An extended block sparse Bayesian learning method for image denoising based on structural similarity

Abstract

The present invention proposes an extended block sparse Bayesian learning image denoising method based on structural similarity, comprising the steps of: reading a specific noisy natural image Y in a data set and preprocessing the image; constructing a DCT dictionary suitable for the target image, wherein the DCT dictionary is a transformation matrix used when performing DCT cosine transform on the image; and denoising and restoring the image according to the initialized denoised image X and the DCT dictionary D. The present invention adopts the EBSBL algorithm to regard the image block as a one-dimensional signal, constructs the block sparse coefficient correlation of the image block, and restores the block sparse signal when the block sparse structure is known or unknown, thereby achieving the purpose of enhancing image denoising. At the same time, due to the excellent signal recovery performance of the sparse representation itself, the algorithm proposed in the present invention also achieves good results in image quality restoration.

Description

Technical Field

[0001] The present invention belongs to the field of traditional image quality restoration and processing based on sparse representation, and in particular relates to a denoising algorithm considering the similarity of image block structures. Background Art

[0002] Image denoising technology is one of the most basic research directions in the field of image processing. Image is one of the important means for humans to obtain information, and the role of image in the process of information dissemination is becoming more and more important. In many cases, image information will be affected by various noises, because the image is easily affected by the device and the surrounding environment during the acquisition process, which makes the image contain noise.

[0003] Image denoising algorithms based on sparse representation, such as the K-SVD algorithm, are a kind of image denoising algorithm that continuously learns dictionaries and optimizes the sparse representation of images based on the dictionary. In the process of image denoising, the sparse representation of the image can be retained as the original useful information, and the approximation residual is regarded as noise and continuously and effectively discarded, so as to achieve the purpose of image signal recovery. Therefore, dictionary learning and optimizing the sparse representation of the original image based on the dictionary are crucial steps in image denoising algorithms such as K-SVD.

[0004] In practice, algorithms that rely on image blocks for image denoising, including K-SVD, often ignore the structural similarity within an image block and the structural similarity between different image blocks (such as repeated textures and shapes in the image). This is reflected in the sparse representation, that is, the sparse coefficients present block structure characteristics. Most existing methods also focus on the structural similarity between image blocks, but do not pay enough attention to the structural similarity within the same image block.

[0005] In addition, the Expanded block sparse Bayesian learning algorithm (EBSBL algorithm for short) is a Bayesian learning signal recovery method that takes into account the block sparse characteristics. It can recover block sparse signals when the block sparse structure of the signal is known or unknown. At the same time, the EBSBL algorithm has not yet been applied to image block-based denoising. Summary of the invention

[0006] The present invention proposes an extended block sparse Bayesian learning image denoising algorithm based on structural similarity.

[0007] An extended block sparse Bayesian learning image denoising method based on structural similarity, characterized by comprising the following steps:

[0008] S1 reads a specific noisy natural image Y in the data set and preprocesses the image;

[0009] S2 constructs a DCT dictionary suitable for the target image. The DCT dictionary (abbreviated as: dictionary D) is a transformation matrix used when performing DCT cosine transform on an image;

[0010] S3 assumes X to be the denoised image; based on the initialized X and DCT dictionary D, the image is denoised and restored.

[0011] In S1, the image preprocessing includes the following steps:

[0012] 1.1 Read a specific noisy natural image Y in the data set, assuming that the length and width of the natural image Y are M and N;

[0013] 1.2 Let X be the denoised image, initialized to Y. On Y, use a sliding window to extract the image of size The image block is a pixel with a sliding step length of one pixel. ij Represents the image blocks taken out in sequence, where If the extraction process is R ij Represents and R ij It consists only of 1 and 0, And x ij ∈R n×1 is a one-dimensional column vector, forming an image matrix No. Column. Let α ij ∈R m×1 For x ij The corresponding sparse coefficient vector is simplified as α∈R m×1 .

[0014] Since the texture structure of a single image block is similar, the corresponding sparse coefficient α also has block sparse structure characteristics, so the EBSBL algorithm can be used for better sparse expression and optimization.

