Thesis Study
Original Title: Reversible Data Hiding of JPEG Image Based on Adaptive Frequency Band Length
Published Journal: TCSVT 2023 (Area 1, Chinese Academy of Sciences)
Authors: Ningxiong Mao, Hongjie He, Fan Chen, Yuan Yuan, Lingfeng Qu
Summary
JPEG images are widely used on the Internet. Reversible data hiding methods for JPEG images based on histogram translation of quantified discrete cosine transform (DCT) coefficients are a research focus. Among them, frequency band selection is a key step that affects the performance of JPEG-RDH. In the existing algorithm, frequency band selection is to evaluate the embedding performance of the entire frequency band, but after DCT block sorting, the distribution of extended AC coefficients is in the front of the frequency band, so the performance evaluation of the entire frequency band will produce errors. This paper proposes an adaptive frequency band length IPEG image RDH method, which determines the use length of the frequency band while selecting the frequency band, so that the invalid translation can be effectively reduced. The entire length of the selected frequency band will not be used anymore, but the used length of each frequency band may be different. Then, a joint solution mechanism is used to solve the optimal frequency band length, and the frequency band selection is also completed while solving the frequency band length. Experimental results show that our algorithm outperforms existing state-of-the-art methods in terms of labeled image visual quality and file size increment.
I. Overview
There are two main research points in the RDH method of JPEG image based on DCT coefficient modification: (i) block selection; (ii) frequency band selection. How to establish an accurate frequency-band distortion cost function is a research focus. In the existing work, all blocks are used to evaluate the performance of a frequency band, but since the distribution of coefficients in the frequency band is different, the estimation of the distortion cost of the entire frequency band will produce errors. Generally AC coefficients 1 and -1 are at the front of the band after the blocks are sorted in descending order by the number of zero AC coefficients. Aiming at the above problems, this paper proposes a JPEG-RDH scheme with adaptive frequency band length. We are not evaluating the embedding performance on the whole frequency band, but only use some DCT blocks in each frequency band and the number of DCT blocks used in each frequency band may be different. Then we adopt an adaptive solution mechanism to determine the usage length of the frequency band at the same time in the process of frequency band selection. The method of adaptive frequency band length can improve the embedding rate and reduce invalid translation, thereby effectively reducing distortion and reducing file growth. Experimental analysis shows that the proposed scheme is superior to other existing advanced algorithms. The main contributions of our scheme are as follows.
- Adaptively select the length of the frequency band. This article does not evaluate the embedding performance of the entire frequency band, but selects the length of the frequency band according to the embedding performance of different frequency band lengths. The optimal length of the used frequency band is chosen so as to reduce invalid translation as much as possible.
- Joint solution mechanism. During the solution process, the frequency band selection and the determination of the frequency band length are carried out simultaneously. The priority of frequency band usage is also determined in the process of solving the frequency band length.
2. Adaptive frequency band length model
Frequency band selection is an important research object in the existing algorithms, but in the existing algorithms, the performance evaluation is performed on all blocks or some blocks of the same length in the frequency band to determine the embedding performance of the frequency band. However, after the blocks are sorted in descending order by the number of zero coefficients, the distribution of non-zero AC coefficients is generally such that the expansion coefficient E is at the front, and most of the translation coefficients S are at the rear. Therefore, when the embedding capacity is satisfied, the coefficients at the front of the frequency band should be used as much as possible. Therefore, it is also necessary to select the length of the frequency band while selecting the frequency band, and the unit capacity distortion corresponding to different lengths of the frequency band is different. In Fig. 2 we give an illustration of adaptively determining the band length. In this paper, the length of the frequency band is selected in the process of selecting the frequency band at the same time.
In the existing work, it can be concluded that the main factors affecting the performance of frequency band embedding are the distortion cost of the frequency band in the spatial domain and the frequency band's embedding rate. The distortion cost of the frequency band is determined by the quantization table Q, but Q cannot be changed. The embedding rate is related to the length of the frequency band, and choosing the optimal frequency band length is to select the optimal embedding rate. For the same frequency band, the higher the proportion of the expansion coefficient E is, the higher the embedding rate is. The embedding rate refers to the ratio of the expansion coefficient E to the non-zero coefficient in the frequency band, and the formula is as follows.
The figure below shows the ER of four images at different frequency band lengths with QF=70 and size 512×512. In the figure, the embedding rate of the first 1,000, 2,000, 3,000, and 4,000 blocks in the frequency band after block sorting is tested respectively. It can be observed that the shorter the frequency band length is, the higher the embedding rate is. If the secret data embedding can be completed by using the first 1000 blocks, no larger frequency band length is used for data embedding. Because the longer the frequency band is used, the higher the proportion of the translation coefficient will be, and the greater the distortion will be. How to determine the optimal length of the selected frequency band is the next problem to be solved.
