embedding rate by tacking the various noise attacks. Miri and Faez [8] proposed the image steganography model based on the integer wavelet transform. The model achieved high adaptation to the human vision system (HVS), but the model failed to consider the changes that were prevailing in the cover and stego image for calculating peak signal to perceived noise ratio (PSPNR). Nipanikar and Hima Deepthi [9] used multiple criteria and the wavelet and edge transformation for building the image steganography model. They had also developed the cost estimation model for identifying the suitable pixels for the embedding process. The scheme has high PSNR for the low-quality images. 2.2. Challenges Various challenges faced by the image steganography scheme are enlisted below: The image steganography hides the sensitive content in the image through the embedding process, and hence, the embedding process should not degrade the quality of the stego media [5]. The medical data contains large sources of images, which can act as a cover media, but it is practically difficult to develop steganographic algorithms for large cover media sources [2]. The steganography process should be developed such that the embedding efficiency of the process needs to be high by preserving the quality of the secret information [7]. The process can be defined as the optimal embedding technique, if and only if the model achieved higher embedding efficiency [3]. Since the image can be affected by noise easily, it is difficult to achieve optimal embedding. Image steganography done in the JPEG images through the extraction of the DCT coefficients faces many challenges since images can be quantized to zero during the JPEG compression process. Also, use of large quantization steps for embedding also affects the quality of the secret image [18]. In [9], the image steganography is achieved with the cost estimation process. The cost estimation process lacks the intelligent schemes for identifying the suitable pixels for the embedding process. This problem can be avoided by the introduction of the prediction-based models for identifying the suitable pixels. 3. PROPOSED PIXEL PREDICTION-BASED IMAGE STEGANOGRAPHY SCHEME This section presents the proposed pixel prediction scheme for hiding the sensitive patient’s information in the medical image. Figure 1 presents the architecture of the proposed pixel prediction based image steganography model. FIGURE 1. Open in new tabDownload slide Proposed pixel prediction based image steganography scheme. FIGURE 1. Open in new tabDownload slide Proposed pixel prediction based image steganography scheme. The proposed pixel prediction-based image steganography technique hides the sensitive information in the image through three subsequent steps, namely identification phase, embedding phase and extraction phase. In the identification phase, the SVNN classifier is involved to identify the suitable pixels in the input medical image for embedding the secret information. Various features, such as wavelet energy, pixel coverage, edge information, scattering value, Gabor feature value and texture features, are extracted from each pixel of the input image and provided to the SVNN classifier training. The SVNN classifier output is collected to form the prediction map, and it contains the information about the suitable pixels for embedding. In the embedding phase, the prediction map is embedded with the secret image (patient’s information) with the use of DWT and the embedding strength. Finally, the secret information available in the embedded image is identified by finding the difference in wavelet coefficients of the embedded and the input image. 3.1. Identification phase Consider the medical image |$M$| of the size |$A\times D$| is subjected to the steganography process, and the secret information of the patient indicated as |$S$| has the size of |$B\times G$|⁠. The medical image used for the steganography process is an RGB image, and hence, the pixel values of the image vary from 0 to 255. The secret image to be embedded in the input image is represented in the binary form. The mathematical expression of the input image and the secret image is indicated as follows, $$\begin{equation} M=\{{m}_{ij}\};\kern0.6em 1\le i\le A;\kern0.6em 1\le j\le D \end{equation}$$$$$$$$$$$$$$$$$$(1) $$\begin{equation} S=\{{s}_{pq}\};\kern0.6em 1\le p\le B;\kern0.6em 1\le q\le G \end{equation}$$$$$$$$$$$$$$$$$$(2) where |${m}_{ij}$|indicates the pixel in the input image, and it varies between 0 and 255, and the term |${s}_{pq}$|indicates the pixel in the secret image, and it has the binary value 0 or 1. 3.1.1. Feature extraction For identifying the suitable pixels for embedding, the SVNN classifier is utilized in this work, and for the training purpose, features are extracted from the input medical image. For each pixel in the medical image |$M$|⁠, six features, such as wavelet energy |$({F}_1)$|⁠, pixel coverage |$({F}_2)$|⁠, edge information |$({F}_3)$|⁠, scattering value |$({F}_4)$|⁠, Gabor feature |$({F}_5)$| and local binary pattern (LBP) |$({F}_6)$| are extracted. The features extracted from the pixel |${m}_{ij}$| of the input image is formed as the feature vector represented as, $$\begin{equation} \left\lfloor{F}_1,\dots, {F}_f,\dots, {F}_6\right\rfloor=F({m}_{ij}) \end{equation}$$$$$$$$$$$$$$$$$$(3) where |$F(.)