Fast deconvolution model based on fussed lasso

Abstract

The application discloses a fast inverse convolution model based on Fussed Lasso, which comprises the following steps: step 1, data input, reading an observation image G < m x n >, a convolution template T < (2p+1) x (2q+1) >, adjusting a parameter λ, and adjusting a parameter μ; step 2, linearly transforming the value range of the observation image pixels and normalizing the convolution template signal; and step 3, fast sparse inverse convolution restoration processing, which is used to improve the spatial resolution of the image. The method has the characteristics of fast processing speed and strong anti-noise ability. For image restoration, some prior knowledge of degradation is used to reconstruct or restore the degraded image.

Description

Technical Field

[0001] This invention belongs to the field of image restoration processing, and specifically relates to an image deconvolution restoration method. Specifically, it is a fast deconvolution model based on Fussed Lasso. This invention is particularly applicable to resolution enhancement of microscopic optical images. Background Technology

[0002] Image restoration aims to improve the quality of degraded images, removing or mitigating image quality degradation that occurs during digital image acquisition to achieve visual improvement. The most typical degradation phenomena are blurring and noise. Deconvolution methods can significantly improve image resolution and are therefore widely used in microscopic optical imaging. With the continuous development of high-throughput microscopic imaging technology, large amounts of data can be accumulated in a short time, necessitating fast deconvolution methods for data analysis. Currently, the principle of fast deconvolution is that the convolution of signals in the time domain is equivalent to the dot product operation of signals in the frequency domain. Correspondingly, the deconvolution operation of signals in the time domain is equivalent to the dot division operation of signals in the frequency domain. The biggest drawback of this method is its poor noise resistance. Here, we propose a new fast sparse deconvolution two-dimensional image restoration method. This method relies on efficient sparse matrix multiplication operations, avoiding frequency domain analysis of the image. Simultaneously, it incorporates prior information about the image, resulting in an image that is closer to the real image and has stronger noise resistance than traditional deconvolution methods.

[0003] As the degradation model shows, the image blurring degradation process can be understood as the result of convolving an image with a blur kernel matrix. Therefore, image deblurring can be seen as the inverse process of image blurring. However, due to the presence of noise, image deblurring becomes an ill-conditioned inverse problem. Summary of the Invention

[0004] The purpose of this invention is to provide a fast deconvolution model based on Fussed Lasso to improve the spatial resolution of images. This method is characterized by its fast processing speed and strong noise resistance. Image restoration utilizes prior knowledge of degradation phenomena to reconstruct or restore degraded images. The image degradation model is shown in (1):

[0005] G = AF + N (1)

[0006] In the formula, G represents the observed image, F represents the original image, A represents the point spread function, T, and other derived blur operator matrices, and AF is the vector-matrix representation of the convolution of the convolution function with the original image. N is a noisy signal. Image deblurring can be viewed as the inverse process of image blurring, that is, the process of recovering the original image F from the observed image G. However, due to the presence of noise, image deblurring becomes an ill-conditioned inverse problem. To overcome the ill-conditioned nature of the deblurring problem itself, Total Variation (TV) regularization methods have attracted much attention from researchers. TV regularization methods require minimizing a cost function, and the model of this method is as follows:

[0007]

[0008] λ is an adjustment parameter, and ||·||2 and ||·||1 are the L2 and L1 norms, respectively. The image is stretched row-wise into a vector, still denoted as F; similarly, G is also a vector. This method can be further expressed as:

[0009]

[0010] In the formula, ||·|| represents the Frobenius norm, is the fidelity term, ||·||₁ represents the L1 norm, |MF|₁ is the discrete form of the total variation regularization term, is the L1 norm of the gradient of image F, and λ is a positive real number that adjusts the parameters before and after the two terms. This type of method can control the smoothness of the restored image and can better preserve the edge details of the image. The form of matrix M is derived as follows:

[0011] remember

[0012]

[0013] Introducing an auxiliary variable b transforms the problem into equation (6), where two optimization problems are solved alternately.

[0014]

[0015] make Its gradient is We obtain it using the nonnegative projected gradient method. The solution involves numerous sparse matrix multiplications in solving the aforementioned optimization problem. The method established in this invention maps these sparse matrix multiplications to image operations, thus enabling a rapid solution to the optimization problem. The minimization of b can be efficiently handled using soft thresholding since the objective function is completely separable.

[0016] This invention provides a fast deconvolution model based on Fussed Lasso, comprising the following steps:

[0017] Step 1: Data input, reading the observed image G<m×n> Convolution template T<(2p+1)×(2q+1)>, adjust parameter λ, adjust parameter μ;

[0018] Step 2 involves linearly transforming the range of pixel values ​​in the observed image and normalizing the convolution template signal.

[0019] Step 3 is fast sparse deconvolution restoration; the specific process is as follows:

[0020] Step 3.1 Initialization: Construct the initial values ​​F of the deconvolutioned image. 0 Construct an initial deconvolution image based on the template size and the observed image; Initial deconvolution image F 0 Its size is the row and column values ​​of the observed image minus the row and column values ​​of the template plus 1; construct the initial values. and It consists of zero matrices of size m×(n-1) and (m-1)×n. The parameter λ is adjusted.

[0021]

[0022] Step 3.2 Parameter setting: Set the total number of iterations K and the initial value of the adjustment parameter λ, and let t be the counter, initially t=1; Implement the first stage, the initial value of λ is 2, K=30, μ;

[0023] Step 3.3 minimizes F²(F), optimizing the solution to the problem, which is obtained using the nonnegative projective gradient method; its gradient is calculated according to the formula:

[0024]

[0025] In solving the above optimization problem, there are a large number of sparse matrix multiplication operations. By adopting the method established here, the multiplication of sparse matrices is mapped to image operations, thereby solving the optimization problem quickly.

[0026] S1 Deconvolution image F k The difference image R is obtained by convolving (k = 0, 1, 2, ..., K) with convolution kernel T and subtracting the observed image G, thus achieving AF. k -G;

[0027] The S2 convolution kernel T is flipped 180° and convolved with the difference image R. Then, the center of the result is taken and its value is taken. k Complete A with matrix blocks of the same size T (AF k -G);

[0028] The MF is implemented by calling L(F). L is a user-defined difference linear operator, and L(x) is defined as L(x) = (p, q), where,

[0029] p i,j =x i,j -x i+1,j ,1≤i≤n1-1,1≤j≤n2

[0030] qi,j =x i,j -x i,j+1 ,1≤i≤n1,1≤j≤n2-1

[0031] The above results were subjected to L T Operation L T (MF) realizes M T MF, L T The definition of (p,q) is

[0032] (L T (p,q)) i,j =(P(p)) i,j +(Q(p)) i,j

[0033] in,

[0034]

[0035] L for u T Operation, i.e., L T (u p ,u q ) Implement M T u k

[0036] L for b T Operation, i.e., L T (b p ,b q ) Implement M T b k

[0037] Calculate the gradient. That is, substitute the above results into... And correct it.

[0038]

[0039] Calculate the objective function value The formula is F. k It is the result of the calculation.

[0040]

[0041] in,‖·‖ F It is the Frobenius norm.

[0042] S3 Deconvolution image F k The difference, or MF, is the deconvolution of the image F. k Subtracting the previous column from the next column yields an m×(n-1) matrix M. (1) F and the deconvolutioned image F kSubtracting the previous row from the next row yields a (m-1)×n matrix M. (2) F.

[0043] S5 pairs and M is completed by performing the same transpose operation as S4. T u k and M T b k ;

[0044] S6. Substitute the above results into equation () to obtain the gradient of (), denoted as . And further gradient Elements in the matrix that are less than 0 or correspond to F k Elements with values ​​greater than 0 remain unchanged, while the rest are set to 0.

[0045]

[0046] S7 Calculates the optimal step size parameter based on the objective function. Find the optimal step length parameter along the descent direction of the echelon. Cumulative sum of errors;

[0047]

[0048] in,‖·‖ F For Frobenius norm (·) + Defined as (x) + =max{x,0};

[0049] S8 calculates β k , in

[0050] Find the deconvolution image F k The difference, or MF, is the deconvolution of the image F. k Subtracting the previous column from the next column yields an m×(n-1) matrix M. (1) F and the deconvolutioned image F k Subtracting the previous row from the next row yields a (m-1)×n matrix M. (2) F, and execute MF = MF + Θ × b

[0051]

[0052] k = k + 1

[0053] Step 3.4 minimizes F1(F), thus obtaining F k+1 And let F k+1 For the new F kIts implementation process uses an iterative threshold reduction algorithm to minimize the L1 norm, as detailed below:

[0054] F k+1 =A λ (β k )

[0055] F k =F k+1

[0056] Among them, A λ ([α1,α2,...,α n ] T )=[t λ (α 1) ),t λ (α2),...,t λ (α n )] T ,t λ (α i )=(|λ-α i |)sgn(α i ).

[0057] Step 3.5 determines whether t is less than K. If it is less than K, then t = t + 1, and proceed to step 3.3; otherwise, proceed to step 3.6. This stage can quickly remove noise and improve the deblurring effect.

[0058] Step 3.6 involves further sparse adjustment and restoration of the weighted L1 minimization model to obtain the final result.

[0059] The specific steps for further sparse adjustment and restoration of the weighted L1 minimization model are as follows:

[0060] S1 sets the convergence threshold ξ, the number of weighted adjustments p, and the number of sparse deconvolution deblurring operations q under each weighted adjustment, and sets the corresponding count variables m=1 and n=1. In this implementation, p is 10 and q is 30.

[0061] S2 in the already obtained F k Based on this, update the weight parameter λ(i,j). ε is a small positive decimal; S3 iteratively solves and updates F. k The method is the same as steps 3.3 to 3.4;

[0062] S4 checks if m is less than q. If it is less than q, then m = m + 1, and then proceed to step S3; otherwise, proceed to step S5.

[0063] S5 determines whether the convergence condition is met; here, we can set F at this point. k With F in step S2 kCheck if the 2-norm of the difference is less than a given threshold ξ, but not limited to this; if the condition is met, terminate the iteration and go to S7, otherwise proceed to step S6.

[0064] S6 checks if n is less than p. If it is less than p, then n = n + 1, and then proceed to step S2; otherwise, proceed to step S7.

[0065] S7 Let F = F k The output is the restored image F. In this stage, the L1 minimization model is improved and weighted threshold reduction is added, which can greatly improve the restoration effect. Attached Figure Description

[0066] Figure 1 This invention provides a flowchart of a fast deconvolution model for image super-resolution reconstruction.

[0067] Figure 2 It is the original high-resolution standard test grayscale image, the Lena image, in the example of this invention;

[0068] Figure 3 This is a degraded observation image with added noise after blurry downsampling in an example of the present invention;

[0069] Figure 4 This is the result image of super-resolution reconstruction and restoration in an example of the present invention. Detailed Implementation

[0070] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described herein are for illustrative and explanatory purposes only and are not intended to limit the scope of the invention. Figure 1 This invention provides a fast sparse deconvolutional two-dimensional image restoration method. The specific implementation is as follows:

[0071] Step 1: Data Input. Input the observed image and convolution template. This invention does not have special requirements for the convolution kernel and noise distribution; the following is just an example. For ease of effect comparison and performance evaluation, we will use the standard grayscale test image LENA, with a size of 256×256 pixels, as shown below. Figure 3 The observed image G obtained by convolving with template T and adding noise is as follows: Figure 4 The verification is performed as shown. The template used in this implementation is...

[0072]

[0073] Add Gaussian noise with a mean of 0 and a standard deviation of 0.03.

[0074] Step 2 involves linearly transforming the range of pixel values ​​in the observed image and normalizing the convolution template signal.

[0075] Step 3: Fast sparse deconvolution restoration process.

[0076] Step 3.1 Initialization. Construct the initial values ​​F of the deconvolutioned image. 0 An initial deconvolution image is constructed based on the template size and the observed image. The initial deconvolution image F 0 Its size is the row and column values ​​of the observed image minus the row and column values ​​of the template plus 1. Construct initial values. and It consists of zero matrices of size m×(n-1) and (m-1)×n. The parameter λ is adjusted.

[0077]

[0078] Step 3.2 Parameter Setting. Set the total number of iterations K and the initial value of the adjustment parameter λ, and let t be a counter, initially t=1. In the first stage, the initial value of λ is 2, K=30, and μ...

[0079] Step 3.3 Minimize F²(F). The solution to the optimization problem is obtained using the nonnegative projective gradient method. Its gradient is calculated according to the formula used in this implementation.

[0080]

[0081] Solving the aforementioned optimization problem involves numerous sparse matrix multiplication operations. The method established in this invention maps sparse matrix multiplication to image computation, thereby enabling a rapid solution to the aforementioned optimization problem.

[0082] The gradient projection algorithm, combined with the fast convolution algorithm disclosed in this invention, minimizes the L2 norm in the model. The algorithm implementation includes the following eight steps, S1 to S8:

[0083] S1 Deconvolution image F k The difference image R is obtained by convolving (k = 0, 1, 2, ..., K) with convolution kernel T and subtracting the observed image G, thus achieving AF. k -G;

[0084] The S2 convolution kernel T is flipped 180° and convolved with the difference image R. Then, the center of the result is taken and its value is taken. k The gradient of a matrix block of the same size is obtained to complete A. T (AF k -G);

[0085] S3 Deconvolution image F k The difference is called MF. That is, the deconvolution of the image F... k Subtracting the previous column from the next column yields an m×(n-1) matrix M. (1) F and the deconvolutioned image F kSubtracting the previous row from the next row yields a (m-1)×n matrix M. (2) F

[0086] S4 completes the transpose of M and the multiplication of MF, i.e., M T MF. A new m×n matrix, M, is generated. (1) T M (1) F, the first and nth columns of this matrix are respectively the S3 matrix M (1) F is the opposite of the first column and M is the sum of the numbers. (1) The (n-1)th column of F, and the middle columns 2 to (n-1)th columns are M. (1) Subtract the next column from the first column of F. This generates a new m×n matrix, M. (2) T M (2) F, the first and nth rows of this matrix are respectively the S3 matrix M (2) F is the opposite of the first row and M is the sum of the numbers. (2) The (n-1)th line of F, and the middle lines 2 to (n-1)th lines of M. (2) Subtract the next row from the first row of F. Then, subtract the first row from the second row of matrix M. (1) T M (1) F and M (2) T M (2) The summation of F completes M. T MF.

[0087] S5 pairs and M is completed by performing the same transpose operation as S4. T u k and M T b k .

[0088] S6. Substitute the above results into equation () to obtain the gradient of (), denoted as . And further gradient Elements in the matrix that are less than 0 or correspond to F k Elements with values ​​greater than 0 remain unchanged, while the rest are set to 0.

[0089]

[0090] S7 Calculates the optimal step size parameter based on the objective function. Find the optimal step length parameter along the descent direction of the echelon. The objective function is the cumulative error summation.

[0091]

[0092] in,‖·‖ FFor Frobenius norm (·) + Defined as (x) + = max{x, 0}.

[0093] S8 calculates β k , in

[0094] Find the deconvolution image F k The difference is called MF. That is, the deconvolution of the image F... k Subtracting the previous column from the next column yields an m×(n-1) matrix M. (1) F and the deconvolutioned image F k Subtracting the previous row from the next row yields a (m-1)×n matrix M. (2) F. And execute MF = MF + Θ × b

[0095]

[0096] k = k + 1

[0097] Step 3.4 minimizes F1(F), thus obtaining F k+1 And let F k+1 For the new F k The implementation process employs an iterative threshold reduction algorithm to minimize the L1 norm, as detailed below:

[0098] F k+1 =A λ (β k )

[0099] F k =F k+1

[0100] Among them, A λ ([α1,α2,…,α n ] T )=[t λ (α 1) ),t λ (α2),…,t λ (α n )] T ,t λ (α i )=(|λ-α i |)sgn(α i ).

[0101] Step 3.5 determines if t is less than K. If it is less than K, then t = t + 1, and proceed to step 3.3; otherwise, proceed to step 3.6. This stage can quickly remove noise and significantly improve the deblurring effect.

[0102] Step 3.6 involves further sparse adjustment and restoration of the weighted L1 minimization model to obtain the final result.

[0103] S1 sets the convergence threshold ξ, the number of weighted adjustments p, and the number of sparse deconvolution deblurring operations q for each weighted adjustment, and sets the corresponding count variables m=1 and n=1. In this implementation, p is 10 and q is 30.

[0104] S2 in the already obtained F k Update the weight parameter λ(i,j) based on the existing parameters. ε is a small positive decimal.

[0105] S3 Iterative solution to update F k The method is the same as steps 3.3 to 3.4.

[0106] S4 checks if m is less than q. If it is less than q, then m = m + 1, and then proceed to step S3; otherwise, proceed to step S5.

[0107] S5 determines whether the convergence condition is met. Here, we can assume that F is satisfied at this time. k With F in step S2 k Check if the 2-norm of the difference is less than a given threshold ξ, but not limited to this. If the condition is met, terminate the iteration and go to S7; otherwise, proceed to step S6.

[0108] S6 determines whether n is less than p. If it is less than p, then n = n + 1, and then proceed to step S2; otherwise, proceed to step S7.

[0109] S7 Let F = F k The restored image F is output. The restored image is shown in the figure. In this stage, the L1 minimization model is improved by adding weighted threshold reduction, which can greatly improve the restoration effect.

[0110] The above description is merely a preferred embodiment of the present invention, but the present invention should not be limited to the content disclosed in this embodiment and the accompanying drawings. Therefore, any equivalent or modified versions made without departing from the spirit of the present invention fall within the scope of protection of the present invention.

Claims

1. A fast deconvolution model based on Fussed Lasso, characterized in that, Includes the following steps: Step 1, Data Input, Read the Observed Image G<m×n> Convolution template T<(2p+1)×(2q+1)>, adjust parameter λ, adjust parameter μ; Step 2: Linearly transform the range of pixel values ​​in the observed image and normalize the convolution template signal; Step 3, fast sparse deconvolution restoration processing; the specific process is as follows: Step 3.1 Initialization: Construct the initial values ​​F of the deconvolutioned image. 0 Construct an initial deconvolution image based on the template size and the observed image; Initial deconvolution image F 0 Its size is the row and column values ​​of the observed image minus the row and column values ​​of the template plus 1; construct the initial values. and Its size is m×(n-1) and (m-1)×n zero matrices, with the parameter λ adjusted. Step 3.2 Parameter setting: Set the total number of iterations K and the initial value of the adjustment parameter λ, and let t be the counter, initially t=1; Implement the first stage, the initial value of λ is 2, K=30, μ; Step 3.3 minimizes F²(F), optimizing the solution to the problem, which is obtained using the nonnegative projective gradient method; its gradient is calculated according to the formula: In solving the above optimization problem, there are a large number of sparse matrix multiplication operations. By adopting the method established here, the multiplication of sparse matrices is mapped to image operations, thereby solving the optimization problem quickly. Step 3.4 minimizes F1(F), thus obtaining F k+1 And let F k+1 For the new F k Its implementation process uses an iterative threshold reduction algorithm to minimize the L1 norm, as detailed below: F k+1 =A λ (b k ) F k =F k+1 Among them, A λ ([a1,a2,...,a n ] T )=[t λ (a 1) ),t λ (a2),...,t λ (a n )] T ,t λ (a i )=(|λ-a i |)sgn(a i ); Step 3.5 determines whether t is less than K. If it is less than K, then t = t + 1, and proceed to step 3.3; otherwise, proceed to step 3.

6. This stage can quickly remove noise and improve the deblurring effect. Step 3.6 involves further sparse adjustment and restoration of the weighted L1 minimization model to obtain the final result.

2. The fast deconvolution model based on Fussed Lasso according to claim 1, characterized in that: In step 3.3, the gradient projection algorithm, combined with the fast convolution algorithm disclosed in this invention, minimizes the L2 norm in the model. The algorithm implementation includes the following eight steps, S1 to S8: S1 Deconvolution image F k The difference image R is obtained by convolving (k = 0, 1, 2, ..., K) with convolution kernel T and subtracting the observed image G, thus achieving AF. k -G; The S2 convolution kernel T is flipped 180° and convolved with the difference image R. Then, the center of the result is taken and its value is taken. k The gradient of a matrix block of the same size is obtained to complete A. T (AF k -G); S3 Deconvolution image F k The difference, or MF, is the deconvolution of the image F. k Subtracting the previous column from the next column yields an m×(n-1) matrix M. (1) F and the deconvolutioned image F k Subtracting the previous row from the next row yields a (m-1)×n matrix M. (2) F; S4 completes the transpose of M and the multiplication of MF, i.e., M T MF, generates a new m×n matrix, i.e., M. (1) T M (1) F, the first and nth columns of this matrix are respectively the S3 matrix M (1) F is the opposite of the first column and M is the sum of the numbers. (1) The (n-1)th column of F, and the middle columns 2 to (n-1)th columns are M. (1) Subtracting the next column from the first column of F generates a new m×n matrix, M. (2) T M (2) F, the first and nth rows of this matrix are respectively the S3 matrix M (2) F is the opposite of the first row and M is the sum of the numbers. (2) The (n-1)th line of F, and the middle lines 2 to (n-1)th lines of M. (2) Subtract the next row from the first row of F to obtain matrix M. (1) T M (1) F and M (2) T M (2) The summation of F completes M. T MF; S5 pairs and M is completed by performing the same transpose operation as S4. T u k and M T b k ; S6 substitutes the above results into equation () to obtain the gradient of (), denoted as . And further gradient Elements in the matrix that are less than 0 or correspond to F k Elements with values ​​greater than 0 remain unchanged, while the rest are set to 0. S7 Calculates the optimal step size parameter based on the objective function. Find the optimal step length parameter along the descent direction of the echelon. Cumulative sum of errors; in,‖·‖ F For Frobenius norm (·) + Defined as (x) + =max{x,0} S8 calculates β k , in Find the deconvolution image F k The difference, or MF, is the deconvolution of the image F. k Subtracting the previous column from the next column yields an m×(n-1) matrix M. (1) F and the deconvolutioned image F k Subtracting the previous row from the next row yields a (m-1)×n matrix M. (2) F, and execute MF = MF + Θ × b; k = k + 1.

3. The fast deconvolution model based on Fussed Lasso according to claim 2, characterized in that: In step S1, the fast convolution operation in the spatial domain of a two-dimensional image is as follows: ① Find the size of the two-dimensional image F, expressed as m×n, and the size of the convolution template T, expressed as (2p+1)×(2q+1), where p and q can be decimals; ② Set the initial value ConF of the convolution result, where ConF is a zero matrix of size (m+2p)×(n+2q); ③ Select elements F(i,j) (1≤i≤m,1≤j≤n) from the two-dimensional image matrix F in sequence and multiply them with the template T; Then, the product is added to the corresponding modules in ConF with rows i to i+2p and columns j to j+2q to obtain a new ConF; ④ Repeat step ③ until all elements in F have completed the operation of step ③; ⑤ Output the convolution result ConF of F and T.

4. The fast deconvolution model based on Fussed Lasso according to claim 2, characterized in that: In step S2, L(F) is called to implement MF, where L is a user-defined difference linear operator, and L(x) is defined as L(x) = (p, q), where... p i,j =x i,j -x i+1,j ,1≤i≤n1-1,1≤j≤n2 q i,j =x i,j -x i,j+1 ,1≤i≤n1,1≤j≤n2-1 The above results were subjected to L T Operation L T (MF) implements M T MF, L T (p,q) is defined as (L T (p,q)) i,j =(P(p)) i,j +(Q(p)) i,j in, L for u T Operation, i.e., L T (u p ,u q ) Implement M T u k ; L for b T Operation, i.e., L T (b p ,b q ) Implement M T b k ; Calculate the gradient, that is, substitute the above results into... And correct it; Calculate the objective function value It is the formula (), F is F k It is the result of the calculation; in,‖·‖ F It is the Frobenius norm.

5. The fast deconvolution model based on Fussed Lasso according to claim 1, characterized in that: In step 3.6, the specific steps for further sparse adjustment and restoration of the weighted L1 minimization model are as follows: S1 sets the convergence threshold ξ, the number of weighted adjustments p, and the number of sparse deconvolution deblurring operations q under each weighted adjustment, and sets the corresponding count variables m=1 and n=1. In this implementation, p is 10 and q is 30. S2 in the already obtained F k Based on this, update the weight parameter λ(i,j). ε is a small positive decimal; S3 Iterative solution to update F k The method is the same as steps 3.3 to 3.4; S4 checks if m is less than q. If it is less than q, then m = m + 1, and then proceed to step S3; otherwise, proceed to step S5. S5 determines whether the convergence condition is met; here, we can set F at this point. k With F in step S2 k Check if the 2-norm of the difference is less than a given threshold ξ, but not limited to this; if the condition is met, terminate the iteration and go to S7, otherwise proceed to step S6. S6 checks if n is less than p. If it is less than p, then n = n + 1, and then proceed to step S2. Otherwise, proceed to step S7; S7 Let F = F k The output is the restored image F. In this stage, the L1 minimization model is improved and weighted threshold reduction is added, which can greatly improve the restoration effect.

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