Efficient feature learning and multi-size image steganalysis based on CNN

07/30/2018 ∙ by Ru Zhang, et al. ∙ Shanghai Jiao Tong University NetEase, Inc 0

For steganalysis, many studies showed that convolutional neural network has better performances than the two-part structure of traditional machine learning methods. However, there are still two problems to be resolved: cutting down signal to noise ratio of the steganalysis feature map and steganalyzing images of arbitrary size. Some algorithms required fixed size images as the input and had low accuracy due to the underutilization of the noise residuals obtained by various types of filters. In this paper, we focus on designing an improved network structure based on CNN to resolve the above problems. First, we use 3x3 kernels instead of the traditional 5x5 kernels and optimize convolution kernels in the preprocessing layer. The smaller convolution kernels are used to reduce the number of parameters and model the features in a small local region. Next, we use separable convolutions to utilize channel correlation of the residuals, compress the image content and increase the signal-to-noise ratio (between the stego signal and the image signal). Then, we use spatial pyramid pooling (SPP) to aggregate the local features, enhance the representation ability of features, and steganalyze arbitrary size image. Finally, data augmentation is adopted to further improve network performance. The experimental results show that the proposed CNN structure is significantly better than other four methods such as SRM, Ye-Net, Xu-Net, and Yedroudj-Net, when it is used to detect two spatial algorithms such as WOW and S-UNIWARAD with a wide variety of datasets and payloads.

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I Introduction

For a long time, steganography and steganalysis always developed in the struggle with each other. Steganography seeks to hide secret information into a specific cover as much as possible and makes the changes of cover as little as possible, so that the stego is close to the cover in terms of visual quality and statistical characteristics[1,2,3]. Meanwhile, steganalysis uses signal processing and machine learning theory, to analyze the statistical differences between stego and cover. It improves detecting accuracy by increasing the number of features and enhancing the classifier performance[4].

Currently, the existing steganalysis methods include specific steganalysis algorithms and universal steganalysis algorithms. Early steganalysis methods aimed at the detection of specific steganography algorithms[5], and the general-purpose steganalysis algorithms usually use statistical features and machine learning[6]. The commonly used statistical features include the binary similarity measure feature[7], DCT[8,9] and wavelet coefficient feature[10], co-occurrence matrix feature[11] and so on. In recent years, higher-order statistical features based on the correlation between neighboring pixels have become the mainstream in the steganalysis. These features improve the detection performance by capturing complex statistical characteristics associated with image steganography, such as SPAM[12], Rich Models[13], and its several variants[14,15]. However, those advanced methods are based on rich models that include tens of thousands of features. Dealing with such high-dimensional features will inevitably lead to increasing the training time, overfitting and other issues. Besides, the success of feature-based steganalyzer to detect the subtle changes of stego largely depends on the feature construction. The feature construction requires a great deal of human intervention and expertise.

Benefiting from the development of deep learning, convolutional neural networks (CNN) perform well in various steganalysis detectors[16,17,18,19]. CNN can automatically extract complex statistical dependencies from images and improve the detection accuracy. Considering the GPU memory limitation, existing steganography analyzers are typically trained on relatively small images (usually

). But the real-world images are of arbitrary size. This leads to a problem that how an arbitrary sized image can be steganalyzed by the CNN-based detector with a fixed size input. In traditional computer vision tasks, the size of the input image is usually adjusted directly to the required size. However, this would not be a good practice for steganalysis as the relation between pixels are very weak and independent. Resizing before classification would compromise the detector accuracy.

In this paper, we have proposed a new CNN network structure named “Zhu-Net” to improve the accuracy of spatial domain steganalysis. The proposed CNN performs well in both the detection accuracy and compatibility, and shows some distinctive characteristics compared with other CNNs, which are summarized as follows:

(1) In the preprocessing layer, we modify the size of the convolution kernel and use 30 basic filters of SRM[13] to initialize the kernels in the preprocessing layer to reduce the number of parameters and optimize local features. Then, the convolution kernel is optimized by training to achieve better accuracy and to accelerate the convergence of the network.

(2) We use two separable convolution blocks to replace the traditional convolution layer. Separable convolution can be used to extract spatial correlation and channel correlation of residuals, to increase the signal to noise ratio, and obviously improve the accuracy.

(3) We use spatial pyramid pooling[20] to deal with arbitrary sized images in the proposed network. Spatial pyramid pooling can map feature maps to fixed lengths and extract features through multi-level pooling.

We design experiments to compare the proposed CNN network with Xu-Net[17], Ye-Net[19], and Yedroudj-Net[21]. The proposed CNN shows excellent detection accuracy, which even exceeds the most advanced manual feature set, such as SRM[13].

The rest of the paper is organized as follows. In Section II, we present a brief review of the framework of popular image steganalysis methods based on convolutional neural networks (CNNs) in the spatial domain. The proposed CNN is described in Section III, which is followed by experimental results and analysis in Section IV. Finally, the concluding remarks are drawn in Section V.

Ii Related Works

The usual ways to improve CNN structure for steganalysis include: using truncated linear units, modifying topology by mimicking the Rich Models extraction process, and using deeper networks such as ResNet[22], DenseNet[23], and others.