$| refers to the feature extraction function, and the feature vector estimated for the pixel |${m}_{ij}$| of the input image has the size of |$[1\times 6]$|⁠. The description to the various features extracted from each pixel of the input image is described below: (i) Wavelet energy: the wavelet energy of the input image |$M$| is obtained by applying the DWT [28]. Applying the DWT to the input image yields four bands, represented as |$\{{N}_1,{N}_2,{N}_3,{N}_4\}$|⁠. Here, |${N}_1$|⁠, |${N}_2$|⁠, |${N}_3$| and |${N}_4$| refer to the LL, LH, HL and HH bands of the wavelet transform. The wavelet bands obtained through the DWT has different energy, and thus, wavelet energy of each pixel in the input image |$M$| depends on the energy of the bands. The wavelet energy feature for the pixel |${m}_{ij}$| is represented as $$\begin{equation} \left\{{N}_1,{N}_2,{N}_3,{N}_4\right\}=W({m}_{ij}) \end{equation}$$$$$$$$$$$$$$$$$$(4) where |$W({m}_{ij})$| indicates the DWT function. The embedding process done in the proposed work concentrates on the |$HL$| band, and hence, the energy consumed by the |$HL$| band is considered as wavelet energy feature, and it is represented as |${F}_1={N}_3({m}_{ij})$|⁠. (ii) Pixel coverage: the pixel coverage provides information about the coverage value of each pixel, and thus, it can be calculated as the mean value of the surrounding neighbor pixel. Consider the pixel |${m}_{ij}$| in the image |$M$| has |$L$| number of neighbor pixels, and thus, the pixel coverage of |${m}_{ij}$| is indicated as $$\begin{equation} {F}_2=\frac{1}{L}\sum \limits_{k=0}^{L-1}{m}_{ij}^k \end{equation}$$$$$$$$$$$$$$$$$$(5) where |${m}_{ij}^k$| refers to the |${k}^{th}$| neighbor pixel of |${m}_{ij}$| and |$L$| indicates the neighborhood. (iii) Edge information: the edge information identifies whether the pixel is an edge/corner pixel or not. This edge information feature gets the value as 1 if the pixel is an edge pixel; otherwise, it takes the value as 0. The edge information for the pixel |${m}_{ij}$| is indicated as $$\begin{equation} u\left(i,j\right)=H({m}_{ij}) \end{equation}$$$$$$$$$$$$$$$$$$(6) where |$H({m}_{ij})$| indicates the edge information of the pixel |${m}_{ij}$|⁠, and it corresponds to the third feature indicated as |${F}_3=u(i,j)$|⁠. It is necessary to identify the edge pixels since the embedding process in the corner pixels may affect the steganography process and leads to information loss during the retrieval phase. (iv) Scattering value: the scattering coefficients from the medical image can be obtained by applying the scattering transform [27]. The scattering transform finds the texture information available in the pixel, and it is obtained through the convolution of the averaging filter with the pixel. This yields the scattering coefficients of the pixels represented as $$\begin{equation} J[M]=|||||M\otimes{\eta}_{v1}|\otimes{\eta}_{v2}|\dots |\otimes{\eta}_{vu}|\otimes H(u)| \end{equation}$$$$$$$$$$$$$$$$$$(7) where |$H(u)$| indicates the average filter, and the term |${\eta}_{v1}$| indicates the filter banks. The features extracted from the scattering transform of the pixel |${m}_{ij}$| are represented as |${F}_4=J({m}_{ij})$|⁠. (v) Gabor feature: the Gabor feature can be obtained by applying the Gabor filter [30] to the pixels of the input medical image. The Gabor feature identifies the time-frequency location of the pixels and provides robustness against the different brightness and contrast of the image. Commonly used Gabor filter for the feature extraction is the 2D Gabor filter, and its filter function is expressed as $$\begin{align} Q\left(i,j,\theta, w,\sigma \right)=&\,\frac{1}{2{\pi \sigma}^2}\exp \left(-\frac{i^2+{j}^2}{2{\sigma}^2}\right)\nonumber\\&\times\, ^\ast \exp \left\{2\pi{i}_m\left( wi\cos \theta + wj\sin \theta \right)\right\} \end{align}$$$$$$$$$$$$$$$$$$(8) where |$Q(i,j,\theta, w,\sigma )$| indicates the Gabor filter function for the pixel |${m}_{ij}$| and |${i}_m$| is the imaginary part and thus, has the value as |$\sqrt{-1}$|⁠. The term |$w$| in Equation (8) indicates the frequency of the sinusoidal wave used in the Gaussian filter. The Gabor filter is applied over the pixel |${m}_{ij}$|⁠; |$Q({m}_{ij})$| yields the fifth feature |${F}_5$| of the vector element, and it is represented as |$O\{i,j\}=Q({m}_{ij})$|⁠. Thus, |${F}_5=O\{i,j\}$|⁠. (vi) Textures from LBP: the LBP [29] features from the image can be obtained by applying the LBP operator over the pixels, and the resulted features contribute to the sixth feature, i.e. |${F}_6=X(i,j)$|⁠. Here, |$X(i,j)$| indicates the texture features obtained through the extraction of the LBP operator, and it is expressed as $$\begin{equation} X\left(i,j\right)= LBP({m}_{ij})=\sum \limits_{k=0}^{L-1}l({o}_k-{o}_y){2}^L \end{equation}$$$$$$$$$$$$$$$$$$(9) where |${o}_k$| and |${o}_y$| indicate the gray value of the neighbor and the centre pixels, respectively, and the function |$l(v)$| has a value of 1 or 0 based on the following condition, $$\begin{equation} l(v)=\left\{\!