[0015] Therefore, the sparse coefficient α is updated in S3 ij The EBSBL algorithm is used to capture the structural characteristics of the image, so that the sparse coefficients are kept sparse enough when they are updated, while having structural characteristics.

[0016] S3 specifically includes:

[0017] S3.1, according to the initialized X and dictionary D, iteratively update the sparse coefficient α ij and dictionary D, J times;

[0018] S3.2, based on the sparse coefficients and dictionary after iteration, the restored image can be shown as formula (1):

[0019]

[0020] In the above formula, X is the denoised and restored image, Y is the noisy image, i.e., the image matrix, D is the dictionary, and β is the Lagrange multiplier.

[0021] S3.1, according to the initialized X and dictionary D, iteratively update the sparse coefficient α ij and dictionary D, for a total of J times, each cycle includes the following steps: S3.1.1 Update sparse coefficient a ij And S3.1.2 updates the dictionary D.

[0022] S3.1.1 Generate sparse coefficients through the EBSBL algorithm. Specifically include the following:

[0023] assumed is the sparse expression of the original signal x, is the signal after adding noise, is a dictionary about the signal y, v is noise and has a Gaussian distribution, then they satisfy the following additive Gaussian noise model:

[0024] y=Dα+v.

[0025] Since α, as a sparse signal, has a block sparse structure characteristic, that is, the signal can be divided into many blocks, the signal in some blocks is not zero, and the signal in other blocks is zero. Assume that α has g block structures, that is, α=[α1,…,α g ] T ,in d i To form block group α i The number of elements of , i = 1,…,g. The block-expressed α can be analyzed.

[0026] To simplify the expression, assume that α is the variable x, the dictionary D is the variable Φ, and each block α i (i.e. x i ) presents a Gaussian distribution, that is:

[0027]

[0028] Among them, B i is a positive definite matrix used to construct the structural correlation between elements within a block, γ i is a non-zero parameter controlling x i The block sparsity of γ. If γ i is 0, block x i is also equal to 0. Based on the fact that each block is uncorrelated, the prior of x follows The law of ∑0=diag{γ1B1,…,γ g B g}. Assume that the noise vector satisfies λ is a positive scalar. Therefore, the posterior of x is:

[0029] in:

[0030] μ x =Σ0Φ T (λI+ΦΣ0Φ T ) -1 y

[0031]

[0032] Once the parameters It is estimated that the maximum a posteriori estimate of x is It can be obtained directly from the average of the posterior as shown in the following formula:

[0033]

[0034] To estimate For different parameter indicators, the corresponding parameters are updated in an iterative manner, and finally the maximum a posteriori estimate of x is obtained. i The learning rule is:

[0035]

[0036] For λ, the learning rule is obtained by the EM algorithm, and its learning rule is as follows:

[0037]

[0038] Using the EM algorithm, we can deduce B i The learning rule is that each block is assigned a different B i Will lead to overfitting, so when the image blocks are of the same size, the parameter averaging method is used to constrain With this constraint, the learning rule for B is as follows:

[0039]

[0040] At this point, the maximum a posteriori estimate of x can be obtained That is, the sparse expression α of a certain image block can restore the original image without noise when the dictionary D is known.

[0041] S3.1.2, based on the sparse coefficients obtained in step S3.1.1, combined with the noise image matrix, update the dictionary D = [d1,…,dm ]. The number of columns in dictionary D is m, l = 1, 2, ..., m, and each column in the dictionary, i.e., an atom, is updated as follows. When the update reaches the lth column d of dictionary D, l , the other atoms remain unchanged. The specific steps are as follows:

[0042] For a certain atom d l , select all image blocks reconstructed using this atom, that is, the positions of image blocks with non-zero sparse coefficients:

[0043] ω l ={(i,j)|α ij (l)≠0}

[0044] For each index (i,j)∈ω l , calculate its reconstruction error:

[0045]

[0046] Assume E l for Then use SVD to decompose E l =UΔV T , where U is the left singular vector matrix, V is the transpose of the right singular vector matrix, and Δ is the diagonal matrix of eigenvalues. Then the dictionary d l The columns are updated as is the first column of U, the new Update to the first column of V multiplied by the first eigenvalue of Δ. In this way, the next column of the dictionary D is updated in sequence until all atoms in the dictionary are updated.

