A Digital Watermarking Method for Color Images Based on Compressed Sensing and NSCT

Abstract

A digital watermarking method for color images based on compressive sensing and NSCT. This method decomposes the color carrier image R, G, B, divides all three color components into non-overlapping blocks of equal area, and randomly selects m blocks from all the blocks to form the embedding array Q1. Perform NSCT decomposition on all the embedding blocks in Q1, take the LU decomposition of its low-frequency components, and perform SVD decomposition on the diagonal matrix to extract singular values; divide the watermark image into m / 2 blocks of equal area, and extract the measurement values of each block with the same compressive sampling operator. Embed the measurement value of the j-th block of the watermark into the singular values of the j-th block and the 2j-th block in the array Q1 respectively. As long as the embedding blocks are selected according to the rules during watermark embedding, the watermark information can be extracted. The present invention reduces the data redundancy by block compressive sensing of the watermark image, ensures the large-capacity embedding of the watermark, and at the same time compressive sensing increases the security of the watermark. This method can effectively resist geometric attacks such as shearing, scaling, JPEG compression, high-pass filtering, salt-and-pepper noise, etc., and is applicable to the copyright protection of color digital images.

Description

Technical Field

[0001] The present invention belongs to the technical field of information security and relates to a color image digital watermarking method based on compressive sensing and NSCT. Background Art

[0002] The digitization of information is an important feature of the development of today's society. With the explosive growth of digital information (images, audio, video, digital publishing, etc.), it has become increasingly convenient for people to obtain digital information through the Internet, while the cost of piracy has become increasingly low. Digital watermarking, as an effective means of intellectual property protection and digital multimedia information anti-counterfeiting, was born precisely to safeguard the rights and interests of original creators and copyright purchasers.

[0003] Due to the large amount of information contained in color images, it has gradually become a hot topic in watermarking research in recent years. However, existing color image digital watermarking algorithms often have the characteristics of small watermark embedding amount and concentrated embedding points, making their ability to resist geometric attacks such as shearing weak, and even having problems such as being unable to extract watermarks. Summary of the Invention

[0004] The purpose of the present invention is, in view of the problems existing in existing color image digital watermarking algorithms, to randomly select an array of watermark embedding blocks on the R, G, and B components of a color image. After the watermark image is compressed and sensed to extract measurement values, the measurement values are repeatedly embedded into the array blocks. On the one hand, the present invention solves the problem of overly concentrated watermark embedding. On the other hand, compressive sensing reduces the redundancy of watermark information, increases the amount of watermark information embedded, and compressive sensing also further enhances the security of watermark information (the seed of the compressive sensing observation matrix and the block size can both be used as keys, serving as a prerequisite for watermark extraction).

[0005] The technical solution of the present invention: A new color image digital watermarking method based on compressive sensing and NSCT is invented, including digital watermark embedding and digital watermark extraction. The present invention selects a color carrier image for RGB decomposition, divides each color into non-overlapping blocks of equal area, randomly selects m (m is a natural number and an integer multiple of 2) embedding blocks from all the blocks to form an embedding array, performs NSCT transformation on each block in the array, obtains a diagonal matrix after performing LU decomposition on its low-frequency components, and then performs SVD decomposition on the diagonal matrix to obtain singular values. The grayscale watermark image is divided into m / 2 non-overlapping blocks of equal area, and measurement values are obtained by compressive sensing for each block. The measurement values are embedded into the singular values of the embedding array according to established rules. Since the number of embedding blocks in the embedding array is twice that of the watermark blocks, it is ensured that each watermark block is embedded twice; during watermark detection, as long as the watermarked carrier blocks in the embedding array are subjected to watermark extraction, the complete watermark information can be obtained. In this solution, the embedding array is randomly selected from the block of three color components, ensuring that the embedded watermark blocks are discretely distributed throughout the carrier image and can effectively resist various geometric attacks.

[0006] The steps of the digital watermark embedding method in the present invention are as follows:

[0007] (1) Decompose the color carrier image O into R, G, and B components, perform non-overlapping equal-area partitioning on each color component to obtain a set of image blocks Q, and randomly select m (m is a natural number and an integer multiple of 2) blocks from the set Q to form an embedding array Q 1 , and save the original positions of these m data blocks as the key key1.

[0008] (2) Perform 3-level NSCT decomposition on each block in the array Q 1 . Assume that X i represents the low-frequency component matrix of the i-th (i = 1, 2... m) block in the embedding array Q 1 . Perform LU decomposition on it:

[0009]

[0010] where l 21 , l 31 , l 32 are non-zero values of the lower triangular matrix L, d 1 , d 2 , d 3 are non-zero values of the diagonal matrix D, and u 12 , u 13 , u 23 are non-zero values of the upper triangular matrix U.

[0011] From equation (1), the diagonal matrix D i can be obtained, where i is the number of each block. Perform SVD decomposition on the matrix D i to get:

[0012]

[0013] where T is the conjugate transpose, U i and V i T are orthogonal matrices, S i is a diagonal matrix, and λ i1 , λ i2 …λ in are the singular values of the matrix S i . Save the values of λ i1 , λ i2 ,…, λ in as key2 for use when extracting the watermark. Save the values of U i , V i T for use when embedding the watermark.

[0014] (3) For the embedding array Q1 Perform step (2) once on the low-frequency subband matrices of all blocks in

[0015] (4) Perform non-overlapping blocking on the grayscale watermark image W. The number of blocks m / 2 is half of the number of embedding blocks in the array Q 1

[0016] (5) Observe each watermark block with the same compressive sampling operator Φ to obtain the corresponding measurement values. Φ and the watermark image block size are saved as the key key3. The number of measurement values for each block is n, and Y j (j = 1, 2... m / 2) represents the measurement value of the j-th watermark block.

[0017]

[0018] (6) Embed the measurement values of the j-th (j = 1, 2,..., m / 2) block of the watermark into the diagonal matrix S 1 of the j-th block and the 2j-th block of the carrier component in the array Q i

[0019]

[0020]

[0021] where α j is the embedding strength of the j-th block and the 2j-th block. Save the value of α j as key4 for watermark extraction.

[0022] Use to replace S in formula (2) i

[0023]

[0024] (7) Use to replace D in formula (1) i

[0025]

[0026] (8) Use to replace the low-frequency component of each embedding block in the array Q 1 After inverse NSCT transformation with its original other frequency domain components, a new watermark-embedded data block is obtained.

[0027] (9) According to the key key1, replace each watermark-embedded data block with its data block in the original R, G, B components respectively to form new watermark-embedded R, G, B components, and synthesize the watermark-embedded carrier image O W ​​​

[0028] The steps of the digital watermark extraction method in the present invention are as follows:

[0029] (1) Decompose the watermarked color image O w into R, G, and B components. Respectively divide the R, G, and B components into non-overlapping blocks of equal area according to the size during watermark embedding. Select blocks according to the key key1 to form the embedding array Q w .

[0030] (2) Perform 3-level NSCT decomposition on each block in the array Q w . Assume that X Wi represents the low-frequency component matrix of the i-th (i = 1, 2... m) block in the embedding array Q w . Perform LU decomposition on it:

[0031]

[0032] (3) The diagonal matrix D Wi can be obtained from Equation (7), where i is the number of each block. Perform SVD decomposition on the diagonal matrix D w in each block of the array Q Wi to obtain:

[0033]

[0034] where λ Wi1 , λ Wi2 … λ Win are the singular values of the SVD decomposition

[0035] (4) The singular values of the SVD decomposition of D i before watermark embedding can be known from the key key2. Let be the measurement value of the j-th watermark block, and extract

[0036]

[0037] The value of α j can be obtained from key4.

[0038] (5) Perform compressive sensing reconstruction on all m / 2 measurement values extracted to obtain the watermark image W*.

[0039] The beneficial effects of the present invention are as follows: By embedding and extracting digital watermarks in color images, the present invention can obtain complete watermark information. When performing watermark detection, this method does not require the provision of the original carrier image. The three color components of the watermarked image are divided into equal-sized and equal-area segments during embedding. Embedding blocks are selected according to the key key1, and the inverse transform of watermark embedding is performed on each block to obtain the watermark image. By performing block compressive sensing on the watermark image, the present invention reduces data redundancy and ensures large-capacity watermark embedding. At the same time, compressive sensing increases the security of the watermark. The method of the present invention can effectively resist geometric attacks such as shearing, scaling, brightness adjustment, lossless compression, and high-pass filtering, and is applicable to the copyright protection of color digital images. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flowchart of the present invention,

[0041] Figure 2(a) Carrier image Kid, Figure 2(b) Carrier image Lena,

[0042] Figure 3 Watermark image,

[0043] Figure 4(a) Watermarked image Kid, Figure 4(b) Watermarked image Lena. DETAILED DESCRIPTION OF THE INVENTION

[0044] The present invention is verified through examples as follows:

[0045] The color carrier images are Kid and Lena with 512×512 pixels. After R, G, and B decomposition, each color component is non-overlappingly segmented into segments of size 64×64, and 64 blocks are randomly selected from all the segments to form the embedding array Q 1 . The watermark image is a 128×128 gray cameraman image, which is non-overlappingly segmented into 32 equal-area segments. To ensure the security of the watermark, each watermark block is embedded twice, so the number of embedding blocks is twice that of the watermark blocks.

[0046] In evaluating the watermark extraction effect, the normalized correlation coefficient NC is used in the experiment for similarity judgment. The larger the value of NC, the higher the similarity between the extracted watermark and the original watermark.

[0047]

[0048] Among them, W represents the original watermark, W' represents the extracted watermark, and M and N are the length and width pixel values of the watermark image respectively.

[0049] The NC values of the watermark extracted after different types of attacks are as follows:

[0050] Attack type: NC (values for Kid and Lena respectively)

[0051]

[0052]

Claims

1. A digital watermark embedding and extraction method for color images based on compressive sensing and wavelet transform, characterized in that, the method includes digital watermark embedding and digital watermark extraction. The steps of the digital watermark embedding method are as follows: (1) Non-overlappingly divide the grayscale watermark image W into p blocks, where p is a positive integer; (2) Perform wavelet transform on all watermark blocks W i (where i = 1, 2, … p) to obtain the high-frequency coefficient matrix H i ; (3) Perform compressive sensing transformation on the high-frequency coefficient matrices of all watermark blocks through the sparse basis Ψ and the observation matrix Φ to obtain the measurement values of each block. Ψ and Φ are saved as the key key1, where (i = 1, 2,... p), and n is the number of measurement values of the watermark block; (4) Decompose the color carrier image O into R, G, and B components. Divide each color component into m non-overlapping equal-area blocks, where m = 3p. Number each block as A kj , k = (R, G, B), j = 1, 2, …, m. Select p blocks from each of the three color blocks of R, G, and B respectively to form 3 embedding arrays k = (R, G, B); Principle for selecting arrays: The numbers A of all the selected blocks kj , whose j values are not allowed to be the same, save the original positions of these m data blocks as the key key2; (5) Perform wavelet transform on each block in the embedded array and take the high-frequency coefficient matrix of each block to perform compressive sensing transform through the sparse basis Ψ k and the observation matrix Φ k to obtain the measurement value of each block. Save Ψ k and Φ k as the key key3; where k = (R, G, B), j = 1, 2, …, m, and n is the number of measurement values obtained for each matrix; save all the Y kj values for use during watermark extraction; (6)Embed the measurement values of the i-th watermark block, where i = 1, 2, …, p, into the i-th block of the array respectively; k = (R, G, B), α i is the embedding strength of the i-th watermark block, and save α i The value of is key4 for watermark extraction; (7)Perform compressive sensing reconstruction on the measured values embedded with watermark to obtain the high-frequency subband coefficient matrix H k ′; (8)Perform the inverse wavelet transform on the high-frequency subband coefficient matrix H k ′ and other frequency-domain subbands in the original image block to obtain the image block A k ′ j ; (9) Replace each piece of A k ′ j with its original block in the R, G, and B components, and after obtaining the watermarked R, G, and B components, synthesize the watermarked image O W .

2. A digital watermark embedding and extraction method for color images based on compressive sensing and wavelet transform according to claim 1, characterized in that, the steps of the digital watermark extraction method are as follows: (1) Decompose the watermarked color image O W into R, G, and B components. For each of the R, G, and B components, perform equal-area non-overlapping block partitioning according to the size during watermark embedding. Select blocks according to the key key2 to form an embedding array k = (R, G, B); (2) Perform wavelet decomposition on each block in the array After extracting the high-frequency coefficient matrix, obtain the sparse basis Ψ from key3 k and the observation matrix Φ k , and obtain the measurement value of each block after compressive sensing processing: (3) Measured value Y of the watermark block W ′ i : α i The value of it can be obtained from key4; (4) Perform compressive sensing reconstruction on the measurement values of all the extracted watermark blocks to obtain the watermark image blocks and then synthesize the watermark image W'.

Images