\!\!\begin{array}{l{@}}1;\kern0.48em v\ge 0\\{}0;\kern0.48em else\end{array}\right\} \end{equation}$$$$$$$$$$$$$$$$$$(10) 3.1.2. Pixel identification: constructing the prediction map with the SVNN classifier The working principle of SVNN is same that of the working principle of SVM. Unlike to SV machines, SVNN does not suffer from any problems related to quadratic programming, and unlike to conventional neural networks, the SVNN’s cost function is always convex. Finding the suitable pixels for embedding is done by constructing the prediction map with the SVNN classifier. The SVNN classifier [25] gets the features as the training input and constructs the prediction map for the input image|$M$|⁠. Figure 2 presents the block diagram of the SVNN classifier for the construction of the prediction map. FIGURE 2. Open in new tabDownload slide Construction of the pixel prediction map based on SVNN classifier. FIGURE 2. Open in new tabDownload slide Construction of the pixel prediction map based on SVNN classifier. The SVNN classifier has six input neurons, and one hidden and output neuron for constructing the binary map, and the expression for the output layer of SVNN for constructing the binary map is defined as follows: $$\begin{equation} {Z}_i={T}_1\,^\ast \log \mathrm{sig}\left[\left(\sum \limits_{f=1}^6{F}_f\,^\ast\, {T}_2{\beta}_{\mathrm{max}}\right)+{a}_1\right]+{a}_2 \end{equation}$$$$$$$$$$$$$$$$$$(11) where |${F}_f$| indicates the |$f\mathrm{th}$|feature provided as the input, |${T}_2$| and |${T}_1$| indicate the weight vector in the hidden and the input layer of the SVNN and the terms |${a}_1$| and |${a}_2$| indicate the necessary biases for the output classification. The weight vectors at the input layer of SVNN has six weights corresponding to each feature, and it is represented as |${T}_1$|⁠, and the value of |$f$| varies from 1 to 6. 3.1.2.1. Fitness for the prediction map construction The SVNN utilizes the minimization function as the fitness, and it concentrates on choosing the weight values for calculating SVNN output with minimum deviation from the ground value. Here, the constrained optimization problem is replaced by the equivalent unconstrained optimization problem, which has the discontinuous objective function |$K$|⁠, which overcomes the problems in the gradient-based optimization techniques; hence, a GA is applied using |$K$| as the fitness function. The expression for the fitness function of the SVNN classifier to construct the suitable prediction map is given as, $$\begin{equation} K={\beta}_{\mathrm{max}}+{\beta}_{\mathrm{min}}+\frac{C}{A}\sum \limits_{i=1}^A\left|{Z}_i-{Z}_i\,^\ast\right| \end{equation}$$$$$$$$$$$$$$$$$$(12) where |${Z}_i\ast$| and |$C$| indicate the ground truth information and the regularization factor, and the terms |${\beta}_{\mathrm{max}}$| and |${\beta}_{\mathrm{min}}$| depend on the eigenvalue of the weight vectors |${T}_1$| and |${T}_2$|⁠, and it can be expressed as $$\begin{equation} {\beta}_{\mathrm{max}}=\max \left(\beta \right) \end{equation}$$$$$$$$$$$$$$$$$$(13) $$\begin{equation} {\beta}_{\mathrm{min}}=\min \left(\beta \right) \end{equation}$$$$$$$$$$$$$$$$$$(14) where the value of |$\beta$| can be expressed as $$\begin{equation} \beta =\mathrm{Eigen}(T\,^\ast\, {T}^T) \end{equation}$$$$$$$$$$$$$$$$$$(15) where |${T}^T$| indicates the transpose of the weight vector |$T$|⁠, and the weight vector has the weight elements in both the input and the hidden layer of SVNN. 3.1.3. Training phase Here, the SVNN classifier is trained with the GA, to obtain the prediction map. For each pixel in the medical image, a total of six features are extracted and hence to declare whether the pixel is suitable for embedding. The training procedure for the SVNN is necessary to find the optimal weights and biases for the prediction map construction. GA is one of the nature-inspired algorithms, which find the optimal solution based on the operations of genes. The genes undergo various functions, such as selection, crossover and mutation, to refine their population. GA uses the crossover property of the genes for updating the solution, and the procedure involved in finding the optimal solutions is described below. FIGURE 3. Open in new tabDownload slide Embedding the secret information in the input image. FIGURE 3. Open in new tabDownload slide Embedding the secret information in the input image. Step 1: Initializing random solutions: the weights and biases involved in the SVNN classifier need to be optimally found to define the characteristics of pixels in the prediction map. Thus, initially, the weights and bias involved in the SVNN classifier are randomly generated for the optimization, and it can be represented as $$\begin{equation} U(t)=\left\{{U}_s(t);\kern0.48em 1\le s\le e\right\} \end{equation}$$$$$$$$$$$$$$$$$$(16) where |${U}_s(t)$| indicates the |$s\mathrm{th}$| chromosome in the GA, and since there are seven weight elements and two bias are involved in the SVNN classifier, the size of the