Tan et.al used a CNN network with four convolution layers for image steganalysis[24]. Their experiments showed that a CNN with random initialized weights usually cannot converge and initializing the first layer’s weights with the KV kernel can improve accuracy. Qian et al.[25] proposed a steganalysis model using standard CNN architecture with Gaussian activation function, and further proved that transfer learning is beneficial for a CNN model to detect a steganography algorithm with low payloads. The performance of these schemes is comparable to or better than the SPAM scheme[12], but is still worse than the SRM scheme[13]. Xu et al.[17] proposed a CNN structure with some techniques used for image classification, such as batch normalization (BN)[26], 1×1 convolution, and global average pooling. They also did pre-processing with a high-pass filter and used an absolute (ABS) activation layer. Their experiments showed better performance. By improving the Xu-CNN, they achieved a more stable performance[27]. In JPEG domain, Xu et al.[18] proposed a network based on decompressed image and achieved better detection accuracy than traditional methods in JPEG domain. By simulating the traditional steganalysis scheme of hand-crafted features, Fridrich et al.[28] proposed a CNN structure with histogram layers, which is formed by a set of Gaussian activation functions. Ye et al.[19] proposed a CNN structure with a group of high-pass filters for pre-processing and adopted a set of hybrid activation functions to better capture the embedding signals. With the help of selection channel knowledge and data augmentation, their model obtained significant performance improvements than the classical SRM. Fridrich[29] proposed a different network architecture to deal with steganalyzed images of arbitrary size by manual feature extraction. Their scheme inputs statistical elements of feature maps to the fully-connected-network classifier.

Generally, there are two disadvantages for the existing networks.

(1) A CNN is composed of two parts: the convolution layer and the fully connected layer (ignoring the pooling layer, etc.). The function of convolution layer is to convolve input and to output the corresponding feature map. The input of the convolution layer does not need a fixed size image, but its output feature maps can be of any size. The fully connected layer requires a fixed-size input. Hence, the fully connected layer leads to the fixed size constraint for network. The two existing solutions are as follows.

  • Resizing the input image directly to the desired size. However, the relationship between the image pixels is fragile and independent in the steganalysis task. Detecting the presence of steganographic embedding changes really means detecting a very weak noise signal added to the cover image. Therefore, resizing the image size directly before inputting image to CNN will greatly affect the detection performance of the network.

  • Using a full convolutional neural network(FCN), because the convolutional layer does not require a fixed image size.

In this paper, we propose the third solution: mapping the feature map to a fixed size before sending it to the fully-connected layer, such as SPP-Net[20]. The proposed network can map feature maps to a fixed length by using spp-module, so as to steganalyze arbitrary size images.

(2) Accuracy of steganalysis based on CNN seriously relies on signal-to-noise ratio of feature maps. CNN network favorites high signal-to-noise ration to detect small differences between stego signals and cover signals. Many steganalyzers usually extract the residuals of images to increase the signal-to-noise ratio. However, some existing schemes directly convolve the extracted residuals without thinking of the cross-channel correlations of residuals, which do not make good use of the residuals.

In this paper, we increase signal-to-noise ratio by three ways as follows.

  • Optimizing the convolution kernels by reducing kernel size and the proposed “forward-backward-gradient descent” method.

  • Using group convolution to process the spatial correlation and channel correlation of residuals separately.

We greatly improve the accuracy of steganalysis by combining the above two ways.

Iii Proposed Scheme

Fig. 1: The architecture of the proposed CNN. For each block, denotes the block with the kernel size for input feature maps and output feature maps. Batch normalization is abbreviated as BN.

Iii-a Architecture

The framework of the proposed CNN based steganalysis is shown in Fig. 1. The CNN accepts an input image of size and outputs a two class labels (stego and cover). The proposed CNN is composed of a number of layers including one image preprocessing layer, two separable convolution (sepconv) block, four basic blocks for feature extraction, a spatial pyramid pooling(SPP) module, and two fully connected layers followed by a softmax.

The convolutional blocks have four blocks marked as ‘Basic Block 1’ through ‘Basic Block 4’ to extract spatial correlation between feature maps and finally transport to the fully connected layer for classification. Each Basic Block is made of the following steps:

Iii-A1 Convolution Layer

Unlike the existing networks that use large convolution kernel(e.g. ), we use small convolution kernels(e.g. ) to reduce the number of parameters. The small convolution kernels can increase the nonlinearity of the network, which significantly increase the capability of feature representation. Therefore, we set the size of the convolutional kernels to

for the Basic Block 1-4. For Basic Block 1 to Basic Block 4, there are 32, 32, 64, 128 channels. The number of channels in each Basic Block is also based on a comprehensive consideration of computational complexity and network performance. Stride and padding size are shown in the Fig. 1.

Iii-A2 Batch Normalization (BN) layer

The Batch normalization(BN)[26] is usually used to normalize the distribution of each mini-batch to a zero-mean and a unit-variance during the training. The advantage of using a BN layer is that it effectively prevents the gradient vanishing/exploding and over-fitting in the deep neural network[26], and allows a relatively large learning rate to speed up the convergence. From the experiments, we found that the networks without BN, such as Ye-Net, are very sensitive to the initialization of parameters and may not converge with inappropriate initializations. Therefore, we use BN in the proposed scheme.

Iii-A3 Non-linear activation function

For all the blocks in Zhu-Net, we use the classical rectifying linear unit (ReLU) as the activation function to prevent gradient vanishing/exploding, produce sparse features, accelerate network convergence and so on. Applying ReLU to neurons can make them selectively respond to useful signals among the inputs, resulting in more efficient features. The ReLU function is also convenient for derivation and benefits back-propagation gradient calculations. We do not use the truncated linear unit (TLU) in our network, because we find that the TLU decreases the non-linearity. To verify that, we compare TLU (threshold

) with ReLU. From the Table I, Zhu-Net with ReLU has lower error rate of detecting various steganography algorithms. ReLU also accelerates the convergence and shows better performance than TLU, as shown in Fig.2.

