Image denoising method and device based on adaptive group sparse residual model
By constructing the adaptive group sparse residual model and iterative processing, the problem of complex calculation of sparse coefficient prediction of sparse residual model is solved, and efficient image denoising effect is achieved.
Patent Information
- Application Number
- CN202510059068.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-15
- Publication Date
- 2025-05-13
AI Technical Summary
The existing sparse residual model has complex estimates for calculating sparse coefficients during image denoising, which increases the computational burden and may limit the denoising performance.
The image denoising method based on the adaptive group sparse residual model is adopted. By constructing the adaptive group sparse residual model, similar image block groups are denoised, and the iterative mechanism is used to optimize the denoising effect.
While ensuring the denoising effect, the calculation complexity is reduced, the accuracy and efficiency of sparse coefficient prediction are improved, and the denoising performance is significantly improved.
Smart Images
Figure CN119991480A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of digital image processing, and in particular to an image denoising method and device based on an adaptive group sparse residual model. Background Art
[0002] Image denoising is a key technology in the field of image processing. Its core goal is to reconstruct the original high-quality image from the observed noisy image as much as possible. However, the image denoising problem is essentially an ill-posed inverse problem, that is, the input data (noise image) is not sufficient to uniquely determine the output data (original image), which leads to multiple possible solutions in the solution space. In order to obtain a stable and expected solution, it is usually necessary to introduce an image prior model to regularize the solution space.
[0003] Among the many prior models for image denoising, sparse models have attracted much attention due to their powerful expressiveness and flexibility. Sparse models believe that natural images can be represented by a linear combination of a set of overcomplete dictionary atoms, and this representation is sparse, that is, only a few dictionary atoms make important contributions to the representation of the image. However, due to the interference of noise, traditional sparse models are difficult to effectively estimate sparse coefficients, which limits the potential of the model and the performance of the algorithm. In order to overcome the limitations of traditional sparse models, sparse residual models came into being. Different from the traditional method of directly estimating sparse coefficients, sparse residual models achieve denoising by minimizing the error between potential sparse coefficients and pre-estimated sparse coefficients, so they have better denoising performance.
[0004] However, although the sparse residual model has achieved remarkable results in image denoising, its practical application still faces some challenges. Among them, how to effectively calculate the estimated sparse coefficients is one of the core issues of the sparse residual model. Existing technologies usually calculate the estimated sparse coefficients by designing complex estimation strategies, which not only increases the computational burden but also may limit the denoising performance of the model. Therefore, how to reduce the computational complexity and improve the accuracy and efficiency of the sparse coefficients estimated while ensuring the denoising effect has become a key issue that needs to be solved in the current sparse residual model in the field of image denoising. Summary of the invention
[0005] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is to provide an image denoising method and device based on an adaptive group sparse residual model, which can reduce the computational complexity while ensuring the image denoising effect.
[0006] In order to solve the above technical problems, a technical solution adopted by the present invention is: to provide an image denoising method based on an adaptive group sparse residual model, comprising the following steps:
[0007] Initialize the denoised image and set the number of iterations, which is the total number of rounds of the algorithm;
[0008] Constructing an adaptive group sparse residual model, constructing a similar image block group matrix and constructing an adaptive group sparse residual model corresponding to each similar image block group matrix;
[0009] Denoising a group of similar image blocks using the adaptive group sparse residual model;
[0010] Reconstruct the entire image based on all denoised similar image block groups;
[0011] Return to the step of building the adaptive group sparse residual model until the set number of iterations is reached and output the final denoised image.
[0012] Furthermore, in the step of initializing the denoised image and setting the number of iterations, the method for initializing the denoised image includes: adding zero-mean Gaussian white noise to the original image without noise pollution to obtain an observed noise image, and setting the initial value of the denoised image to the observed noise image.
[0013] Furthermore, the steps of constructing a similar image block group matrix and constructing a corresponding adaptive group sparse residual model for each similar image block group matrix include the following sub-steps:
[0014] Divide the current denoised image into blocks;
[0015] Block matching based on Euclidean distance searches for several image blocks with similar structures for each image block to form a similar image block group matrix;
[0016] For each similar image block group matrix, a corresponding adaptive group sparse residual model is constructed.