solution vector is |$e=9$|⁠. Step 2: Fitness evaluation: then, the fitness of each randomly generated solution is analyzed. Since the fitness is a minimization function, a solution with low fitness value is considered to be the better solution. Step 3: Solution update based on a crossover operator: GA uses the crossover operator to generate a new set of solutions. The crossover operator requires two random chromosomes for the solution generation, and it can be represented as |${U}_c$| and |${U}_d$|⁠. The required solution update based on the crossover operator of GA is specified below: $$\begin{equation} {U}_s^{\mathrm{crossover}}\left(t+1\right)=\eta{U}_c(t)+\left(\eta -1\right){U}_d(t) \end{equation}$$$$$$$$$$$$$$$$$$(17) where |${U}_c(t)$| and |${U}_d(t)$| indicate the |$c\mathrm{th}$| and |$d\mathrm{th}$| chromosomes selected for the solution update, and the value of |$\eta$| varies in the interval [0,1]. The chromosomes suitable for the crossover function are selected based on the following expressions: $$\begin{equation} c=\mathrm{round}\left[\left(e-1\right)\frac{\exp^{gh_1}-1}{\exp^g-1}+1\right] \end{equation}$$$$$$$$$$$$$$$$$$(18) $$\begin{equation} d=\mathrm{round}\left[\left(e-1\right)\frac{\exp^{gh_2}-1}{\exp^g-1}+1\right] \end{equation}$$$$$$$$$$$$$$$$$$(19) where |${h}_1$| and |${h}_2$| are two random numbers selected for the crossover operation, and |$g$|indicates the selective pressure. Step 4: Fitness evaluation of updated solution: here, the fitness of each solution based on Step 3 is evaluated based on the fitness function expressed in Equation (12). Finally, the solution with the lowest fitness value is termed as the best solution, and it replaces the current solution. Step 5: Termination: the training process gets terminated at the end of the iteration |$I$|⁠, and finally the optimal solution is obtained. 3.1.4. Testing phase In the testing phase, for the medical test image|${M}^{\mathrm{test}}$|⁠, a predicted map is created by the SVNN classifier based on its feature. The predicted map from the SVNN classifier has two states 0 and 1 and has the same size as the input image, and the expression for the predicted map is given as follows: $$\begin{equation} P=\{{b}_{ij}\}=\left\{\begin{array}{@{}l@{}}1;\kern0.72em \mathrm{Pixel}\kern0.17em \mathrm{suitable}\kern0.17em \mathrm{for}\kern0.17em \mathrm{prediction}\\{}0;\kern0.72em \mathrm{Pixel}\kern0.17em \mathrm{not}\kern0.17em \mathrm{suitable}\kern0.17em \mathrm{for}\kern0.17em \mathrm{prediction}\end{array}\right\} \end{equation}$$$$$$$$$$$$$$$$$$(20) where |${b}_{ij}$| indicates the pixels in the prediction map, and it has the value 1 if the pixel is suitable for the prediction, or else it has the value as 0. 3.2. Embedding phase In the embedding phase, the secret message is embedded into the input image, and the predicted map constructed through the SVNN classifier acts as a key in the embedding process. Figure 3 presents the block diagram of the embedding phase of the proposed pixel-based prediction scheme. The initial step in the embedding process is the application of the DWT to the input image |$M$|⁠. The DWT is more advantageous to other techniques, such as Fourier transform since it identifies the frequency and location information in the image. The DWT transform to the input image produces the four bands, and it is expressed as $$\begin{equation} \left[{N}_1,{N}_2,{N}_3,{N}_4\right]=W\left[M\right] \end{equation}$$$$$$$$$$$$$$$$$$(21) Here, each band specifies the frequency and energy of the wavelet coefficient. The wavelet bands obtained through the application of the DWT has different properties. This work carries out the embedding of the secret message in the HL band,|${N}_3$|⁠. The secret message |$S$| is embedded in |${N}_3$| with the use of the embedding strength and the predicted map from the SVNN classifier. The predicted map |$P$| from the SVNN classifier identifies the suitable pixels for embedding, and the embedding strength defines the intensity of the embedding process. The expression for embedding the secret message in the |${N}_3$| band of the input image is given as $$\begin{equation} {N}_3\,^\ast ={N}_3+S\,^\ast \gamma \, ^\ast P \end{equation}$$$$$$$$$$$$$$$$$$(22) where |${N}_3\, ^\ast$| indicates the band with the secret message embedded, and the term |$\gamma$| refers to the embedding strength of the embedding process. Now, the bands from the DWT after embedding of the secret message into the |${N}_3$| band is modified as |$[{N}_1,{N}_2,{N}_3\, ^\ast, {N}_4]$|⁠. After embedding the secret message into the |${N}_3$| band, the inverse DWT (IDWT) is applied to the bands. The IDWT to the modified band yields the required embedded input image |$M\,^\ast$| and it is represented as $$\begin{equation} M\,^\ast = IW\left[{N}_1,{N}_2,{N}_3 \,{^\ast}, {N}_4\right] \end{equation}$$$$$$$$$$$$$$$$$$(23) Algorithm 1. Pseudo code of the proposed pixel prediction scheme based image steganography. Open in new tab Algorithm 1. Pseudo code of the proposed pixel prediction scheme based image steganography. Open in new tab 3.3. Extraction phase Finally, in the extraction