A digital watermarking algorithm based on the robustness of DWT-DCT transform

1 Introduction

The rapid development of network technology has made the transmission of multimedia data easier. Information hiding and copyright protection have become urgent problems to be solved. Digital watermarking technology is an effective way to protect data. Invisibility and robustness are the two most important characteristics of digital watermarking systems. The watermark is embedded in some important coefficients of the image, and its robustness against attacks is good, but if the important coefficients change too much, the image will be seriously distorted. Therefore, robustness and invisibility are contradictory. Watermarking technology can be divided into spatial domain watermarking technology and transform domain watermarking technology. The spatial domain watermarking algorithm has poor robustness. The transform domain algorithm can disperse the energy of the embedded watermark signal to all pixels in the space, which is conducive to ensuring the invisibility of the watermark and strong robustness. The discrete cosine transform DCT (Discrete Cosine Transformation) algorithm is easy to implement quickly in a digital signal processor. The discrete cosine transform domain image watermark is compatible with the commonly used image compression standard JPEG and has strong robustness against compression, filtering and some other attacks. Discrete Wavelet Transformation (DWT) is a linear operation that decomposes a signal into components of different scales. It is achieved by convolving the signal with a filter of varying scales. Discrete wavelet transform is a multi-resolution analysis method that can characterize local signal features in both the time domain and the frequency domain. Wavelet decomposition decomposes the original image into a series of low-frequency components and high-frequency components. Based on the masking effect of the human sensory system, the digital watermark information can be embedded into the area of ​​the original carrier that is not easily perceived, making the digital watermark highly invisible.

Since wavelet transform has good local time-frequency analysis and multi-resolution analysis characteristics, and discrete cosine transform has good energy-gathering effect, a digital watermarking technology based on joint transform of DWT and DCT is proposed here by combining the advantages of the two transforms.

2 Watermark Embedding Algorithm

The main idea of ​​the watermark embedding algorithm: In order to improve the security of the watermark, chaotic encryption is performed before the watermark is embedded, and then the host image is subjected to DWT to obtain 4 sub-bands: LL, LH, HL, HH, and HL is selected as the embedding sub-band. In order to make the embedded watermark evenly distributed in the HL sub-band, the HL sub-band is divided into blocks and DCT transformed. The watermark is embedded in the intermediate frequency coefficient after DCT transformation. Here, the classic comparative intermediate frequency coefficient method is used for watermark embedding, and the embedding process is shown in Figure 1.

The algorithm steps are as follows:

(1) Perform chaotic scrambling encryption on the original watermark image. Scrambling the watermark image can enhance the security of the watermark algorithm. The watermark image is scrambled by making full use of the characteristics of the chaotic sequence, which is highly sensitive to the initial value, has strong security, and has a large key space. The chaotic sequence is generated by the Logistic mapping, and the sequence is obtained by iterating according to the Logistic mapping formula (1):

Where xn∈(0,1) and μ is the bifurcation parameter.

From the calculation of Lyapunov exponent, we know that when 3.569 9≤μ≤4, the Logistic mapping is in a chaotic state. Studies have shown that the mapping has the strongest chaotic characteristics when and only when μ=4, so μ=4 is taken when generating chaotic sequences. xn is a real-valued sequence, which is not conducive to computer processing. It is usually necessary to quantize the real-valued sequence, and quantize xn to obtain the binary sequence Xn.

Logistic sequence is sensitive to initial value. As long as the number of iterations and initial value are set, many pseudo-random sequences can be obtained. Therefore, the initial value is used as the user's key, and the chaotic sequence Xp is generated using formula (1). There are many methods for encrypting digital watermarks. Here, the watermark image W is represented as a vector form Wp, P = 1, 2, ... MxN. Wp is used as the plaintext space, and the chaotic sequence Xp is used to encrypt the watermark image to obtain the encrypted watermark image Vp:

Here + performs an XOR operation. The decryption process is the same as the encryption process, using the encrypted watermark and chaotic sequence for an XOR operation. Let x0 = 0.800 000 000 1 be the user's key, and Figure 2 is the encrypted watermark image. The chaotic sequence is extremely sensitive to the initial value, and even if the key (initial value) is slightly different, the watermark image cannot be correctly decrypted.

(2) Perform a first-level DCT transform on the host image. Obtain four sub-bands LL, LH, HL, and HH. In order to balance transparency and robustness, HL is selected as the embedded sub-band. Extract the matrix A composed of HL coefficients.

(3) The matrix A composed of HL coefficients is divided into blocks of size 8x8. The purpose of dividing into 8x8 blocks is to be compatible with the JPEG compression standard.

(4) Perform DCT transformation on the matrix after partitioning.

