An image restoration method based on a hybrid structured sparse model

Abstract

This invention discloses an image restoration method based on a hybrid structured sparse model, specifically including the following steps: initializing the restored image and setting the number of iterations; constructing a matrix of similar image patch groups; establishing a hybrid structured sparse model; using the hybrid structured sparse model to sparsely encode each similar image patch group; reconstructing each similar image patch group; and restoring the entire image based on all reconstructed similar image patch groups. The image restoration method of this invention better reconstructs details such as edges and textures, and effectively suppresses unwanted visual artifacts, further improving the image restoration effect.

Description

Technical Field

[0001] This invention belongs to the field of digital image processing technology, specifically relating to an image restoration method based on a hybrid structured sparse model. Background Technology

[0002] Images are an important source of information for both humans and machines. However, images are inevitably subject to various degradation interferences, such as noise and blurring, during acquisition, compression, transmission, and reception, which severely affect their subsequent processing and applications. Image restoration technology, which reconstructs potentially realistic images from observed degraded images at the algorithm and software levels, has significant practical implications.

[0003] Image restoration is a linear ill-conditioned inverse problem, thus requiring the use of image prior models to regularize the solution space and obtain stable solutions. In recent years, structured sparse models using similar image patch groups as basic units have been widely applied to various image restoration tasks and have achieved good results. Existing sparse models often only use a single L1 or L2 constraint on the sparse coefficients. However, soft thresholding, corresponding to L1 constraints, directly inactivates sparse coefficients with small absolute values, while Wiener filtering, corresponding to L2 constraints, produces oversmoothed solutions. Neither is conducive to preserving image details. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides an image restoration method based on a hybrid structured sparse model. Its purpose is to compensate for the first-norm constraint using the second-norm constraint, and to sharpen the second-norm constraint through the first-norm constraint, thereby effectively preserving image details and further improving the image restoration effect.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] An image restoration method based on a hybrid structured sparse model includes the following steps:

[0007] Step 1, initialize the restored image x 0 = y, where y represents the degraded image, and the number of iterations t = 1, 2, 3, ..., T;

[0008] Step 2, construct a matrix of similar image patch groups

[0009] Step 3: Establish a hybrid structured sparse model;

[0010] Step 4: Apply a hybrid structured sparse model to each group of similar image patches. Perform sparse coding;

[0011] Step 5, Reconstruct each group of similar image patches

[0012] Step 6: Reconstruct the entire image x using all the reconstructed similar image patch groups. t ;

[0013] Step 7: Iterate through steps 2-6 for a total of T times, and output the final restored image x. T .

[0014] Furthermore, the degraded image mentioned in step 1 includes a noisy degraded image and a blurred degraded image.

[0015] Furthermore, the construction of the similar image patch group matrix in step 2 is performed as follows:

[0016] Step 2.1, for the current restored image x t-1 Divide into blocks;

[0017] Step 2.2, perform block matching for each image block using Euclidean distance. Search for n similar image patches and form a matrix of similar image patch groups.

[0018]

[0019] Among them, R k (·) denotes the similar image patch group matrix extraction operation, R k,j This represents the extraction matrix for the j-th similar image patch.

[0020] Furthermore, the hybrid structured sparse model described in step 3 is established as follows:

[0021]

[0022] Where λ1, λ2, and ρ represent three positive regularization parameters. Let ||·||1 represent the F-norm operation, ||·||2 represent the L1-norm operation, and D represent the L2-norm operation. k Z represents a dictionary. k =Λ k (B k +A k ) represents the sparse coefficient matrix, Λ k It is a diagonal matrix representing the scale factor matrix, logΛ k =∑ i log(θ k,i +ε), θ k,i ≥0 represents Λ k The i-th diagonal element, ε is a small positive constant, A k B represents the norm constraint part. k This represents the L2 norm constraint part.

[0023] Furthermore, in step 4, a hybrid structured sparse model is used for each similar block group. Sparse coding is performed as follows:

[0024] Step 4.1, using principal component analysis for... Learning Dictionary D k ,as follows:

[0025]

[0026] Among them, S k express The covariance matrix, U k and P k S represents k The eigenvector matrix and eigenvalue matrix;

[0027] Step 4.2, fix B k and A k Optimize Λ k :

[0028]

[0029] The above equation can be equivalently transformed into:

[0030]

[0031] in, F k =B k +A k ;

[0032] Solving the above equation is equivalent to solving the following equation:

[0033]

[0034] in, and They represent C respectively k and F k The i-th row, where T represents the transpose operation;

[0035] Therefore, the solution is:

[0036]

[0037] in, as well as,

[0038]

[0039] Step 4.3, fix Λ k and A k Optimize Bk :

[0040]

[0041] The above equation can be equivalently transformed into:

[0042]

[0043] Therefore, its closed-form solution can be obtained as:

[0044]

[0045] Where I is the identity matrix;

[0046] Step 4.4, fix Λ k and B k Optimize A k :

[0047]

[0048] The above equation can be equivalently transformed into:

[0049]

[0050] Therefore, its closed-form solution can be obtained as:

[0051]

[0052] Where sgn(·) represents the sign operation, ⊙ represents the element-wise multiplication operation, |·| represents the absolute value operation, and 1 represents a matrix with all elements being 1.

[0053] Furthermore, in step 5, each group of similar image patches is reconstructed. for:

[0054]

[0055] Furthermore, in step 6, the entire image x is restored. t The objective function is constructed as follows:

[0056]

[0057] Where η represents a positive constant and H represents a degenerate operator;

[0058] The closed-form solution to the above equation is:

[0059]

[0060] in, express The j-th column.

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] This invention establishes a hybrid structured sparse model for image restoration. Compared to existing technologies, the established hybrid structured sparse model utilizes both L1 and L2 norms to simultaneously constrain the sparse coefficients, thereby allowing the L1 and L2 constraints to mutually suppress their deficiencies. Specifically, the L2 constraint compensates for the L1 constraint, and the L1 constraint sharpens the L2 constraint. Therefore, the image restoration method based on the hybrid structured sparse model proposed in this invention helps preserve image details and further improves the image restoration effect. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating the implementation of an image restoration method based on a hybrid structured sparse model according to the present invention.

[0064] Figure 2 These are simulation comparison diagrams of the present invention. Detailed Implementation

[0065] The present invention will be further described in detail below with reference to the accompanying drawings.

[0066] like Figure 1 As shown, this invention discloses an image restoration method based on a hybrid structured sparse model. The method uses a structured sparse model with both L1 and L2 norm constraints on the sparse coefficients as prior constraints to achieve image restoration. The method includes the following steps:

[0067] Step 1, initialize the restored image x 0 = y, where y represents the degraded image, and the number of iterations is set to t = 1, 2, 3, ..., T.

[0068] Specifically, the degraded image mentioned in step 1 includes a noisy degraded image and a blurred degraded image.

[0069] Step 2, construct a matrix of similar image patch groups

[0070] Specifically, step 2 is performed as follows:

[0071] Step 2.1, for the current restored image x t-1 Divide into blocks;

[0072] Step 2.2, perform block matching for each image block using Euclidean distance. Search for n similar image patches and form a matrix of similar image patch groups.

[0073]

[0074] Among them, Rk (·) denotes the similar image patch group matrix extraction operation, R k,j This represents the extraction matrix for the j-th similar image patch.

[0075] Step 3: Establish a hybrid structured sparse model.

[0076] Specifically, the hybrid structured sparse model established in step 3 is as follows:

[0077]

[0078] Where λ1, λ2, and ρ represent three positive regularization parameters. Let ||·||1 represent the F-norm operation, ||·||2 represent the L1-norm operation, and D represent the L2-norm operation. k Z represents a dictionary. k =Λ k (B k +A k ) represents the sparse coefficient matrix, Λ k It is a diagonal matrix representing the scale factor matrix, logΛ k =∑ i log(θ k,i +ε), θ k,i ≥0 represents Λ k The i-th diagonal element, ε is a small positive constant, A k B represents the norm constraint part. k This represents the L2 norm constraint part.

[0079] Step 4: Apply a hybrid structured sparse model to each similar block group. Perform sparse coding.

[0080] Specifically, step 4 is performed as follows:

[0081] Step 4.1, using principal component analysis for... Learning Dictionary D k ,as follows:

[0082]

[0083] Among them, S k express The covariance matrix, U k and P k S represents k The eigenvector matrix and eigenvalue matrix.

[0084] Step 4.2, fix B k and A k Optimize Λ k :

[0085]

[0086] The above equation can be equivalently transformed into:

[0087]

[0088] in, F k =B k +A k .

[0089] Solving the above equation is equivalent to solving the following equation:

[0090]

[0091] in, and They represent C respectively k and F k The i-th row, T represents the transpose operation.

[0092] Therefore, the solution is:

[0093]

[0094] in, as well as,

[0095]

[0096] Step 4.3, fix Λ k and A k Optimize B k :

[0097]

[0098] The above equation can be equivalently transformed into:

[0099]

[0100] Therefore, its closed-form solution can be obtained as:

[0101]

[0102] Where I is the identity matrix.

[0103] Step 4.4, fix Λ k and B k Optimize A k :

[0104]

[0105] The above equation can be equivalently transformed into:

[0106]

[0107] Therefore, its closed-form solution can be obtained as:

[0108]

[0109] Where sgn(·) represents the sign operation, ⊙ represents the element-wise multiplication operation, |·| represents the absolute value operation, and 1 represents a matrix with all elements being 1.

[0110] Step 5, Reconstruct each group of similar image patches

[0111] Specifically, in step 5, each similar image patch group Reconstructed as:

[0112]

[0113] Step 6: Reconstruct the entire image x based on all reconstructed similar image patch groups. t .

[0114] Specifically, in step 6, the entire image x is restored. t The objective function is constructed as follows:

[0115]

[0116] Where η represents a positive constant and H represents a degenerate operator.

[0117] The closed-form solution to the above equation is:

[0118]

[0119] in, express The j-th column.

[0120] Step 7: Iterate through steps 2-6 for a total of T times, and output the final restored image x. T .

[0121] The effectiveness of this invention is further illustrated by the following simulation experiments.

[0122] 1. Simulation conditions:

[0123] The simulation experiments of this invention were conducted in the Matlab 2019a environment under Windows 10 system.

[0124] 2. Simulation Results and Analysis:

[0125] Figure 2The images presented here are the restoration results of three image restoration methods based on the present invention: one based on a hybrid structured sparse model, one based on a norm-1 constrained structured sparse model, and one based on a norm-2 constrained structured sparse model. Figure 2 (a) is the original blurred and degraded image; Figure 2 (b) is a simulation result of the image restoration method based on the first norm constrained structured sparse model for the restoration of degraded images; Figure 2 (c) is a simulation result of the image restoration method based on the L2-norm constrained structured sparse model for the restoration of degraded images; Figure 2 (d) is a simulation result of the image restoration method based on the hybrid structured sparse model of the present invention for the restoration of degraded images.

[0126] Comparison Appendix Figure 2 In Figure 2 (b) Figure 2 (c) and Figure 2 (d) It can be seen that both the image restoration method based on the first norm constrained structured sparse model and the image restoration method based on the second norm constrained structured sparse model will over-smooth the image edges. Furthermore, the image restoration method based on the second norm constrained structured sparse model will produce unwanted visual artifacts. In contrast, the restoration method of this invention can better reconstruct high-frequency details and effectively suppress visual artifacts.

[0127] In summary, the method of the present invention overcomes the problem of existing technologies being unfavorable for protecting image details, and further improves the image restoration effect.

[0128] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. An image restoration method based on a hybrid structured sparse model, characterized in that, Includes the following steps: Step 1, Initialize the restored image ,in Represents a degraded image, sets the number of iterations. ; Step 2, construct a matrix of similar image patch groups ; Step 3, establish a hybrid structured sparse model, specifically as follows: in, , and This represents three positive regularization parameters. Indicates the F-norm operation, This represents a norm operation. This represents the L2 norm operation. Represents a dictionary. Represents a sparse coefficient matrix. It is a diagonal matrix representing the scale factor matrix. , express The diagonal elements, It is a small normal number. This represents the norm constraint part. Represents the L2 norm constraint part; Step 4: Apply a hybrid structured sparse model to each group of similar image patches. Sparse coding is performed as follows: Step 4.1, using principal component analysis for... Learning Dictionary ,as follows: in, express The covariance matrix, and They represent The eigenvector matrix and eigenvalue matrix; Step 4.2, Fix and ,optimization : The above equation can be equivalently transformed into: in, , ; Solving the above equation is equivalent to solving the following equation: in, , , and They represent and The OK, Indicates the transpose operation; Therefore, the solution is: in, ,as well as, Step 4.3, Fix and ,optimization : The above equation can be equivalently transformed into: Therefore, its closed-form solution can be obtained as: in, It is a unit array; Step 4.4, Fix and ,optimization : The above equation can be equivalently transformed into: Therefore, its closed-form solution can be obtained as: in, Indicates symbolic operations, This indicates an element-wise multiplication operation. This indicates the absolute value operation. Represents a matrix whose elements are all 1s; Step 5, Reconstruct each group of similar image patches ; Step 6: Reconstruct the entire image using all the reconstructed similar image patch groups. ; Step 7, iteratively execute steps 2-6. Next, output the final restored image. .

2. The image restoration method based on a hybrid structured sparse model according to claim 1, characterized in that, The degraded images mentioned in step 1 include noisy degraded images and blurred degraded images.

3. The image restoration method based on a hybrid structured sparse model according to claim 1, characterized in that, The construction of the similar image patch group matrix in step 2 is performed as follows: Step 2.1, for the current restored image Divide into blocks; Step 2.2, perform block matching for each image block using Euclidean distance. search Similar image patches are grouped into a matrix of similar image patches. : in, This represents the similar image patch group matrix extraction operation. Indicates the first Extraction matrix of similar image patches.

4. The image restoration method based on a hybrid structured sparse model according to claim 1, characterized in that, In step 5, reconstruct each group of similar image patches. for: 。 5. The image restoration method based on a hybrid structured sparse model according to claim 1, characterized in that, Step 6 involves restoring the entire image. The objective function is constructed as follows: in, Represents positive numbers. Represents a degenerate operator; The closed-form solution to the above equation is: in, express The List.

Images