[0017] Furthermore, the similar image block group matrix is expressed as:
[0018]
[0019] In formula (1), Represents the similarity group matrix of the image block of the current denoised image, z k-1 represents the current denoised image, k represents the number of iterations, k = 1, 2, 3..., K, R i,j represents the jth similar image block extraction matrix, n represents each image block There are n image patches with similar structures;
[0020] The adaptive group sparse residual model is expressed as:
[0021]
[0022] In formula (II), A i represents the potential group sparseness coefficient, B i represents the estimated group sparse coefficient, D i Represents a dictionary, v i Indicates A i and B i The standard deviation of the error between i represents the regularization parameter vector, and σ represents the standard deviation of zero-mean Gaussian white noise.
[0023] Furthermore, the step of denoising the similar image block group using the adaptive group sparse residual model includes the following sub-steps:
[0024] Learning a dictionary D for groups of similar image patches via principal component analysis i ;
[0025] Fix the potential group sparsity factor A i , calculate the estimated group sparse coefficient B i ;
[0026] Based on the estimated B of the group sparse coefficients i , update the potential group sparse coefficient A i ;
[0027] Based on the learned dictionary D i and the potential group sparsity coefficient A of similar block groups i Reconstruct the similar image block group to obtain the denoised similar image block group.
[0028] Furthermore, when the potential group sparsity coefficient A is fixed i , calculate the estimated group sparse coefficient B i In the steps, set Pre-estimate of the group sparse word coefficients B i Obtained by the following formula:
[0029]
[0030] By calculation, we can get B in formula (III) i The closed-form solution is:
[0031]
[0032] In formula (IV), 1 represents a column vector whose elements are all 1;
[0033] Based on the pre-estimation of the group sparse coefficients B i , update the potential group sparse coefficient A i In the step of i Obtained by the following formula:
[0034]
[0035] By calculation, we can get A in formula (5) i The closed-form solution is:
[0036]
[0037] In formula (6),
[0038] Furthermore, based on the learned dictionary D i and the potential group sparsity coefficient A of similar block groups i In the step of reconstructing a similar image block group to obtain a denoised similar image block group, the method for reconstructing a similar image block group includes: i and the potential group sparsity coefficient A of similar block groups i Multiply them to get the denoised similar image block group.
[0039] Furthermore, in the step of reconstructing the entire image based on the denoised similar image block group, the objective function of reconstructing the entire image is:
[0040]
[0041] In formula (VII), z k represents the entire reconstructed image, that is, the denoised image output by the kth iteration, x represents the observed noisy image, z represents the original image without noise pollution, and R i (z)=[R i,1 z,…,R i,j z,…,R i,n z],R i (·) represents the matrix extraction operation of similar image block groups, and η represents a positive constant;
[0042] By calculation, we can get z in formula (VII) k The closed-form solution is:
[0043]
[0044] In formula (8), I represents the unit matrix, express The jth column of .
[0045] In order to solve the above technical problems, another technical solution adopted by the present invention is to provide an image denoising device based on an adaptive group sparse residual model, comprising:
[0046] An initialization module is used to initialize the denoised image and set the number of iterations, which is the total number of rounds of the algorithm;
[0047] A model building module is used to build an adaptive group sparse residual model, build a similar image block group matrix and build an adaptive group sparse residual model corresponding to each similar image block group matrix;
[0048] A denoising module, used for denoising a group of similar image blocks using the adaptive group sparse residual model;
[0049] A reconstruction module, used to reconstruct the entire image based on all denoised similar image block groups;
[0050] The output module is used to output the final denoised image when the set number of iterations is reached.
[0051] Furthermore, the model building module includes:
[0052] A block submodule, used to divide the current denoised image into blocks;
[0053] The block group matrix construction submodule is used to search for a number of image blocks with similar structures for each image block based on block matching of Euclidean distance to form a similar image block group matrix;
[0054] The model building submodule is used to build an adaptive group sparse residual model corresponding to each similar image block group matrix.