The usage length of each band is sequentially updated according to the unit capacity distortion of the band length. Each update is a solution, and the capacity greater than or equal to the given load is a feasible solution. In the update process, we also have a constraint condition, the current update frequency band length must be greater than the previous update frequency band length, otherwise the skip this update frequency band length remains unchanged.
3. Embedding/extraction process
It mainly introduces the process details of secret data embedding, auxiliary information processing, data extraction and restoration of marked JPEG images.
Embedding process
1) Decode the original JPEG image to obtain the quantized DCT coefficient matrix and quantization table Q.
2) Sort all DCT blocks according to the number of zero AC coefficients in the DCT block, and perform zig-zag scan expansion on the blocks to generate a coefficient matrix.
3) By Equation (11) we can calculate the unit capacity distortion UT of each length of the frequency band, and then sort the frequency band lengths according to the order of the unit capacity distortion. According to Algorithm 1, we can get a set of feasible solutions and find the optimal solution D.
4) After obtaining the optimal frequency band length D, we can refer to the histogram translation method in the paper [23] for data embedding and DCT coefficient modification.
5) Encoding the modified DCT coefficients to obtain a marked JPEG image.
Auxiliary information
After the data embedding is completed, some auxiliary information needs to be saved in order to ensure reversibility. The auxiliary information includes: the length of the payload (log_2P), the frequency band selection bitmap (63 bits), the frequency band division step size K (7 bits), and the length bitmap of the selected frequency band. Assuming that the number of selected frequency bands is V, the size of the bitmap required to record the length of the selected frequency band is V*log_2(N/K). Then, these auxiliary information are embedded into the header of the tagged JPEG image.
Extraction and recovery process
After getting the marked JPEG image, first decode the JPEG image to obtain the quantized DCT coefficient matrix, quantization table Q and auxiliary information. After obtaining auxiliary information, we can extract secret data and restore DCT coefficients according to the secret data extraction rules in the paper [23].
Encode the restored DCT coefficients to restore the image to the original JPEG image without distortion.
4. Experimental results
Compared schemes include Huang et al. [23], Hou et al. [24], Wedaj et al. [25], He et al. [28], Yin et al. [29]. This article mainly compares two data sets, the six classic images in the USC-SIPI (http://sipi.usc.edu/database/) database are Lena, Baboon, Peppers, Barbara, Boat and Elaine.
The other is the BOSSbase v1.01 (http://agents.fel.cvut.cz/boss) dataset, from which we randomly select 200 images for testing. By comparing the experimental results, it is verified that the overall performance of this scheme is superior to other advanced algorithms.
Parameter Determination
We can see that the number of frequency band division lengths is determined by the division step size K. The value of K will affect the division length of the frequency band and the size of the solution space. Table 1 shows the performance of Lena and Peppers images under different embedding capacities when the segmentation step size K takes different values. In Table 1, we can observe that when K=100, all images can get the best PSNR value except lena under 10,000bits capacity. The average value of the Lena and Peppers images at the three capacity points all get the optimal PSNR value when K=100, so the frequency band segmentation step size in this paper is K=100.
The figure below shows the optimal solution D with image size 512x512 of the frequency band length obtained under the load of 5000bits, 10,000bits and 15000bits of the Lena image. In Fig. 4, we can see the difference between the algorithm in this paper and the traditional existing method. The existing method uses a fixed frequency band length, which is generally the entire frequency band. The length of each frequency band selected by the algorithm in this paper may be different, and the length of the frequency band can be determined adaptively according to the embedding performance of the frequency band.
The figure below shows the average SSIM of 200 test images on the BOSSbase dataset. The average SSIM values of the scheme in this paper under the four quantization factors are 0.9985, 0.9990, 0.9994 and 0.9997 respectively. We can see that the SSIM values are all greater than 0.99 and close to 1, indicating that the original JPEG image and the marked JPEG image are very similar. The average SSIM value of this scheme is also better than other advanced schemes. The above PSNR and SSIM experimental results all prove that our scheme has better image visual quality than other advanced schemes.
in conclusion
A JPEG reversible data hiding algorithm with adaptive frequency band length is proposed. In the traditional frequency band selection, the embedding performance of the entire frequency band is evaluated, but after the DCT block sorting, the extended AC coefficients are distributed in the front of the frequency band, so the performance evaluation of the entire frequency band will produce errors. We will adaptively select the length of the frequency band according to the distribution of extended AC coefficients in the frequency band, and reduce the number of translational AC coefficients as much as possible. The selection optimization model of the frequency band length is established, and the optimal solution of the frequency band length is determined through a joint solution mechanism. Using the joint solution mechanism we are able to select the frequency bands while solving for the band lengths.