phase, the secret message from the embedded image is extracted by applying the DWT to the embedded image |$M\,^\ast$|⁠. The embedded image |$M\,^\ast$| has four wavelet bands along with the secret message in the third band. The secret message from the embedded information can be obtained by applying DWT to the embedded image, and the process is expressed in the following expression: $$\begin{equation} \left[{N}_1^{Er},{N}_2^{Er},{N}_3^{Er\ast },{N}_4^{Er}\right]=W\left[M\,^\ast \right] \end{equation}$$$$$$$$$$$$$$$$$$(24) where |${N}_1^{Er}$|⁠, |${N}_2^{Er}$| and|${N}_4^{Er}$| indicate the LL, LH and HH bands of the DWT process, and |${N}_2^{Er\ast }$| represents the HL band of the IDWT process from the embedded image during the extraction phase. The secret message can be retrieved from the embedded image by finding the difference band obtained by DWT of |$M$| and DWT of |$M\,^\ast$|⁠. The secret message obtained after the extraction is expressed as $$\begin{equation} {Y}^{Er}={N}_3^{Er\ast }-{N}_3 \end{equation}$$$$$$$$$$$$$$$$$$(25) The secret message obtained from the above expression has a larger size than the actual size of the secret message. Hence, to create the actual secret message, decimal conversion is needed, and it is done by applying a threshold |$\omega$|⁠. The secret message is extracted from |${Y}^{Er}$| based on the following condition: $$\begin{equation} {S}_{pq}^{Er}=\left\{\!\!\!\begin{array}{l{@}}1\kern0.48em ;{Y}^{Er}>\omega \\{}0\kern0.48em ; else\end{array}\right\} \end{equation}$$$$$$$$$$$$$$$$$$(26) where |${S}_{pq}^{Er}$| indicates the pixel in the binary format for the extracted secret message. The secret message from the extraction phase is indicated as |${S}^{Er}=\{{S}_{pq}^{Er}\}$|⁠, and it has the same size as the secret message provided for steganography process. Algorithm 1 shows the algorithmic description of the proposed pixel prediction scheme based image steganography. The input medical image considered for the analysis is a brain tumor image from the BRATS database. Initially, in the identification phase, various features are extracted from each pixel of the input image and the feature vector is generated. Then, the feature vector is provided as the input to the SVNN classifier and the prediction map is constructed. In this work, the SVNN classifier is trained with the GA for constructing the prediction map. In the embedding phase, the secret message is embedded into the input image. Here, the DWT transform is applied to the input image, which produces the four bands. Then, the secret message is embedded the HL band |${N}_3$|⁠. Finally, in the extraction phase, the secret message is extracted from the medical image without the information loss and distortion. FIGURE 4. Open in new tabDownload slide Experimental results of the proposed pixel prediction based image steganography scheme, (a) input medical image, (b) secret message, (c) embedded image without noise, (d) extracted secret message without noise, (e) embedded image with impulse noise, (f) extracted secret message with impulse noise, (g) embedded image with salt and pepper noise and (h) extracted secret message with salt and pepper noise. FIGURE 4. Open in new tabDownload slide Experimental results of the proposed pixel prediction based image steganography scheme, (a) input medical image, (b) secret message, (c) embedded image without noise, (d) extracted secret message without noise, (e) embedded image with impulse noise, (f) extracted secret message with impulse noise, (g) embedded image with salt and pepper noise and (h) extracted secret message with salt and pepper noise. 4. RESULTS AND DISCUSSION This section presents the results of the proposed pixel prediction scheme with the SVNN classifier. The experimental results achieved by the proposed scheme for various noises and without noise are depicted here. 4.1. Experimental setup The experimentation of the proposed pixel prediction based image steganography scheme is simulated in the MATLAB tool. The simulation environment for the proposed image steganography scheme requires PC with Windows 10 OS, Intel I3 processor and 4 GB RAM. Parameters: Embedding strength |$\gamma$| = 0.001. 4.1.1. Database description This work performs the image steganography in the medical images, and the required medical images for the experimentation are accessed from the BRATS database [26]. The BRATS database provides a set of brain tumor images of four modalities. Here, images are accessed from one modality. The BRATS database contains the collection of over 300 high and low-grade glioma images. 