[0047] If the number of cycles is reached at this time, return to step S3.2.

[0048] Beneficial effects of the present invention:

[0049] The present invention mainly adopts a block sparse Bayesian learning algorithm (EBSBL algorithm, Expanded Block SparseBayesian Learning Algorithm) to fully consider the block structure characteristics (ieblock sparse) of the sparse coefficients of a single image block, to achieve better image restoration and denoising, and thus to achieve the purpose of optimizing the original K-SVD denoising algorithm. The EBSBL algorithm regards the image block as a one-dimensional signal, constructs the block sparse coefficient correlation of the image block, and restores the block sparse signal (ie image block) when the block sparse structure is known or unknown, to achieve the purpose of enhanced image denoising, and at the same time, due to the excellent signal recovery performance of the sparse representation itself, the algorithm proposed in the present invention also achieves good results in image quality restoration. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of the extended block sparse Bayesian learning image denoising algorithm based on structural similarity of the present invention.

[0051] Figure 2 It is an example of the natural image dataset used in the present invention.

[0052] Figure 3 The following are the image samples before and after denoising used by the present invention and the comparison with the traditional method ((a) is the original image, (b) is the image after adding noise, (c) the denoising effect of the traditional K-SVD algorithm, and (d) the denoising effect of the algorithm of the present invention).

[0053] Figure 4 It is the comparative effect of the denoising algorithm adopted by the present invention and the traditional K-SVD algorithm on the two indicators of PSNR value and SSIM value. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described below with reference to examples. It should be understood that the specific examples described herein are only used to explain the present invention and are not intended to limit the present invention.

[0055] Example

[0056] Image denoising algorithms based on sparse representation, such as Figure 1 As shown:

[0057] Step 1 (such as Figure 2 As shown in the figure, read a specific noisy natural image Y in the data set, and set the length and width of the natural image Y to M and N; set X to be the denoised image, initialized to Y. Use a sliding window on Y to extract a size of The image block is a pixel with a sliding step length of one pixel. ij Represents the image blocks taken out in sequence, where If the extraction process is R ij Represents and R ij It consists only of 1 and 0, And x ij ∈R n×1 is a one-dimensional column vector, forming an image matrix No. Column. Let α ij ∈R m×1 For x ij The corresponding sparse coefficient vector is simplified as α∈R m×1 .

[0058] Step 2: Construct a DCT dictionary suitable for the target image. (DCT dictionary is the transformation matrix used when performing DCT cosine transform on an image);

[0059] Step 3: According to the initialized X and dictionary D, iteratively update the sparse coefficient α ij (using EBSBL algorithm) and dictionary D, J times;

[0060] Step 4: According to the sparse coefficients and dictionary after iteration, the restored image is restored as shown in the formula:

[0061]

[0062] Comparison of visual effects before and after denoising Figure 3 (b) and (d). Comparison of the denoising visual effects of the denoising algorithm (ieE-SVD) proposed in this invention and the traditional K-SVD algorithm Figure 3 As shown in (d) and (c), from the comparison of these two figures, it can be seen that the method of the present invention is significantly better than the traditional K-SVD method in denoising effect, especially in edge preservation. In addition, the quantitative comparison effects of the two methods in terms of PSNR value and SSIM value are shown as follows: Figure 4 As shown, it fully demonstrates the superiority of the proposed algorithm.

Claims

1. Extended block sparse Bayesian learning image denoising method based on structural similarity, characterized in that: The following steps are involved: S1 reads a specific noisy natural image Y in a data set and preprocesses the natural image Y; the preprocessing includes the following steps: 1.1 Read a specific noisy natural image Y in the data set, assuming that the length and width of the natural image Y are M and N; 1.2 Let X be the denoised image, initialized to Y; On Y, a sliding window is used to extract the size of The image block is a pixel with a sliding step length of one pixel; x ij Represents the image blocks taken out in sequence, where The extraction process is done using R ij Represents and R ij It consists only of 1 and 0, And x ij ∈R n×1 is a one-dimensional column vector, forming a noise image matrix, which is the natural image Y. Therefore No. List; Let α ij ∈R m×1 For x ij The corresponding sparse coefficient vector is simplified as α∈R m×1 ; S2: Construct a DCT dictionary D∈R for the natural image Y n×m , the DCT dictionary is a transformation matrix used when performing DCT cosine transform on an image; S3 updates the sparse coefficient a according to the denoised image X and the DCT dictionary D ij and update the dictionary D, the update sparse coefficient α ij The EBSBL algorithm is used to capture the structural characteristics of the image, so that the sparse coefficients are kept sufficiently sparse when updating, and at the same time have structural characteristics; finally, the denoised image is denoised and restored; S3 specifically includes the following steps: S3.1, according to the initialized X and dictionary D, iteratively update the sparse coefficient α ij and dictionary D, a total of J times, each cycle includes two steps: S3.1.1 Update the sparse coefficient a ij and S3.1.2 update dictionary D; S3.1.1 Update the sparse coefficient a ij , specifically including the following: assumed is the sparse expression of the original signal x, is the signal after adding noise, is a dictionary about the signal y, v is noise and has a Gaussian distribution, then it satisfies the following additive Gaussian noise model: y=Dα+v; α has a g block structure, that is, α=[α1,…,α g ] T ,in d i To form block group α i The number of elements of , i = 1,…,g, parse the α after the block expression; To simplify the expression, assume that α is the variable x, the dictionary D is the variable Φ, and each block α i That is x i Gaussian distribution: Among them, B i is a positive definite matrix used to construct the structural correlation between elements within a block, γ i is a non-zero parameter controlling x i Block sparsity; Based on the irrelevance between each block, the prior of x follows The law of ∑0=diag{γ1B1,…,γ g B g }; Assume that the noise vector satisfies λ is a positive scalar; the posterior of x is: in: m x =S0F T (λI+ΦΣ0Φ T ) -1 y parameter After estimation, the maximum a posteriori estimate of x is It is obtained directly from the mean of the posterior, as shown in the following formula: To estimate For different parameter indicators, the corresponding parameters are updated in an iterative manner, and finally the maximum a posteriori estimate of x is obtained; where γ i The learning rule is: For λ, the learning rule is obtained by the EM algorithm, and its learning rule is as follows: Using the EM algorithm, we can deduce B i The learning rule is to use the parameter averaging method when the image blocks are of the same size, and constrain With this constraint, the learning rule for B is as follows: At this point, the maximum a posteriori estimate of x is obtained That is, the sparse expression α of a certain image block can restore the original image without noise when the dictionary D is known; S3.1.2 Update dictionary D, including the following: According to the sparse coefficients obtained in step S3.1.1, combined with the noise image matrix, update the dictionary D = [d1,…,d m ]; the number of columns in dictionary D is m, l = 1, 2, ..., m, and each column in the dictionary, i.e., an atom, is updated as follows. When the update reaches the lth column d of dictionary D l , the other atoms remain unchanged; the specific steps are as follows: For a certain atom d l , select all image blocks reconstructed using this atom, that is, the positions of image blocks with non-zero sparse coefficients: oh l ={(i,j)∣∣a ij (l)≠0} For each index (i,j)∈ω l , calculate its reconstruction error: Assume E l for The concatenated matrix is ​​then decomposed using SVD l =UΔV T , where U is the left singular vector matrix, V is the transpose of the right singular vector matrix, and Δ is the diagonal matrix of eigenvalues, then the dictionary d l The columns are updated as is the first column of U, the new Update to the first column of V multiplied by the first eigenvalue of Δ; and update the next column of the dictionary D in turn until all atoms in the dictionary are updated; If the number of cycles J is reached at this time, the iteration ends and the process goes to step S3.2; S3.2, based on the sparse coefficients and dictionary after iteration in S3.1, the denoised image X is as follows: Where β is the Lagrange multiplier.

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