[0055] The image denoising method and device based on the adaptive group sparse residual model of the present invention have at least the following beneficial effects: by constructing an adaptive group sparse residual model, the present invention not only focuses on the sparse representation of the image, but also further considers the error between the sparse representation and a certain pre-estimation, namely, the sparse residual, thereby achieving better reconstruction of the image texture details and providing a high-quality denoised image; in terms of the pre-estimation of the sparse coefficient, by incorporating the pre-estimation of the group sparse coefficient into the sparse residual model and using similar image block groups for adaptive estimation, it is not only possible to more accurately capture the similarity and structural information within the image, which helps to improve the algorithm's sensitivity and accuracy to the image content and improve the denoising effect, but also reduces additional calculation steps and parameter tuning, simplifies the estimation process, and significantly improves the efficiency of the algorithm; through iterative processing, the image data can be gradually adjusted to optimize the denoising effect. This iterative mechanism enables the algorithm to adapt to images with different noise levels and achieve a satisfactory denoising effect by adjusting the number of iterations. BRIEF DESCRIPTION OF THE DRAWINGS
[0056] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:
[0057] Figure 1The figure is a flowchart of an embodiment of an image denoising method based on an adaptive group sparse residual model of the present invention.
[0058] Figure 2 for Figure 1 Flowchart of step S2 in FIG.
[0059] Figure 3 for Figure 1 Flow chart of step S3 in FIG.
[0060] Figure 4 It is a structural block diagram of an embodiment of an image denoising device based on an adaptive group sparse residual model of the present invention. DETAILED DESCRIPTION
[0061] The present invention will be further described below in conjunction with the accompanying drawings.
[0062] See also Figure 1 , is a flow chart of an embodiment of an image denoising method based on an adaptive group sparse residual model of the present invention. This embodiment may specifically include the following steps:
[0063] S1. Initialize the denoised image and set the number of iterations.
[0064] Specifically, the method for initializing the denoised image includes: adding zero-mean Gaussian white noise to the original image without noise pollution to obtain an observed noise image, and setting the initial value of the denoised image to the observed noise image. 0 =x, where x represents the observed noisy image, x=z+e, where z represents the original image without noise pollution, and e represents zero-mean Gaussian white noise with a standard deviation of σ. The number of iterations is the total number of rounds of the algorithm, and the number of iterations k=1, 2, 3, ..., K. The appropriate number of iterations can be set based on experience to achieve the desired denoising effect.
[0065] S2. Construct an adaptive group sparse residual model.
[0066] Specifically, a similar image block group matrix is constructed and a corresponding adaptive group sparse residual model is constructed for each similar image block group matrix. Figure 2 , this step S2 may include the following sub-steps:
[0067] S21, dividing the current denoised image into blocks.
[0068] Specifically, the current denoised image is divided into a plurality of small blocks, each of which contains a certain number of pixels.
[0069] S22, constructing a similar image block matrix.
[0070] Specifically, the block matching based on Euclidean distance searches for a number of image blocks with similar structures for each image block to form a similar image block group matrix, and uses the block group as the basic processing unit to process each block group independently. The similar image block group matrix is expressed as:
[0071]
[0072] in, Represents the similar image block group matrix of the image block of the current denoised image, k represents the number of iterations, z k-1 represents the current denoised image, k-1 is because when the kth processing is performed, the denoised image output by the k-1th iteration is processed, and R i,j represents the jth similar image block extraction matrix, n represents each image block There are n image blocks with similar structures, and i represents the index of the similar image block group.
[0073] S23. Construct an adaptive group sparse residual model corresponding to the similar image block matrix.
[0074] Specifically, for each similar image block group matrix, a corresponding adaptive group sparse residual model is constructed. The adaptive group sparse residual model is expressed as:
[0075]
[0076] Among them, A i represents the potential group sparseness coefficient, B i represents the estimated group sparse coefficient, D i Represents a dictionary, v i Indicates A i and B i The standard deviation of the error between i represents the regularization parameter vector, and σ represents the standard deviation of zero-mean Gaussian white noise.
[0077] S3, denoising similar image block groups.
[0078] Specifically, the adaptive group sparse residual model is used to denoise the similar image block group. Figure 3 , this step S3 may include the following sub-steps:
[0079] S31, learning a dictionary for similar image block groups.
[0080] Specifically, we learn a dictionary D for similar image blocks through principal component analysis. i. In order to effectively represent and denoise similar image block groups, we need to learn a dictionary. In this embodiment, similar image block groups are used as input data, and the principal component analysis (PCA) method is used to learn a dictionary, which will be used in the subsequent sparse representation and denoising process. PCA is a data dimensionality reduction and feature extraction technology that can construct a low-dimensional dictionary by finding the main components (i.e., eigenvectors) in the data.
[0081] S32. Calculate an estimate of the group sparse coefficient.
[0082] Specifically, fix the potential group sparsity coefficient A i , calculate the estimated group sparse coefficient B i .set up Pre-estimate of group sparse coefficient B i The calculation formula is as follows:
[0083]
[0084] By calculating B i The closed-form solution is:
[0085]
[0086] Here, 1 represents a column vector whose elements are all 1.
[0087] S33. Update the potential group sparsity coefficient.
[0088] Specifically, based on the estimated B of the group sparse coefficients i , update the potential group sparse coefficient A i , the updated A i The calculation formula is as follows:
[0089]
[0090] By calculating A i The closed-form solution is:
[0091]
[0092] in,
[0093] In the existing sparse residual model, the potential group sparse coefficient is estimated by pre-estimating the group sparse coefficient, and the existing methods are to design some complex weighting strategies or use some external knowledge to obtain the pre-estimation of the group sparse coefficient. iIncorporating it into the sparse residual model and using similar image block groups for direct adaptive estimation can more accurately capture the similarity and structural information within the image, which helps to improve the algorithm's sensitivity and accuracy to image content, thereby improving the denoising effect. The method of directly using the original image block group for estimation reduces additional calculation steps and parameter tuning, simplifies the estimation process, and improves the efficiency and operability of the algorithm.
[0094] S34: Reconstruct similar image block groups.
[0095] Specifically, based on the learned dictionary D i and the potential group sparsity coefficient A of similar block groups i Reconstruct the similar image block group to obtain the denoised similar image block group. i and the potential group sparsity coefficient A of similar image blocks i Multiply them to get the denoised similar image block group, that is, in, Represents a group of similar image blocks after reconstruction.
[0096] S4. Reconstruct the entire image.
[0097] Specifically, the entire image is reconstructed based on all denoised similar image block groups, and the objective function of reconstructing the entire image is expressed as:
[0098]
[0099] Among them, z k represents the entire reconstructed image, that is, the denoised image output by the kth iteration, x represents the observed noisy image, z represents the original image without noise pollution, and R i (z)=[R i,1 z,…,R i,j z,…,R i,n z],R i (·) represents the matrix extraction operation of similar image block groups, and η represents a positive constant;
[0100] By calculating z k The closed-form solution is:
[0101]
[0102] Where I represents the identity matrix, express The jth column of .
[0103] S5. Repeat the iteration and output the denoised image.
[0104] Specifically, steps S2 to S4 are iteratively executed until the set number of iterations (i.e., k=K) is reached, and the final denoised image is output. A single denoising process may not be able to completely remove all noise in the image. Through multiple iterations, the algorithm can cumulatively remove noise, and each iteration may further reduce the residual noise, thereby improving the overall denoising effect. Through iterative processing, the algorithm can gradually adjust the image data so that it gradually approaches an optimal solution, that is, a state in which the noise is minimized and the image details are preserved. Different images may contain different levels of noise, and the number of iterations can be adjusted according to actual conditions to adapt to images with different noise levels. For example, for images with higher noise levels, more iterations can be set to achieve a satisfactory denoising effect.
[0105] The denoising effect of this embodiment is further illustrated by the following simulation experiment.
[0106] 1. Simulation conditions:
[0107] The simulation experiment of the present invention was carried out in the Matlab 2019a environment under Windows 10 system.
[0108] 2. Simulation results and analysis:
[0109] Two existing sparse residual model denoising techniques are used for denoising. The existing GSRCNLP technology comes from the article "Groupsparsity residual constraint with non-local priors for image restoration" (IEEE Transactions on Image Processing, 2020, 29: 8960-8975); the existing NSSRC technology comes from the article "Nonconvex structural sparsity residual constraint for image restoration" (IEEE Transactions on Cybernetics, 2021, 52 (11): 12440-12453). The GSRCNLP method will over-smooth the image, while the NSSRC method has limited ability to reconstruct texture details. In contrast, the image denoising method based on the adaptive group sparse residual model of the present invention can better reconstruct image texture details. Table 1 shows the denoising time of the image denoising method based on the adaptive group sparse residual model of the present invention and two existing denoising methods (GSRCNLP and NSSRC) for an image of size 256×256 when σ=50. It can be seen from Table 1 that the time efficiency of the image denoising method based on the adaptive group sparse residual model of the present invention is much better than that of the GSRCNLP and NSSRC methods.