4.1.2. Evaluation metrics The experimentation of the proposed pixel-prediction based image steganography is analyzed with the metrics, such as peak signal to noise ratio (PSNR), Structural Similarity Index (SSIM) and the correlation factor. The expression for the evaluation metrics is defined below. PSNR: The image considered for the analysis may be corrupted due to noise, and hence, it is necessary to measure how effective the noise is in the image, and it can be expressed through PSNR measure. The expression for the PSNR is given as follows: $$\begin{equation} \mathrm{PSNR}=10{\log}_{10}\left(\frac{{m_{\mathrm{max}}}^2}{\mathrm{MSE}}\right) \end{equation}$$$$$$$$$$$$$$$$$$(27) where |${m}_{\mathrm{max}}$| indicates the maximum value of the pixel in the image |$M$|⁠, and |$MSE$| refers to the mean square error. SSIM: the SSIM indicates the similarity measure between the embedded and the original image, and it is measured by considering two windows |${\rho}_1$| and |${\rho}_2$| of the same size, and the expression for the SSIM is measured as follows: $$\begin{equation} \mathrm{SSIM}\left({\rho}_1,{\rho}_2\right)=\frac{\left(2{\mu}_{\rho_1}{\mu}_{\rho_2}+{\tau}_1\right)\left(2{\sigma}_{\rho_1{\rho}_2}+{\tau}_2\right)}{\left({\mu_{\rho_1}}^2+{\mu_{\rho_2}}^2+{\tau}_1\right)\left({\sigma_{\rho_1}}^2+{\sigma_{\rho_2}}^2+{\tau}_2\right)} \end{equation}$$$$$$$$$$$$$$$$$$(28) where |${\mu}_{\rho_1}$| and |${\mu}_{\rho_2}$| indicate the mean value of pixels in the windows |${\rho}_1$| and |${\rho}_2$|⁠, the terms |${\sigma}_{\rho_1}$| and |${\sigma}_{\rho_2}$| indicate the variance of pixels, |${\tau}_1$| and |${\tau}_2$| are used for stabilizing the division done by the denominator. Correlation factor: the correlation coefficient identifies the statistical relation between the samples, and it is measured based on the covariance and the standard deviation. The expression for the correlation factor is expressed as follows: $$\begin{equation} CF\left({\rho}_1,{\rho}_2\right)=\frac{Cov\left({\rho}_1,{\rho}_2\right)}{\sigma_{\rho_1}{\sigma}_{\rho_2}} \end{equation}$$$$$$$$$$$$$$$$$$(29) where |$Cov({\rho}_1,{\rho}_2)$| is the covariance. 4.1.3. Comparative methods The simulation results of the proposed scheme are compared with other existing techniques, such as CICC and M-MRSLS [5], Tomas Denemark and Jessica Fridrich [4], random order-based embedding [31], sequential order-based embedding [32], Cost Function Using Wavelet and Edge Transformation for Medical Image Steganography (CWSM) [9] and optimal order embedding [24], and the comparative models are described below. Random order-based embedding: the random order embedding strategy finds the random pixels in the input image for embedding the secret image. Sequential order-based embedding: in the sequential order embedding, the secret message is embedded in the input image in the sequential order. CWSM: in this work, embedding of the secret message into the input medical image is done by developing a cost function with the parameters, such as the wavelet coefficient, edge transformation and pixel intensity. FIGURE 5. Open in new tabDownload slide Comparative analysis of the models for an image without noise based on (a) PSNR, (b) SSIM and (c) correlation factor. FIGURE 5. Open in new tabDownload slide Comparative analysis of the models for an image without noise based on (a) PSNR, (b) SSIM and (c) correlation factor. Optimal order embedding: here, the embedding of the secret message into the input image is done through the optimal order, and clustering modification directions were used for the embedding process. 4.2. Experimental results The experimental results achieved by the proposed pixel prediction scheme with the SVNN classifier are presented in Fig. 4. The experimental results are obtained for the various scenarios, such as input image affected by impulse noise, affected by salt and pepper noise and image not affected by noise. The input medical and the secret message utilized for the experimentation are shown in Fig. 4a and b. The embedded and the secret message provided the pixel prediction scheme without the noise is given in Fig. 4c and d. For the medical image affected by the impulse noise, the output of the proposed pixel prediction model is given in Fig. 4e and f. The output of the proposed model when the image is affected by the salt and pepper noise is indicated in Fig. 4g and h. 4.3. Comparative performance This section presents the comparative performance of the proposed pixel prediction with the SVNN and DWT coefficients. The performance of the proposed scheme is measured against the existing works, such as CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich, random order embedding, sequential order embedding, optimal order and CWSM techniques. 4.3.1. Analysis using the image without noise Figure 5 presents the comparative results of the models while the image is not affected by noise. PSNR analysis, as shown in Fig. 5a, shows that the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich, random order, sequential order, optimal order and the CWSM techniques achieved PSNR values of 53.1353, 58.4873, 44.57364, 44.5755, 44.57593 and 69.40557 dB, respectively, but the proposed SVNN + DWT model achieved high PSNR value of 89.3059 dB while embedding the fourth image. Analyzing the comparative techniques based on SSIM metric for the fourth image shown that CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich, random order, sequential order and optimal order, and the CWSM techniques have low SSIM value of 0.7249, 0.7799, 0.45, 0.45, 0.999401 and 0.999997, respectively. The proposed SVNN + DWT scheme achieved high SSIM value of 1 while embedding the secret image in the fourth image. Figure 5c presents the performance of the comparative models based on the correlation factor, and the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich and random order model have Correlation factor of 0.9854, 0.9989, 0.994537, while all the other models have a high value of 1. 