(5) For the coefficients of the ith block after DCT transformation, the watermark is embedded by comparing the DCT intermediate frequency coefficients. The idea of ​​the intermediate frequency coefficient comparison method is to select two positions Bi(v1, v1) and Bi(v2, v2) from the intermediate frequency region for comparison, and the subscript i represents the ith block. 22 intermediate frequency coefficients can be embedded, as shown in Figure 3. In the figure, FL represents the low frequency part of the block, and FH represents the high frequency part. FM is the intermediate frequency region that can be selected for embedding, because embedding in the FM region can avoid image quality degradation and can provide better anti-attack capabilities. In order to obtain better anti-compression attack performance, the JPEG quantization table in Table 1 can be referred to when selecting coefficients. The two DCT coefficients selected should meet the requirement that adjusting their size will not cause serious degradation of the carrier image. Therefore, coefficients with the same brightness quantization value in the JPEG compression algorithm should be selected. From Table 1, it can be observed that the quantization values ​​of coefficients (4, 1) and (3, 2) or (1, 2) and (3, 0) are equal, which is more suitable for comparison.

Specific implementation of the watermark embedding algorithm: For each 8x8 block, select a pair of coefficients (4, 1) and (3, 2), compare their sizes, and ensure that they satisfy equation (3). If not, swap the values ​​of the two coefficients. ωi is the value of the information bit embedded in the i-th block.

In order to improve the robustness, the algorithm is further improved. The control amount α is introduced to expand the difference between the two DCT coefficients. Although the introduction of α will degrade the image, it can reduce the detection error.

When ωi=1, the coefficient (4, 1) is greater than the coefficient (3, 2), and the difference between the two is less than α, adjust according to formula (4):

When ωi=0, the coefficient (3, 2) is greater than the coefficient (4, 1) and the difference between the two is less than α, adjust according to formula (5):

(6) Perform IDCT transformation on the coefficients of the ith block after embedding the watermark information.

(7) Embed watermarks in other blocks according to steps (5) and (6).

(8) Perform IDWT transformation to obtain the image with watermark embedded.

3 Watermark extraction algorithm

This algorithm is a blind watermark algorithm, and the original host image of the watermark image is not needed when extracting. Extracting watermark is the inverse process of embedding. Figure 4 shows the watermark extraction process.

The steps can be described as follows:

(1) Perform DWT transformation on the watermarked image.

(2) Select the HL subband and divide it into 8x8 blocks for DCT transformation.

(3) Extract the watermark according to formula (6).

(4) Reconstruct the watermark image according to the extracted watermark bits to obtain the encrypted watermark.

(5) The watermark image is chaotically decrypted using the chaotic key to obtain the decrypted watermark.

(6) Calculate the similarity between the restored watermark signal and the original watermark signal.

4 Test results

The experiment uses a host image of size 512×512. After the first level of DWT transformation, the size of the HL subband is 256×256. The selected HL subband is divided into 8×8 blocks, resulting in 1 024 blocks. Using these blocks, a 1 024-bit watermark can be embedded into the host image. A 32×32 binary image is used as a watermark and embedded into the host image.

4.1 In the absence of an attack

Figure 5 shows the host image and watermark image used in the experiment. Figures 6a and 6b respectively describe the image after the watermark is embedded by the algorithm and the extracted watermark. In order to verify the performance of the algorithm, the algorithm is compared with the results of direct application of DCT for watermark embedding. Figure 7 shows the image and the extracted watermark after direct application of DCT for watermark embedding. It can be seen that the watermark can be correctly extracted from the watermark image, but the image after the watermark is embedded by direct application of DCT algorithm is less invisible.

Table 2 gives the PSNT and NC values ​​of this method and the single DCT method, from which it can be seen that when not attacked, the NC of both algorithms is 1. However, the peak signal-to-noise ratio of this method is higher, reaching 36.7777 dB, so the image quality is better.

4.2 In case of attack

In order to measure the invisibility and robustness of the algorithm, some common attack experiments are conducted on the watermarked image. Including Gaussian noise, salt and pepper noise, Gaussian low-pass filter, JPEG compression, rotation and other attacks. The experimental results are shown in Table 3. When the watermarked image is attacked by 10% Gaussian noise and 10% salt and pepper noise, the NC value is still above 0.9. When the watermarked image is attacked by 50% JPEG compression, the NC value is close to 1. It can also be observed from the table that the algorithm has a strong ability to resist Gaussian low-pass filter attacks, but a poor ability to resist rotation attacks, because the spatial relationship between the original image and the watermarked image is disrupted.

5 Conclusion

A new digital image watermarking algorithm based on joint DWT-DCT transform is proposed. The host image is first transformed by DWT to extract the HL subband, and then the DCT is calculated for the selected HL subband, and the encrypted watermark is embedded into the coefficients after DCT transform. The characteristics of this algorithm are as follows: (1) The original watermark is encrypted by chaotic sequence to increase the confidentiality of the watermark; (2) The watermark is embedded in the data block after DWT-DCT transform, which has better invisibility and stronger robustness than the single transform domain technology; (3) In the embedding process, the comparison of intermediate frequency coefficients is adopted, and the JPEG compression model is referred to to improve the compression resistance of the watermark; (4) The embedding position of the watermark is selected in the intermediate frequency band of the block DCT domain after a large number of experiments, which can achieve a better balance between robustness and transparency; (5) Watermark detection does not require the original image, and blind detection is achieved. This algorithm can be used to protect the copyright of digital images and has certain practical value.