Algorithms
Zhu-Net with
TLU
Zhu-Net with
ReLU
WOW(0.2bpp) 0.257 0.233
WOW(0.4bpp) 0.138 0.118
S-UNIWARD(0.2bpp) 0.316 0.285
S-UNIWARD(0.4bpp) 0.188 0.153
TABLE I: Steganalysis error rates comparison of Zhu-Net with TLU and Zhu-Net with ReLU against two algorithms WOW and S-UNIWARD at 0.2 bpp and 0.4 bpp. Both networks are trained and tested on BOSS dataset.
Fig. 2: Comparing convergence performances of training Zhu-Net with TLU and Zhu-Net with ReLU against two algorithms WOW and S-UNIWARD at 0.2 bpp and 0.4 bpp. Both networks are trained and tested on BOSS dataset.

Iii-A4 Average pooling layer

Average pooling layers are used in Basic Block 1 to Basic Block 3. It down-samples feature maps, better abstracts the image features, reduces the size of feature map and enlarges the receptive fields. With invariance, the average pooling also enhances the generalization ability of the network.

Note that we design separable convolution blocks to enhance SNR (signal noise ratio of stego signal to image) and remove the image content effectively from features. In the last block, we use a SPP module to better extract features. The SPP module enriches feature expressions by multi-level pooling, such that our network can train and test with multi-size images. Details are elaborated in Section III-D.

Iii-B Improving Kernels

The embedding operation of steganography can be viewed as adding a smaller amplitude noise signal to the cover signal. Therefore, it is a good idea to perform residual calculation prior to feature extraction in network. In the preprocessing layer, we use a set of high-pass filter (for example, 30 basic high-pass filters of SRM[12], that is, the “spam” filters and their rotated counterparts, Similar to Ye-Net [19] and Yedroudj-Net[21]) to extract noise residuals map from input image. In [24], the authors showed that without such preliminary high-pass filter, CNN convergence rate should be very slow. Hence, using multiple filters can effectively improve network performance.

We use the following strategy to initialize the weights of the preprocessing layer.

Iii-B1 Small sized kernels

Small sized convolution kernels can reduce the number of parameters and prevent modeling larger regions, to effectively reduce calculations. As some existing schemes showed, the kernel size of is suitable for some filters in SRM, such as “SQUARE ”, “EDGE ”. But for the remaining 25 filters, the convolution kernel will model residual elements in a big local region. So we keep “SQUARE ” and “EDGE ”, and use size for the remaining 25 high-pass filters. We initialize the central part of convolution kernels with the SRM kernels and pad the remaining elements to zero, as shown in Fig. 3. Two parts of the residuals calculated by these filters are stacked together as the input of the next convolutional layer.

Fig. 3: An example of initializing convolution kernels wiht different sized high-pass filters. (a) SQUARE high-pass filter. (b) The convolution kernel corresponding to (a). (c) EDGE high-pass filter. (d) The convolution kernel corresponding to (c).

Iii-B2 Optimizing kernels

Modeling residuals instead of pixel values can extract more robust features. In Yedroudj-Net and Xu-net, convolution kernels in the preprocessing layer are fixed during the training. To optimize the SRM hand-crafted feature set designed with domain knowledge, we design a method named “forward-backward-gradient descent”, and use it in preprocessing layer. We calculate the residual as follows:

For each image , the residual is:

(1)

where is the residual order, is the neighboring pixels of and is a predictor of defined on . In practice, we usually use high-pass filters to achieve .

The complete process of optimizing the kernel is given as follows:

The forward-backward-gradient descent Method

Forward propagation:

Input: An image , the high-pass filter

Output: The noise residuals map

Step 1: Initialization: The convolution kernel of the preprocessing layer is initialized by a high-pass filter in the SRM, and the weights of the convolution kernel are described by .

Step 2: Calculate residuals:

(2)

where denotes the convolution operator, and are the corresponding index of the kernel .

Back propagation:

Input: The gradient of the previous layer , the high-pass filter .

Output: The gradient of the preprocessing layer

1: Let the backward gradient of the previous layer be . Then the gradient of the preprocessing layer is:

(3)

2: Return the gradient of the preprocessing layer .

Gradient descent:

Input: The gradient of the preprocessing layer , the high-pass filter , the learning rate .

Output: The optimized kernels

1: Optimize the weight of the preprocessing layer by:

(4)

2: Return the optimized kernels .

The corresponding experiment results are shown in Fig. 4 and Table II. We compared the Zhu-Net with fixed kernels, and the network Zhu-Net with optimizable kernels.

Algorithms
Zhu-Net with
fixed kernels
Zhu-Net with
optimized kernels
WOW(0.2bpp) 0.243 0.233
WOW(0.4bpp) 0.130 0.118
S-UNIWARD(0.2bpp) 0.324 0.285
S-UNIWARD(0.4bpp) 0.169 0.153
TABLE II: Steganalysis error rates comparison between Zhu-Net with fixed kernels and Zhu-Net with optimized kernels against two steganography algorithms WOW and S-UNIWARD at 0.2 bpp and 0.4 bpp. Both networks are trained and tested on BOSS dataset.
Fig. 4: Comparing convergence performances of training Zhu-Net with fixed kernels and Zhu-Net with optimized kernels against two algorithms WOW and S-UNIWARD at 0.2 bpp and 0.4 bpp. Both networks are trained and tested on BOSS dataset.

From Table II, it is observed that using the “forward-backward-optimize” method, Zhu-Net achieves higher accuracy than the network with fixed kernels for detecting various steganography algorithms. According to Fig. 4, our network is more quickly converged and has less training loss than the network with fixed kernels.

Iii-C Separable Convolution

Iii-C1 Problem Formulation

Existing steganalysis schemes directly learn filters in a 3D space without thinking of cross-channel correlations of the residuals, so that the residual information is not well utilized. To resolve this problem, we used two separable convolution blocks (i.e. the sepconv blocks) consisting of a convolution and a convolution after preprocessing the layer (as shown in Fig. 1).

Separable convolution has recently made great progress in computer vision tasks, such as Inception[30], Xception[31] and other structures. Xception, a variant of an Inception module is shown in Fig. 5(a). This extreme version of inception completely separates the correlation between channels, reducing storage space and enhancing the expressiveness of the model. Therefore, we use Xception structure to design the corresponding sepconv block to achieve the group convolution of residuals.

Fig. 5: (a) A variant version of Inception module[31]; (b) structure of sepconv blocks

In our scheme, we assume that the channel correlation and spatial correlation of residuals are independent. The sepconv block can perform group convolution for each feature map generated by a high-pass filter, which makes full use of the residual information and removes image contents from features to improve the signal-to-noise ratio. The design of the sepconv blocks is shown in Fig. 5(b).

First, pointwise convolution is performed in a sepconv block to extract residual channel correlations. Then depthwise convolution is performed to extract spatial correlations, where the number of groups is 30 and a sepconv block includes pointwise convolution and

depthwise convolution. Note that there is no activation function in these two convolutions. After the 1×1 convolutional layer of sepconv block1, considering domain knowledge, we insert an Absolute Activation (ABS) layer to make our network learning the symbol symmetry of the residual noise. We also use residual connections in the two sepconv blocks, for accelerating network convergence, preventing gradient vanishing/exploding and improving classification performance.

Iii-C2 Experimental Verification and Analysis

In order to compare Zhu-Net with Yedroudj-Net, we visualize the feature map in the first convolutional layer (the feature map of the CNN is difficult to interpret and visualize when the layer is deeper). The feature map is a good description of the feature extraction process.

Both Yedroudj-Net and Zhu-Net are trained using WOW, at the payload of 0.2 bpp. We visualize the feature map of the first convolutional layer for Yedroudj-Net and the feature map of the sepconv block 2 for our network. The comparisons of the feature maps of stego and cover are shown in the Fig. 6.

Fig. 6: The comparison of feature maps between Zhu-Net and Yedroudj-Net. (a) Cover image. (b) Stego image. (c) The feature map of cover generated by Zhu-Net. (d) The feature map of cover generated by Yedroudj-Net. (e) The feature map of stego generated by Zhu-Net. (f) The feature map of stego generated by Yedroudj-Net.

It is observed that the feature maps generated by the proposed scheme remain less image content information, and keep an increasing signal-to-noise ratio between stego signal and image signal. For either a cover or a stego, the proposed scheme can extract features with strong expression ability. Meanwhile, the similarity between every feature maps is relatively low, so that sepconv blocks facilitates subsequent convolution and classification. Comparative speaking, the feature maps generated by Yedroudj-Net remain more image contents, and the differences among feature maps are not obvious.

Algorithms Yedroudj-Net Zhu-Net
WOW(0.2bpp) 0.278 0.233
WOW(0.4bpp) 0.141 0.118
S-UNIWARD(0.2bpp) 0.367 0.285
S-UNIWARD(0.4bpp) 0.228 0.153
TABLE III: Steganalysis error rates comparison between Yedroudj-Net and Zhu-Net against two steganography algorithms WOW and S-UNIWARD at 0.2 bpp and 0.4 bpp. Both networks are trained and tested on BOSS dataset.

In addition, we compare the detection error rate of Zhu-Net and Yedroudj-Net. Table III shows the performance of these two CNN networks against two steganography schemes such as S-UNIWARD and WOW. Experiment results show that, Zhu-Net obviously achieves better performance compared with Yedroudj-Net, reducing the detection error rate by 2.3%-8.2%.

Table IV shows the performance of detection error rate of Zhu-Net and Zhu-Net with full sepconv block against the algorithm WOW. The experiment results show that the detection accuracy goes down when all basic blocks are replaced by sepconv blocks. But the accuracy of Zhu-Net with all sepconv block is still better than Yedroudj-Net at a low embedding rate (e.g., 0.2 bpp). How to embed more sepcov blocks in CNN requires follow-up studies. Now, we choose the network with two sepconv block in our implementation so as to achieve a good detection performance.

Algorithms
Zhu-Net with
full sepconv blocks
Zhu-Net with
two sepconv blocks
WOW(0.2bpp) 0.249 0.233
WOW(0.4bpp) 0.152 0.118
TABLE IV: Steganalysis error rates comparison using Zhu-Net with different numbers of sepconv blocks against WOW at 0.2 bpp and 0.4 bpp. Both networks are trained and tested on BOSS dataset.

Iii-D Spatial pyramid pooling module

Fig. 7: A network structure with a spatial pyramid pooling layer

For some steganalysis networks[18,21], a global average pooling (GAP) layer is added after the last convolution layer for down-sampling, which can greatly reduce the feature dimension. For image classification, GAP is generally used to replace full connected layer to prevent overfitting and reduce computational complexity. This global averaging operation equals to modeling the entire feature map, which leads to information loss of local features. However, for steganalysis networks, modeling local information is of key importance.

In our network, we use spatial pyramid pooling (SPP) to model local feature map, as shown in Fig. 7. SPP has the following properties[20]:

(1) SPP outputs a fixed-length feature for any size input.

(2) SPP uses multi-level pooling to effectively detect object deformation.

(3) Since input is of arbitrary size, SPP can perform feature aggregation for any scale or size images.

Similar to [20], we divide the feature maps into several bins. In each spatial bin, we pool the responses of each feature map (we use average pooling hereinafter). The output of the spatial pyramid pool is a fixed

dimensional vector, where

is the number of bins and is the number of filters in the final convolution layer. The major steps of the SPP-module mapping feature maps to fixed length vector are listed as follows:

The steps of SPP-module mapping feature maps to fixed length vector

Input: The feature maps after basic block 4 with a size of and channels of . an -level pyramid with bins in each level.

Output: The fixed length feature with a size of , where is the number of bins.

Step 1: For a pyramid level of bins, implement this pooling level as a sliding window pooling, where the window size win = , and stride str = with and denoting ceiling and floor operations.

Step 2: Implement windows pooling on every feature map, obtain the generated feature with the length of .

Step 3: Repeat step1-step2 for every pyramid level in an -lever pyramid.

Step 4:

Stack all generated feature vectors together (in Pytorch we use torch.cat function). Pre-compute the length of each feature map by

, and the total length of feature is .

Step 5: Resize the output feature to a size of .

We use a 3-level pyramid pool (, , ), which means that the number of bins is 21( + + ). For a given size image, we pre-calculate the size of the output fixed-length vector. Assume that after the basic block 4 there is (for example, ) size feature maps. When the pooling level is , we divide the feature map into 16 small blocks, that is, the size of each small block is . Then a GAP is performed on each block to obtain a 16-dimensional feature vector. In the pytorch toolbox, we can use average pooling (strinde:8, kernel:8) to achieve such sliding window pooling operations. The pooling level of and are similar. Finally, we can get a ( dimensional vector, where is the number of filters in the last convolutional layer.

Interestingly, the level pooling actually equal to the global average pooling layer used in many steganalysis networks. This shows that we have gathered the information from feature maps at different levels, which not only integrates features of different scales but also better models the local features.

In order to verify the effectiveness of the SPP module in feature extraction, we compare Zhu-Net (with SPP-module) with Ye-Net and Yedroudj-Net (with GAP-module). All the networks are trained against WOW and S-UNIWARD, at the payload of 0.2 bpp. The experiment results are shown in Table V. Considering GPU computing power and time limitation, we construct a training set with two predefined sizes: and . We resampled all the images to images and images. In order to compare with the existing networks, the size of testing images is still .

Algorithms
WOW
(0.2bpp)
S-UNIWARD
(0.2bpp)
Ye-Net
0.331 0.400
Yedroudj-Net
0.278 0.248
Zhu-Net wiht 256-size Tested
0.234 0.281
Zhu-Net with multi-size Tested
0.241 0.289
TABLE V:

Steganalysis error probability comparison of Zhu-Net with different training schemes and Yedroudj-Net against the two algorithms WOW and S-UNIWARD at 0.2bpp. Both networks are trained and tested on BOSS dataset.

The experiment results have shown that Zhu-Net has a higher accuracy than Yedroudj-Net and Ye-Net. That is, compared with the single-size training, the multi-size training can slightly improve the accuracy. We believe that the multi-size training relieves overfitting to a certain extent, and the multi-size dataset enhances the generalization ability of the network.

Besides, we create a random-sized test set whose image sizes range from [224, 256]. The error rate of Zhu-Net against WOW and S-UNIWARD at 0.2 bpp is 0.241 and 0.289.

The experiment results show that the detection with SPP-module is better than the detection with GAP, and the former network has better feature expression ability. Another advantage of using SPP-module is that it can handle inputs with arbitrary sizes.

Iv Experiments

Iv-a The environments

In our experiments, we use two well-known content-adaptive staganographic methods, i.e. S-UNIWARD [3], and WOW [2], by Matlab implementations with random embedding key.

Our proposed CNN network is compared with four popular networks: Xu-Net[17], Ye-Net[19], Yedroudj-Net[21], and SRM + EC standing for the hand-crafted feature set named Spatial-Rich-Model [13] and Ensemble Classifier[32]. All the five networks are tested on the same datasets. All the experiments were run on an Nvidia GTX 1080Ti GPU card.

Iv-B Datasets

In this paper, we use standard datasets to test the performance of the proposed networks. The two standard datasets are as follows:

  • the BOSSBase v1.01[33] consisting of 10,000 grey-level images of size , never compressed, and coming from 7 different cameras.

  • the BOWS2[34] consisting of 10,000 grey-level images of size , never compressed, and whose distribution is close to BOSSBase.

Due to our GPU computing power and time limitation, we do all the experiments on images of pixels. The specific training set and test set division will be detailed in Section IV-D.

Iv-C Hyper-parameters

We apply a mini-batch stochastic gradient descent (SGD) to train the CNN networks. The momentum and the weight decay of networks are set to 0.9 and 0.0005 respectively. Due to GPU memory limitation, the mini-batch size in the training is set to 16 (8 cover/stego pairs). All layers are initialized using Xavier method[35]. Based on the above settings, the networks are then trained to minimize the cross-entropy loss. During the training, we adjust the learning rate as follows (initialized to 0.005).

When the training iteration equals to one of the specified step values, the learning rate will be divided by 5. Concretely, the learning rate will be decreased at epochs 50, 150 and 250 respectively. During later training, using a smaller learning rate can effectively reduce training loss and improve accuracy. CNN training is up to 400 epochs. Actually, we often stop training before 400 epochs to prevent over-fitting. That is, when cross-entropy loss on training set keeps decreasing but detecting accuracy on validation set begins declining, we stop training. We choose the best trained model on validation set.

Iv-D Results

Iv-D1 Results without data augmentation

Algorithms
WOW
(0.2bpp)
WOW
(0.4bpp)
S-UNIWARD
(0.2bpp)
S-UNIWARD
(0.4bpp)
SRM+EC 0.365 0.255 0.366 0.247
Xu-Net 0.324 0.207 0.391 0.272
Ye-Net 0.331 0.232 0.400 0.312
Yedroudj-Net 0.278 0.141 0.367 0.228
Zhu-Net 0.233 0.118 0.285 0.153
TABLE VI: Steganalysis error rates comparison using Yedroudj-Net, Xu-Net, Ye-Net, and SRM+EC against two steganography algorithms WOW and S-UNIWARD at 0.2 bpp and 0.4 bpp. All networks are trained and tested on BOSS dataset.
Fig. 8: Steganalysis error rates comparison of the five steganalysis methods against two algorithms WOW and S-UNIWARD at 0.2 bpp and 0.4 bpp. All networks are trained and tested on BOSS dataset.

In Table VI, we report the performance comparison among steganalyzers without data augmentation. The BOSSBase images were randomly split into a training set with 4,000 cover and stego image pairs, a validation set with 1,000 image pairs, and a testing set containing 5,000 image pairs. For a fair comparison, we report the performance of Yedroudj-Net, Ye-Net, Xu-Net, and the Spatial Rich Model + the Ensemble Classifier (SRM + EC), against the embedding algorithm WOW and S-UNIWARD at payload 0.2 bpp and 0.4 bpp.

As Fig. 8 shows, the proposed network has significantly better performance than the other networks, regardless of the embedding method and payload. Due to the ability of CNN feature extraction, the proposed network has reduced error rate by 8.1% to 13.7%, comparing with the traditional network SRM+EC. Results also show that it is effective to use proposed network to optimize feature extraction and classification in a unified framework.

In addition, for S-UNIWARD and WOW with different payloads, the proposed network is 8.9% to 11.9% better than Xu-Net, 9.8% to 15.9% better than Ye-Net, and 2.3% to 8.2% better than Yedroudj-Net. It demonstrates that the proposed network effectively extracts the correlation of residuals, and has a good network structure including the multi-level pooling of SPP-module to improve the accuracy. Briefly, experiments prove that Zhu-Net outperforms other networks against various steganography schemes at any payloads. Note that above experiments were operated without tricks such as transfer-learning or virtual expansion of databases.

Iv-D2 Result with data augmentation

Algorithms
BOSS
BOSS+BOWS2
BOSS+BOWS2+DA
Ye-Net 0.331 0.261 0.222
Yedroudj-Net 0.278 0.237 0.208
Zhu-Net 0.233 0.178 0.131
TABLE VII: Steganalysis error rates comparison using Yedroudj-Net, Ye-Net and Zhu-Net on WOW at 0.2 bpp with a learning base augmented with BOWS2, and Data Augmentation
Algorithms
BOSS
BOSS+BOWS2
BOSS+BOWS2+DA
Ye-Net 0.400 - 0.335
Yedroudj-Net 0.366 0.344 0.311
Zhu-Net 0.285 0.243 0.171
TABLE VIII: Steganalysis error rates comparison using Yedroudj-Net, Ye-Net and Zhu-Net on S-UNIWARD at 0.2 bpp with a learning base augmented with BOWS2, and Data Augmentation
Algorithms
Payload
(bpp)
Ye-Net[13]
Yedroudj-Net[31]
Zhu-Net
WOW 0.1 0.348 0.330 0.233
0.2 0.262 0.208 0.131
0.3 0.225 0.189 0.084
0.4 0.184 0.158 0.065
S-UNIWARD 0.1 0.400 0.383 0.268
0.2 0.335 0.331 0.171
0.3 0.256 0.221 0.125
0.4 0.226 0.171 0.081
TABLE IX: Steganalysis error rates comparison using Yedroudj-Net, Ye-Net and Zhu-Net on WOW at different payloads with Data Augmentation
Fig. 9: Steganalysis error rates comparison using YedroudjNet, Ye-Net and Zhu-Net on S-UNIWARD and WOW at different payloads. (a)WOW (b) S-UNIWARD

Data augmentation can effectively improve the performance of the network by increasing the size of training database. Using a large database can improve accuracy and avoid overfitting. But, traditional data augmentation solutions such as clipping and resizing are not good choices for steganalysis because these solutions will destroy the correlation of pixels and drastically reduce the performance of network.

In order to study the effect of increasing datasets on the performance, we use the following data enhancement schemes. All photos are resampled into the size of pixels (using ”imresize()” function in Matlab with default settings);

(1) training set BOSS: The BOSSBase images were randomly divided into a training set with 4,000 cover and stego image pairs, a validation set with 1,000 image pairs, and a testing set containing 5,000 image pairs.

(2) training set BOSS+BOWS2: Based on training set BOSS, 10,000 additional pairs of cover/stego pair (obtained by resampling BOWS2Base[36]) were added to the training set. The training database now contains 14,000 pairs of cover/stego images and the validation set contains 1,000 pairs from BOSS.

(3) training set BOSS+BOWS2+DA: The database BOSS+BOWS2+DA is virtually augmented by performing the label-preserving flips and rotations on the BOSS+BOWS2 training set. The size of the BOSS+BOWS2 training set is thus increased by a factor of 8, which gives a final learning database made of 112,000 pairs of cover/stego images. The validation set contains 1,000 pairs from BOSS.

(4) testing set BOSS: it contains the remaining 5,000 images in BOSSbase other than the ones in training set BOSS.

Table VII and Table VIII shows the comparisons of Yedroudj-Net, Ye-Net and Zhu-Net trained on different training sets, against the embedding algorithm WOW and S-UNIWARD at payload 0.2 bpp. The experiment results show that when the training set is incremented, the detection performance for all the network will be improved compared with that using the BOSS training set only. For WOW at 0.2 bpp, using training set BOSS+BOSW2 comparing to using only BOSS training set, Zhu-Net reduced the error rate by 5.5% and achieved best results in all counterparts. The Yedroudj-Net and YeNet error rates are reduced by 4.1% and 7%. Similarly, for S-UNIWARD at 0.2 bpp, the detection error rates of the Ye-Net, Yedroudj-Net, Zhu-Net decreased by 2.2% and 3.6% comparing to only using BOSS training dataset, respectively. Zhu-Net still achieved best performance in all counterparts. The result shows that over-fitting is effectively mitigated by data augmentation.

This prompted us to use larger datasets for training. We further train three networks on BOSS + BOWS2 + DA. The results show that all CNN-based methods have improved performance. Compared those training only using BOSS, Zhu-Net still achieves best performance such as the decreased detection error by 10.2% and 11.4% against WOW and S-UNIWARD (Ye-Net by 10.9% and 6.5%, and Yedroudj-Net by 7% and 5.5%).

In Table IX and Fig. 9, we further illustrate the detection errors of three CNN-based steganalyzer against WOW and S-UNIWARD at different payloads. We note that Zhu-Net achieves significant improvements and best results compared with other CNN-based networks on different datasets against various steganography algorithms. Similarly, we attribute this improvement to the good network structure of Zhu-Net including sepconv block and SPP-module.

All the experiments have shown that in order to effectively perform feature extraction and classification, CNN requires enough samples for training, even 112,000 pairs of pictures may not be enough. How to further increment dataset to meet the requirement of the steganalysis tasks needs further research.

V Conclusion

It is significantly superior for steganalysis researchers to use CNN instead of traditional handcraft features - the ensemble classifier trained on the Rich Model. In this paper, we focus on designing a new CNN structure for steganalysis. The proposed network achieves a great improvement compared with existing CNN-based networks. The advantages of proposed network focus on: (1) We improve convolution kernel in preprocessing layer to extract the image residuals. Better convolution kernels reduce number of parameters and model local features; (2) We use separable convolution to extract channel correlation and spatial correlation of residuals, and thus the image content is removed from the features and the signal-to-noise ratio is improved. Utilization of residual in the preprocessing layer is more effective; (3) We use SPP-module instead of global pooling layer. By using different levels of average pooling to obtain multi-level features, the network performance is improved. Meanwhile, the SPP-module is a flexible solution for handling different sizes. It can map feature maps to a fixed number of dimensions, enabling detecting arbitrary sized images without any loss of accuracy. Finally, the performance of the proposed CNN is further boosted by using larger data sets. Experiment results show that the proposed CNN network is significantly better in the detection accuracy compared with the other networks.

References

  • [1] T. Pevny, T. Filler, and P. Bas, “Using high-dimensional image models to perform highly undetectable steganography,” in Proc. 12th Information Hiding Workshop (IH’2010), 2010, pp. 161–177.
  • [2] V. Holub and J. Fridrich, “Designing steganographic distortion using directional filters,”in Proc. IEEE 2012 International Workshop on Information Forensic and Security (WIFS’2012), 2012, pp. 234–239
  • [3] V. Holub, J. Fridrich, and T. Denemark, “Universal distortion function for steganography in an arbitrary domain,” EURASIP Journal on Information Security, vol. 2014, no. 1, pp. 1–13, 2014.
  • [4] M. Chen, “Reasearch on algorithms and pratices of steganography and Steganalysis”. (Doctoral dissertation, Beijing University of Posts and Telecommunications), 2008.
  • [5] J. Fridrich, M. Goljan and Rui Du, “Detecting LSB steganography in color, and gray-scale images,” in IEEE MultiMedia, vol. 8, no. 4, pp. 22-28, Oct-Dec 2001.
  • [6] J. Kodovsky and J. Fridrich, “Quantitative Structural Steganalysis of Jsteg,” in IEEE Transactions on Information Forensics and Security, vol. 5, no. 4, pp. 681-693, Dec. 2010.
  • [7] I. Avcibas, N. Memon and B. Sankur, “Image steganalysis with binary similarity measures,” in Proceedings. International Conference on Image Processing, 2002, pp. 645-648 vol.3.
  • [8] J. Fridrich, “Feature-Based Steganalysis for JPEG Images and Its Implications for Future Design of Steganographic Schemes,” in Proceedings of the 6th International Workshop, LNCS,3200, pp. 67-81, 2004.
  • [9] T. Pevny and J. Fridrich, “Merging Markov and DCT Features for Multi-class JPEG Steganalysis,” in Electronic Imaging, Security, Steganography, and Watermarking of Multimedia Contents IX, Proceedings of SPIE, 6505, pp. 3-4, 2007.
  • [10] X. Y. Luo, F. L. Liu, S. G. Lian, C. F. Yang and S. Gritzalis, “On the Typical Statistic Features for Image Blind Steganalysis,” in IEEE Journal of Selected Areas in Communications, 29(7), pp.1404-1422, 2011.
  • [11] Y. Wang, J. Liu and W. Zhang, “Blind JPEG Steganalysis Based on Correlations of DCT Cofficients in Multi-directions and Calibrations,” in Multimedia Information Networking and Security, Hubei, 2009, pp. 495-499.
  • [12] T. Pevny, P. Bas, and J. Fridrich, “Steganalysis by subtractive pixel adjacency matrix,” IEEE Trans. Inf. Forensics Security, vol. 5, no. 2, pp. 215–224, 2010.
  • [13] J. Fridrich and J. Kodovsky, “Rich models for steganalysis of digital images,” IEEE Trans. Inf. Forensics Security, vol. 7, no. 3, pp. 868–882, June 2012.
  • [14] V. Holub and J. Fridrich, “Random projections of residuals for digital image steganalysis,” IEEE Trans. Inf. Forensics Security, vol. 8, no. 12, pp. 1996–2006, 2013.
  • [15] T. Denemark, V. Sedighi, V. Holub, R. Cogranne and J. Fridrich, “Selection-channel-aware rich model for Steganalysis of digital images,” in 2014 IEEE International Workshop on Information Forensics and Security (WIFS), Atlanta, GA, 2014, pp. 48-53.
  • [16] Y. Qian, J. Dong, W. Wang and T. Tan, “Feature learning for steganalysis using convolutional neural networks.” Multimedia Tools and Applications, 1-25, 2017(2).
  • [17] G. Xu, H.-Z. Wu, and Y.-Q. Shi, “Structural design of convolutional neural networks for steganalysis,” IEEE Signal Process. Lett., vol. 23, no. 5, pp. 708–712, May 2016.
  • [18] G. Xu, “Deep Convolutional Neural Network to Detect J-UNIWARD,” in Proceedings of the 5th ACM Workshop on Information Hiding and Multimedia Security, Drexel University in Philadelphia, PA, June 2017, IHMMSec’17, pp. 67–73.
  • [19] J. Ye, J. Ni and Y. Yi, “Deep Learning Hierarchical Representations for Image Steganalysis,” in IEEE Transactions on Information Forensics and Security, vol. 12, no. 11, pp. 2545-2557, Nov. 2017.
  • [20] K. He, X. Zhang, S. Ren and J. Sun, “Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition,” in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 37, no. 9, pp. 1904-1916, Sept. 1 2015.
  • [21] M. Yedroudj, F. Comby, and M. Chaumont, “Yedrouj-Net: An efficient CNN for spatial steganalysis,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP’2018. Calgary, Alberta, Canada: IEEE, Apr. 2018.
  • [22] K. He, X. Zhang, S. Ren and J. Sun, “Deep Residual Learning for Image Recognition,” in

    2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

    , Las Vegas, NV, 2016, pp. 770-778.
  • [23] G. Huang, Z. Liu, L. v. d. Maaten and K. Q. Weinberger, “Densely Connected Convolutional Networks,” 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, 2017, pp. 2261-2269.
  • [24] S. Tan and B. Li, “Stacked convolutional auto-encoders for steganalysis of digital images,” in Proceedings of Signal and Information Processing Association Annual Summit and Conference, APSIPA’2014, SiemReap, Cambodia, Dec. 2014, pp. 1–4.
  • [25] Y. Qian, J. Dong, W. Wang, and T. Tan, “Deep learning for steganalysis via convolutional neural networks,” in SPIE Media Watermarking, Security, and Forensics, San Francisco, California, USA, vol. 9409, 2015.
  • [26] S. Ioffe and C. Szegedy, “Batch normalization: accelerating deep network training by reducing internal covariate shift,” in Proceedings of the 32nd International Conference on Machine Learning (ICML), vol. 37, 2015, pp. 448– 456.
  • [27] G. Xu, H.-Z. Wu, and Y. Q. Shi, “Ensemble of CNNs for steganalysis: An empirical study,” in Proc. 4th ACM Workshop Inf. Hiding Multimedia Secur., Jun. 2016, pp. 103–107.
  • [28] V. Sedighi and J. Fridrich, “Histogram layer, moving convolutional neural networks towards feature-based steganalysis,” in Proc. Media Watermarking, Security, and Forensics, Part of IST International Symposium on Electronic Imaging (EI’2017), 2017, pp. 50–55.
  • [29] Tsang C F, Fridrich J. “Steganalyzing Images of Arbitrary Size with CNNs,” Binghamton, 2017
  • [30] C. Szegedy et al., “Going deeper with convolutions,” in 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA, 2015, pp. 1-9.
  • [31] F. Chollet, “Xception: Deep Learning with Depthwise Separable Convolutions,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, 2017, pp. 1800-1807.
  • [32] J. Kodovsky, J. Fridrich, and V. Holub, “Ensemble Classifiers for Steganalysis of Digital Media,” IEEE Transactions on Information Forensics and Security, TIFS, vol. 7, no. 2, pp. 432–444, 2012.
  • [33] P. Bas, T. Filler, and T. Pevný, “Break our steganographic system”: The ins and outs of organizing boss,” in Proc. Int. Workshop Inf. Hiding, 2011, pp. 59–70.
  • [34] P. Bas and T. Furon. (Jul. 2007). Bows-2. [Online]. Available: http://bows2.gipsa-lab.inpg.fr
  • [35] X. Glorot and Y. Bengio, “Understanding the difficulty of training deep feedforward neural networks,” in

    Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, AISTATS’2010

    , Chia Laguna Resort, Sardinia, Italy, May 2010, vol. 9 of Proceedings of Machine Learning Research, pp. 249–256.
  • [36] Simonyan K, Zisserman A. “Very Deep Convolutional Networks for Large-Scale Image Recognition,” Computer Science, 2014.