4.3.2. Analysis using image affected by impulse noise Figure 6 presents the comparative analysis of the models when the image is affected by the impulse noise, and varying impulse noise density does the analysis. Figure 6a presents the analysis based on PSNR for image affected by the impulse noise. For the impulse noise density |$IN$| = 0.25, the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich random order, sequential order, optimal order and CWSM techniques have achieved PSNR value of 30.0804, 34.7181, 7.317708, 40.39218, 40.42452 and 40.4394 dB, respectively, while the proposed SVNN + DWT model has a high PSNR value of 45.01653 dB. Figure 6b presents the analysis based on SSIM for image affected by the impulse noise. For the impulse noise density |$IN$| = 0.25, the existing CICC and M-MRSLS as well as Tomas Denemark and Jessica Fridrich have the SSIM values of 0.4638 and 0.4665, respectively. For the same noise density, the existing random order, sequential order, optimal order and the CWSM techniques have achieved SSIM value of 0.45, respectively, while the proposed SVNN + DWT model has high SSIM value of 0.532619. Figure 6c presents the analysis based on the correlation factor for image affected by the impulse noise. For the impulse noise density |$IN$| = 0.25, the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich, random order, sequential order, optimal order and the CWSM techniques have achieved correlation factor value of 0.5485, 0.6512, 0.45, 0.45, 0.45 and 0.917918, while the proposed SVNN + DWT model has a high correlation factor value of 0.987912. 4.3.3. Analysis using image affected by salt and pepper noise Figure 7 presents the comparative analysis of the models when the image is affected by the salt and pepper noise, and the analysis is done by varying salt and pepper noise density, denoted as |$SPN$|⁠. Figure 7a presents the analysis based on PSNR for image affected by the salt and pepper noise. For the salt and pepper noise density |$SPN$| = 0.25, the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich, random order, sequential order, optimal order and the CWSM techniques have achieved PSNR values of 31.6204, 37.1644, 5.974798, 43.94171, 43.9467 and 43.94907 dB, respectively, while the proposed SVNN + DWT model has high PSNR value of 48.00955 dB. Figure 7b presents the analysis based on SSIM for image affected by the salt and pepper noise. For the salt and pepper noise density |$SPN$| = 0.25, the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich have attained the SSIM values of 0.4556 and 0.4575. For the same noise density, the existing random order, sequential order, optimal order and the CWSM techniques have achieved SSIM value of 0.45, respectively, while the proposed SVNN + DWT model has high SSIM value of 0.487294. Figure 7c presents the analysis based on the correlation factor for image affected by the salt and pepper noise. For the salt and pepper noise density |$SPN$| = 0.25, the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich, random order, sequential order, optimal order and the CWSM techniques have achieved correlation factor value of 0.5448, 0.6512, 0.45, 0.45, 0.45 and 0.917918. However, the proposed SVNN + DWT model has high correlation factor value of 0.987912. FIGURE 6. Open in new tabDownload slide Comparative analysis of the models for an image with impulse noise based on (a) PSNR, (b) SSIM and (c) correlation factor. FIGURE 6. Open in new tabDownload slide Comparative analysis of the models for an image with impulse noise based on (a) PSNR, (b) SSIM and (c) correlation factor. FIGURE 7. Open in new tabDownload slide Comparative analysis of the models for an image with salt and pepper noise based on (a) PSNR, (b) SSIM and (c) correlation factor. FIGURE 7. Open in new tabDownload slide Comparative analysis of the models for an image with salt and pepper noise based on (a) PSNR, (b) SSIM and (c) correlation factor. FIGURE 8. Open in new tabDownload slide Comparative analysis of the models for an image with Gaussian noise based on (a) PSNR, (b) SSIM and (c) correlation factor. FIGURE 8. Open in new tabDownload slide Comparative analysis of the models for an image with Gaussian noise based on (a) PSNR, (b) SSIM and (c) correlation factor. 