[0110]
[0111] Table 1
[0112] It can be seen that the image denoising method based on the adaptive group sparse residual model of the present invention overcomes the problems of poor image denoising performance and efficiency in the prior art, and improves the performance and efficiency of image denoising.
[0113] See also Figure 4 , is a structural block diagram of an embodiment of an image denoising device based on an adaptive group sparse residual model of the present invention. The image denoising device based on an adaptive group sparse residual model of this embodiment is used to implement the image denoising method based on an adaptive group sparse residual model as described in the above embodiment. Specifically, the image denoising device based on an adaptive group sparse residual model of this embodiment includes an initialization module 100, a model building module 200, a denoising module 300, a reconstruction module 400 and an output module 500.
[0114] in:
[0115] The initialization module 100 is used to initialize the denoised image and set the number of iterations. The number of iterations is the total number of rounds of the algorithm, and the number of iterations k=1, 2, 3, ..., K. The appropriate number of iterations can be set based on experience to achieve the desired denoising effect.
[0116] The model construction module 200 is used to construct an adaptive group sparse residual model, construct a similar image block group matrix and construct a corresponding adaptive group sparse residual model for each similar image block group matrix. Specifically, the model construction module of this embodiment includes a block submodule 210, a block group matrix construction submodule 220 and a model construction submodule 230. Among them: the block submodule 210 is used to block the current denoised image. The block group matrix construction submodule 220 is used to search for a number of image blocks with similar structures for each image block based on block matching of Euclidean distance to form a similar image block group matrix. The model construction submodule 230 is used to construct a corresponding adaptive group sparse residual model for each similar image block group matrix obtained by the block group matrix construction submodule 220.
[0117] The denoising module 300 is used to denoise the similar image block group using the adaptive group sparse residual model constructed by the model construction module 200. Incorporating the pre-estimation of the group sparse coefficient into the sparse residual model and directly performing adaptive estimation using the similar image block group can more accurately capture the similarity and structural information inside the image, which helps to improve the sensitivity and accuracy of the algorithm to the image content, thereby improving the denoising effect. At the same time, the estimation process is simplified, and the efficiency and operability of the algorithm are improved.
[0118] The reconstruction module 400 is used to reconstruct the entire image based on all the denoised similar image block groups obtained by the denoising module 300. After the entire image is reconstructed, the reconstructed image is once again input into the model building module 200, and the iteration is repeated to further perform denoising.
[0119] The output module 500 is used to output the final denoised image when a set number of iterations is reached.
[0120] The present invention not only focuses on the sparse representation of the image by constructing an adaptive group sparse residual model, but also further considers the error between the sparse representation and a certain pre-estimation, namely, the sparse residual, thereby achieving better reconstruction of the image texture details and providing a high-quality denoised image; in terms of the pre-estimation of the sparse coefficient, by incorporating the pre-estimation of the group sparse coefficient into the sparse residual model and using similar image block groups for adaptive estimation, it can not only more accurately capture the similarity and structural information inside the image, which helps to improve the algorithm's sensitivity and accuracy to the image content and improve the denoising effect, but also reduces additional calculation steps and parameter tuning, simplifies the estimation process, and significantly improves the efficiency of the algorithm; through iterative processing, the image data can be gradually adjusted to optimize the denoising effect. This iterative mechanism enables the algorithm to adapt to images with different noise levels and achieve a satisfactory denoising effect by adjusting the number of iterations.
[0121] The above content only expresses the preferred embodiments of the present invention, and its description is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached claims.
Claims
1. An image denoising method based on an adaptive group sparse residual model, characterized in that: The following steps are involved: Initialize the denoised image and set the number of iterations, which is the total number of rounds of the algorithm; Constructing an adaptive group sparse residual model, constructing a similar image block group matrix and constructing an adaptive group sparse residual model corresponding to each similar image block group matrix; Denoising a group of similar image blocks using the adaptive group sparse residual model; Reconstruct the entire image based on all denoised similar image block groups; Return to the step of building the adaptive group sparse residual model until the set number of iterations is reached and output the final denoised image.
2. The image denoising method based on the adaptive group sparse residual model according to claim 1, characterized in that: In the step of initializing the denoised image and setting the number of iterations, the method for initializing the denoised image includes: adding zero-mean Gaussian white noise to the original image without noise pollution to obtain an observed noise image, and setting the initial value of the denoised image to the observed noise image.
3. The image denoising method based on the adaptive group sparse residual model according to claim 2, characterized in that: The steps of constructing a similar image block group matrix and constructing a corresponding adaptive group sparse residual model for each similar image block group matrix include the following sub-steps: Divide the current denoised image into blocks; Block matching based on Euclidean distance searches for several image blocks with similar structures for each image block to form a similar image block group matrix; For each similar image block group matrix, a corresponding adaptive group sparse residual model is constructed.
4. The image denoising method based on the adaptive group sparse residual model according to claim 3, characterized in that: The similar image block group matrix is expressed as: In formula (1), Represents the similarity group matrix of the image block of the current denoised image, z k-1 represents the current denoised image, k represents the number of iterations, k = 1, 2, 3…, K, R i,j represents the jth similar image block extraction matrix, n represents each image block There are n image patches with similar structures; The adaptive group sparse residual model is expressed as: In formula (II), A i represents the potential group sparseness coefficient, B i represents the estimated group sparse coefficient, D i Represents a dictionary, v i Indicates A i and B i The standard deviation of the error between i represents the regularization parameter vector, and σ represents the standard deviation of zero-mean Gaussian white noise.
5. The image denoising method based on the adaptive group sparse residual model according to claim 4, characterized in that: The step of denoising a group of similar image blocks by using the adaptive group sparse residual model includes the following sub-steps: Learning a dictionary D for groups of similar image patches via principal component analysis i ; Fix the potential group sparsity factor A i , calculate the estimated group sparse coefficient B i ; Based on the estimated B of the group sparse coefficients i , update the potential group sparse coefficient A i ; Based on the learned dictionary D i and the potential group sparsity coefficient A of similar block groups i Reconstruct the similar image block group to obtain the denoised similar image block group.
6. The image denoising method based on the adaptive group sparse residual model according to claim 5, characterized in that: With a fixed latent group sparsity coefficient A i , calculate the estimated group sparse coefficient B i In the steps, set Pre-estimate of group sparse coefficient B i Obtained by the following formula: By calculation, we can get B in formula (III) i The closed-form solution is: In formula (IV), 1 represents a column vector whose elements are all 1; Based on the pre-estimation of the group sparse coefficients B i , update the potential group sparse coefficient A i In the step of i Obtained by the following formula: By calculation, we can get A in formula (5) i The closed-form solution is: In formula (6), 7. The image denoising method based on the adaptive group sparse residual model according to claim 6, characterized in that: Based on the learned dictionary D i and the potential group sparsity coefficient A of similar block groups i In the step of reconstructing a similar image block group to obtain a denoised similar image block group, the method for reconstructing a similar image block group includes: i and the potential group sparsity coefficient A of similar block groups i Multiply them together to get the denoised similar image block group.
8. The image denoising method based on the adaptive group sparse residual model according to claim 7, characterized in that: In the step of reconstructing the entire image based on the denoised similar image block group, the objective function of reconstructing the entire image is: In formula (VII), z k represents the entire reconstructed image, that is, the denoised image output by the kth iteration, x represents the observed noisy image, z represents the original image without noise pollution, and R i (z)=[R i,1 z,…,R i,j z,…,R i,n z],R i (·) represents the matrix extraction operation of similar image block groups, and η represents a positive constant; By calculation, we can get z in formula (VII) k The closed-form solution is: In formula (8), I represents the unit matrix, express The jth column of .
9. An image denoising device based on an adaptive group sparse residual model, characterized in that: include: An initialization module is used to initialize the denoised image and set the number of iterations, which is the total number of rounds of the algorithm; A model building module is used to build an adaptive group sparse residual model, build a similar image block group matrix and build an adaptive group sparse residual model corresponding to each similar image block group matrix; A denoising module, used for denoising a group of similar image blocks using the adaptive group sparse residual model; A reconstruction module, used to reconstruct the entire image based on all denoised similar image block groups; The output module is used to output the final denoised image when the set number of iterations is reached.
10. The image denoising device based on the adaptive group sparse residual model according to claim 9, characterized in that: The model building module includes: A block submodule, used to divide the current denoised image into blocks; The block group matrix construction submodule is used to search for a number of image blocks with similar structures for each image block based on block matching of Euclidean distance to form a similar image block group matrix; The model building submodule is used to build an adaptive group sparse residual model corresponding to each similar image block group matrix.