4.3.4. Analysis using image affected by Gaussian noise Figure 8 presents the comparative analysis of the models when the image is affected by the Gaussian noise, and the analysis is done by varying the variance obtained between two images. Figure 8a presents the analysis based on PSNR for image affected by the Gaussian noise. For the variance = 0.1, the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich, random order, sequential order, optimal order and the CWSM techniques have achieved PSNR value of 31.5769, 37.1183, 6.75478, 43.40857, 43.42703 and 43.44265 dB, respectively, while the proposed SVNN + DWT model has high PSNR value of 48.55848 dB. Figure 8b presents the analysis based on SSIM for image affected by the Gaussian noise. For the variance = 0.1, the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich have attained the SSIM values of 0.458 and 0.46. For the same noise density, the existing random order, sequential order, optimal order and the CWSM techniques have achieved SSIM value of 0.45, respectively, while the proposed SVNN + DWT model has high SSIM value of 0.500098. Figure 8c presents the analysis based on the correlation factor for the image affected by the Gaussian noise. For the variance = 0.1, the existing CICC and M-MRSLS, Tomas Denemark and Jessica Fridrich, random order, sequential order, optimal order and the CWSM techniques have achieved correlation factor value of 0.5394, 0.6487, 0.45, 0.45, 0.45 and 0.917918. Meanwhile, the proposed SVNN + DWT model has high correlation factor value of 0.975433. 4.4. Discussion Table 2 presents the comparative discussion of the proposed prediction scheme with the SVNN classifier and DWT for the image affected by the noise factors. Here, the best performance of the comparative models is discussed, and from the analysis, it is evident that the proposed prediction scheme has the overall best performance. When the image is affected by the noise factors, the proposed prediction scheme has achieved high performance with the values of 48.558 dB, 0.50009 and 0.9879 for the PSNR, SSIM and correlation factor, respectively. TABLE 2. Comparative discussion. Comparative models . Evaluation metrics . PSNR (dB) . SSIM . Correlation factor . CICC and M-MRSLS 33.0686 0.4769 0.7814 Tomas Denemark and Jessica Fridrich 38.9008 0.4824 0.8744 Random order 6.754 0.45 0.45 Sequential order 43.408 0.45 0.45 Optimal order 43.427 0.45 0.45 CWSM 43.442 0.45 0.9179 Proposed SVNN + wavelet 48.558 0.50009 0.9879 Comparative models . Evaluation metrics . PSNR (dB) . SSIM . Correlation factor . CICC and M-MRSLS 33.0686 0.4769 0.7814 Tomas Denemark and Jessica Fridrich 38.9008 0.4824 0.8744 Random order 6.754 0.45 0.45 Sequential order 43.408 0.45 0.45 Optimal order 43.427 0.45 0.45 CWSM 43.442 0.45 0.9179 Proposed SVNN + wavelet 48.558 0.50009 0.9879 Open in new tab TABLE 2. Comparative discussion. Comparative models . Evaluation metrics . PSNR (dB) . SSIM . Correlation factor . CICC and M-MRSLS 33.0686 0.4769 0.7814 Tomas Denemark and Jessica Fridrich 38.9008 0.4824 0.8744 Random order 6.754 0.45 0.45 Sequential order 43.408 0.45 0.45 Optimal order 43.427 0.45 0.45 CWSM 43.442 0.45 0.9179 Proposed SVNN + wavelet 48.558 0.50009 0.9879 Comparative models . Evaluation metrics . PSNR (dB) . SSIM . Correlation factor . CICC and M-MRSLS 33.0686 0.4769 0.7814 Tomas Denemark and Jessica Fridrich 38.9008 0.4824 0.8744 Random order 6.754 0.45 0.45 Sequential order 43.408 0.45 0.45 Optimal order 43.427 0.45 0.45 CWSM 43.442 0.45 0.9179 Proposed SVNN + wavelet 48.558 0.50009 0.9879 Open in new tab FIGURE 9. Open in new tabDownload slide Illustration of ROC curve FIGURE 9. Open in new tabDownload slide Illustration of ROC curve 4.5. Steganalysis Steganalysis attempts to conquer the objective of steganography. It aims to expose the presence of the hidden message and to separate the stego content from the cover image. Here, the security of the proposed steganography approach and the existing steganographic approaches, such as random order, sequential order, optimal order and proposed SVNN + wavelet is evaluated by the steganalysis method introduced in [33]. Figure 9 shows the illustration of the ROC curve, in which the proposed method has high performance than the existing methods. For instance, at the false positive rate of 0.7, the detection rate of the proposed SVNN + wavelet, random order, sequential order, optimal order and CWSM is 0.7513, 0.6557, 0.5591, 0.5152 and 0.4623, respectively. From the figure, it can be shown that the detection rate of the proposed method is minimum than the detection rate of the existing methods. Hence, we conclude that the proposed method is more secure than the comparative methods. 5. CONCLUSION This work presents a novel pixel prediction based image steganography scheme by employing the SVNN and DWT techniques. The proposed scheme uses the medical image for hiding the sensitive information of the patients. Initially, the pixels suitable for embedding the secret message is identified by training the SVNN classifier with the features extracted from the medical image. The SVNN constructs the prediction map for the input image, and by applying the DWT coefficients, the secret message is embedded into the input image. 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TI - Pixel Prediction-Based Image Steganography by Support Vector Neural Network
JF - The Computer Journal
DO - 10.1093/comjnl/bxaa017
DA - 2020-04-13
UR - https://www.deepdyve.com/lp/oxford-university-press/pixel-prediction-based-image-steganography-by-support-vector-neural-A0JHTqxrrB
SP - 1
EP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -