Image restoration method

Abstract

The invention discloses an image restoration method, and belongs to the technical field of image processing, and the method comprises the steps: obtaining a first vector, so as to build a target function of an image restoration model; the first vector is formed by stretching a to-be-restored image; according to the plug-and-play precondition Kranoselski-Mann algorithm, an objective function is divided into different sub-problems through a fixed point theory, two precondition matrixes are introduced, and values are assigned to the two precondition matrixes according to an image restoration model and meeting a convergence condition; and the plug and play precondition Kranoselski-Mann algorithm is subjected to iteration for a plurality of steps to obtain a restored image. According to the image restoration method, the plug-and-play precondition Kranoselski-Mann algorithm is adopted, different weighting of each pixel point is achieved, meanwhile, the algorithm is stably converged to a real solution, and therefore the purpose of plug-and-play local restoration is achieved, and the robustness and the restoration effect of the algorithm are improved.

Description

Technical Field

[0001] The invention relates to image processing technology, and in particular to an image restoration method. Background Art

[0002] With the continuous advancement of information technology, digital images have become increasingly important in daily life and all walks of life. However, due to the limitations of acquisition equipment, interference during transmission, and the influence of compression and storage methods, people often obtain degraded images with low resolution, noise, and quality loss. Image restoration technology aims to restore the details and clarity of degraded images, improve their visual quality and practical value, and lay the foundation for subsequent high-level image tasks.

[0003] Traditional image restoration algorithms rely on interpolation, filtering and other techniques, but these methods often fail to restore high-frequency details and texture features. Image restoration algorithms based on deep learning achieve end-to-end restoration by learning the intrinsic mapping from degraded images to original images. Although the effect is significant, this method lacks physical explanation and requires separate training of network parameters for different degradation processes, which increases the complexity of the application.

[0004] The plug-and-play algorithm is a modern algorithm framework for image restoration. Its main idea is to solve the fidelity term and penalty term of the optimization model respectively through an alternating update method, combined with numerical calculation and deep neural network denoiser. This can ensure that the restoration result conforms to the physical degradation process and that the image conforms to the intrinsic distribution under natural conditions. However, in some degradation processes, different pixels are damaged to different degrees. The existing algorithms apply the same regularization weight to each pixel during the optimization process, which causes the real information carried by pixels with less damage to be ignored. The existing algorithms improve this by introducing a preconditioning matrix, but the selection of the preconditioning matrix and parameters lacks theoretical proof, resulting in poor results. Therefore, there is room for further improvement in the restoration effect of the existing algorithms. Considering the importance of image restoration tasks in the field of image processing, it is particularly urgent to study an image restoration method with faster speed and better restoration performance. Summary of the invention

[0005] The object of the present invention is to overcome the deficiencies of the above-mentioned prior art and to provide an image restoration method based on a locally adjustable image restoration of a plug-and-play preconditioned Krasnoselskii-Mann algorithm to improve the restoration effect of the algorithm and improve the recovery performance of sparse signals.

[0006] To achieve the above object, the technical solution of the present invention is: An image restoration method, comprising: Obtaining a first vector to establish an objective function of an image restoration model; the first vector is formed by stretching the image to be restored; Combined with Gaussian denoising prior, a regularization term is constructed, and the objective function is solved based on the plug-and-play preconditioned Krasnoselskii-Mann algorithm. The plug-and-play preconditioned Krasnoselskii-Mann algorithm divides the objective function into different sub-problems through fixed point theory, and introduces two preconditioned matrices, which are assigned values ​​according to the image restoration model and the convergence condition. The plug-and-play preconditioned Krasnoselskii-Mann algorithm iterates for several steps to obtain a restored image.

[0007] Compared with the prior art, the present invention has the following beneficial effects: The image restoration method provided in this embodiment adopts the plug-and-play preconditioned Krasnoselskii-Mann algorithm. The plug-and-play preconditioned Krasnoselskii-Mann algorithm divides the objective function into different sub-problems through fixed point theory, and introduces two preconditioned matrices. The two preconditioned matrices are assigned values ​​according to the restoration model and the convergence conditions. While realizing different weightings for each pixel point, the algorithm stably converges to the true solution, thereby achieving the purpose of plug-and-play local restoration and improving the robustness and restoration effect of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0009] Figure 1 is a flow chart of the image restoration method of the present invention; Figure 2 A schematic diagram of a process of restoring a downsampled image using an image restoration method based on a plug-and-play preconditioned Krasnoselskii-Mann algorithm according to the present invention; Figure 3 A schematic diagram of a process of restoring a Poisson noise image using an image restoration method based on a plug-and-play preconditioned Krasnoselskii-Mann algorithm according to the present invention; Figure 4 The flowchart of the plug-and-play precondition Krasnoselskii-Mann algorithm of the present invention; FIG5(a)-FIG5(b) are schematic diagrams showing the comparison of the peak signal-to-noise ratio and the number of algorithm iterations in the upsampling simulation experiment of the present invention; FIG5(a) is a line graph of the peak signal-to-noise ratio after 9 iterations, and FIG5(b) is an enlarged graph of the 5th to 9th iterations; FIG6 (a) to FIG6 (c) are schematic diagrams showing the comparison results of the visual effects in the upsampling simulation experiment of the present invention; wherein FIG6 (a) is a lossless image before downsampling, FIG6 (b) is the restoration effect of the pre-conditioned plug-and-play ADMM, and FIG6 (c) is the restoration effect of the plug-and-play pre-conditioned Krasnoselskii-Mann algorithm; FIG7 (a)-FIG7 (b) are schematic diagrams showing the comparison of the peak signal-to-noise ratio and the number of algorithm iterations in the demosaicing simulation experiment of the present invention; FIG7 (a) is a line graph of the peak signal-to-noise ratio after 50 iterations, and FIG7 (b) is an enlarged graph of the 40th to 50th iterations; Figure 8 A schematic diagram showing the comparison results of the visual effects in the demosaicing simulation experiment. The restoration algorithm used has been marked in the figure. DETAILED DESCRIPTION

[0010] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0011] Embodiment 1: The existing preconditioned plug-and-play algorithm introduces a preconditioned matrix into the objective function by variable substitution, and uses the alternating direction method of multipliers (ADMM) for iterative solution. However, the selection of the preconditioned matrix and hyperparameters lacks theoretical support and relies on a good initialization method, which cannot guarantee the convergence of the algorithm. When the initialization variable is far from the true solution, the image may be overly smoothed, details may be lost, and the image structure may be deformed during the iteration process. To solve this technical problem, refer to Figure 1 As shown, this embodiment provides an image restoration method, which mainly includes the following steps: 101. Obtain a first vector to establish an objective function of an image restoration model; the first vector is formed by stretching the image to be restored; 102. Combining the Gaussian denoising prior, constructing a regularization term, and solving the objective function based on the plug-and-play preconditioned Krasnoselskii-Mann algorithm, wherein the plug-and-play preconditioned Krasnoselskii-Mann algorithm divides the objective function into different sub-problems through fixed point theory, and introduces two preconditioned matrices, and assigns values ​​to the two preconditioned matrices according to the image restoration model and the convergence condition. 103. The plug-and-play preconditioning Krasnoselskii-Mann algorithm is iterated for several steps to obtain a restored image.

[0012] It can be seen that the image restoration method provided in this embodiment adopts the plug-and-play preconditioned Krasnoselskii-Mann algorithm. The plug-and-play preconditioned Krasnoselskii-Mann algorithm divides the objective function into different sub-problems through the fixed point theory, and introduces two preconditioned matrices. The two preconditioned matrices are assigned values ​​according to the restoration model and the convergence conditions. While realizing different weightings for each pixel point, the algorithm stably converges to the true solution, thereby achieving the purpose of plug-and-play local restoration and improving the robustness and restoration effect of the algorithm.

[0013] In a specific embodiment, the height of the image to be restored is , width is , stretched to the first vector , express Euclidean space, , establish the objective function of the image restoration model:

[0014] in, , is the fidelity term of the objective function, Included in middle, is the regularization term.

[0015] Specifically, the plug-and-play precondition Krasnoselskii-Mann algorithm is improved based on the precondition Krasnoselskii-Mann algorithm. The iterative format of the precondition Krasnoselskii-Mann algorithm is: ; in, It was carried out The restored image generated after rounds of iterations; Preconditioning Matrix is a diagonal matrix with non-negative diagonal elements; is the momentum scalar, and It is the intermediate variable of the iterative algorithm; is an auxiliary variable related to the artifact image, It was carried out The artifact image generated after rounds of iterations; Indicates about and The proximal operator of for The inverse matrix of Different, There are different ways to solve it; Scalar is the regularization parameter, express The conjugate function of Indicates about and The proximal operator of for The inverse matrix of .

[0016] From Moreau decomposition, we know that , the second step of the iteration can be rewritten as: ; in, represents the unit operator, and according to the definition of the proximal operator, we get: , When is a diagonal matrix, the minimization problem can be viewed as an image The removed covariance matrix is , the denoising problem of Gaussian noise with a mean of 0, use Alternative , the preconditioned Krasnoselskii-Mann algorithm iteration format is rewritten as: ; in, represents a universal Gaussian denoiser that performs The standard deviation of pixels is The Gaussian noise is denoised when When given, the larger the diagonal element corresponding to the pixel, the greater the denoising strength. Therefore, by constructing the preconditioning matrix , locally adjustable image restoration can be achieved.

[0017] In order to ensure the convergence of the plug-and-play preconditioned Krasnoselskii-Mann algorithm, the preconditioning matrix Need to meet: ; is the momentum scalar, The construction is: ; initialization and , using the plug-and-play preconditioned Krasnoselskii-Mann algorithm iteration Step 2: Get the restored image .

[0018] In a specific embodiment, the specific method of the fidelity term of the established image restoration model is: Determine the degradation process of the image; When the restoration model is downsampling, pixel missing or mosaic array sampling, the fidelity term of the constructed objective function is: ; in, Represents the sampling matrix of the image; When the image restoration model is Poisson denoising, the fidelity term of the constructed objective function is: ; in represents the vector inner product; In a specific embodiment, Different The closed form solution is: When the image restoration model is downsampling, pixel missing or mosaic array sampling, The closed form solution is: ; When the image restoration model is Poisson denoising, The closed form solution is: ; In one embodiment, the regularization parameter The specific implementation in the iteration process is: When the restoration model is downsampling, pixel missing, or mosaic array sampling, it is defined as: , in is the standard deviation of the actual additive noise. When there is no noise Set as , is greater than The starting standard deviation of is a hyperparameter that fixes the number of rounds, As the algorithm iterates from Gradually shrink to , can accelerate the convergence of the algorithm. When the number of iterations exceeds hour, Fixed to , thus making a more accurate restoration; When the restoration model is Poisson denoising, it is defined as: ; In a specific embodiment, the general Gaussian denoising prior used uses a DRUNet convolutional neural network, the input of the network is a noise image and a noise standard deviation map, the output of the network is a clean image, and the training process of the network is as follows: In the training phase, the network first In the training set of clean images, Clean pictures , randomly generate noise standard deviation graph , each diagonal element of the noise standard deviation plot is sampled as follows:

[0019] in, are mutually independent random variables with values ​​in [0,1] that follow a uniform distribution; Then randomly generate noise based on the generated noise standard deviation map , and add it to the clean picture to generate the input and output of the network, and then solve the parameters of the network according to the loss function. The loss function is:

[0020] The Adam optimizer is used to solve the problem of minimizing the loss function and obtain a universal Gaussian denoiser. ; In one embodiment, the preconditioning matrix The specific structure is: ; In super-resolution, image completion, and image demosaicing tasks, The specific structure is: , in is a hyperparameter scalar, is defined as: , in represents a two-dimensional convolution operation, The parameters are Two-dimensional Gaussian filtering, express The sampled pixels in correspond to the set of subscripts in the restored image; In the Poisson denoising task, its specific construction is: ; In one embodiment, the preconditioning matrix The specific structure is: In the tasks of super-resolution, image completion, and image demosaicing, the specific structure is: , in, To ensure Hyperparameters of For the Poisson denoising task, its specific construction is: ; in, To ensure Hyperparameters of In summary, the present invention trains the deep denoising network DRUNet, and inserts the trained network and the fidelity term as two different information into the objective function. The fidelity term can restore the image according to the image degradation process, and the network prior model can implicitly model the data prior term in a data-driven manner. The fixed point theory is used to divide the different priors of the objective function into different sub-problems, and a preconditioning matrix is ​​introduced. The preconditioning matrix is ​​assigned according to the restoration model, and different weights are implemented for each pixel point to achieve the purpose of plug-and-play local restoration. Finally, the convergence of the algorithm is guaranteed according to the KM theory. The present invention is an innovative solution based on the preconditioned Krasnoselskii-Mann algorithm. This method combines the plug-and-play algorithm, preconditioning technology, and split matrix technology to improve the image restoration quality while ensuring convergence.

[0021] like Figure 2 As shown, this embodiment also discloses a noise-free The down-sampled image restoration method comprises the following steps: Get a noise-free downsampled degraded image ; According to the downsampling degradation coefficient, the image restoration model is established and the fidelity term is constructed. The sampling matrix in ; Specifically, assuming the degraded image The size is The restoration of the downsampled image starts from Recover The restored image , and The relationship is: , The sampling matrix Defined as: , in is the index after downsampling, is the index of the original image; Finally, , fidelity item , General Gaussian Denoiser , As input to the algorithm, the plug-and-play preconditioned Krasnoselskii-Mann algorithm is executed, such as Figure 4 As shown, the specific steps are: Step 1: Get the degraded image , the actual noise level , fidelity item , General Gaussian Denoiser , initialize the number of iterations , and according to right and Initialize; Common initialization methods include bilinear interpolation and bicubic interpolation. Specifically, in order to show that the algorithm can still converge to a better result under poor initialization conditions, this embodiment uses 0-filling initialization, that is, filling 0 elements at unknown pixel positions; Initialize to all 0 vector; Step 2: Set the maximum number of iterations , the number of hyperparameters fixed , momentum hyperparameter , initial penalty coefficient ; Step 3: Get the updated preconditioning matrix and ; Specifically, the preconditioning matrix The specific update rules are: ; in, The update rule is: , in is a hyperparameter scalar, is defined as: , in represents a two-dimensional convolution operation, The parameters are Two-dimensional Gaussian filtering, express The sampled pixels in correspond to the set of subscripts in the restored image; Step 4: Update the regularization parameters ,when When updated to ,otherwise ; Step 5: Update , specifically, The calculation method is: ; Step 6: Update , specifically, The calculation method is: ; in, represents the unit operator, represents a universal Gaussian denoiser that performs The standard deviation of pixels is The Gaussian noise is denoised.

[0022] Step 7: Update the momentum parameters , and update the restored image , auxiliary variables , specifically, , , The calculation method is:

[0023] Step 8: Increment the number of iterations And determine whether the maximum number of iterations has been reached, and if so, output the restored image If not reached, return to step 3.

[0024] like Figure 3 As shown, the present embodiment also discloses a method for restoring a noisy mosaic image, comprising the following steps: Get a downsampled degraded image containing noise ; According to the downsampling degradation coefficient, the image restoration model is established and the fidelity term is constructed. The sampling matrix in ; Specifically, assuming the degraded image The size is , the restoration of the mosaic image is based on Recover The restored image , and The relationship is: , in, The sampling matrix Defined as: , in is the index after downsampling, is the index of the original image; Will , fidelity item , General Gaussian Denoiser , As input to the algorithm, the plug-and-play preconditioned Krasnoselskii-Mann algorithm is executed, such as Figure 4 As shown, the specific steps are: Step 1: Get the degraded image , the actual noise level , fidelity item , General Gaussian Denoiser , initialize the number of iterations , and according to right and Initialize; Common initialization methods include bilinear interpolation and bicubic interpolation. Specifically, in order to show that the algorithm can still converge to a better result under poor initialization conditions, this embodiment uses 0-filling initialization, that is, filling 0 elements at unknown pixel positions; Initialize to all 0 vector; Step 2: Set the maximum number of iterations , the number of hyperparameters fixed , momentum hyperparameter , initial penalty coefficient ; Step 3: Get the updated preconditioning matrix and ; Specifically, the preconditioning matrix The specific update rules are: ; in, The update rule is: , in is a hyperparameter scalar, is defined as: , in represents a two-dimensional convolution operation, The parameters are Two-dimensional Gaussian filtering, express The sampled pixels in correspond to the set of subscripts in the restored image; Step 4: Update the regularization parameters ,when When updated to ,otherwise ; Step 5: Update , specifically, The calculation method is: ; Step 6: Update , specifically, The calculation method is: ; in, represents the unit operator, represents a universal Gaussian denoiser that performs The standard deviation of pixels is The Gaussian noise is denoised.

[0025] Step 7: Update the momentum parameters , and update the restored image , auxiliary variables , specifically, , , The calculation method is:

[0026] Step 8: Increment the number of iterations And determine whether the maximum number of iterations has been reached, and if so, output the restored image If not reached, return to step 3.

[0027] The technical effects of the present invention are further verified and explained below in conjunction with the accompanying drawings: Image restoration simulation experiment based on Python. The present invention uses the plug-and-play preconditioned Krasnoselskii-Mann algorithm to restore the image in Figure 6 (a) and Figure 8 The leftmost image is noise-free. Restoration of downsampled images and restoration of noisy mosaic images.

[0028] As shown in Figure 5(a)-Figure 5(b), this example shows the noise-free performance of the plug-and-play preconditioned Krasnoselskii-Mann algorithm and the existing preconditioned plug-and-play ADMM algorithm. In the downsampled image restoration example, the average peak signal-to-noise ratio on the test set varies with the number of iterations. Figure 5(a) shows that although the preconditioned plug-and-play ADMM algorithm converges faster in the initial steps, Figure 5(b) shows that the best result that the preconditioned plug-and-play ADMM algorithm can converge to is not as good as the plug-and-play preconditioned Krasnoselskii-Mann algorithm. Figure 6(a)-Figure 6(c) The figure shows the comparison results of the visual effects in the upsampling simulation experiment of the present invention. FIG6(a) is a lossless image before downsampling, FIG6(b) is the restoration effect of the preconditioned plug-and-play ADMM, and FIG6(c) is the restoration effect of the plug-and-play preconditioned Krasnoselskii-Mann algorithm. It can be observed that the result of the preconditioned plug-and-play ADMM algorithm shown in FIG6(b) suffers from structural damage, while the plug-and-play preconditioned Krasnoselskii-Mann algorithm achieves better restoration effect.

[0029] like Figure 7(a)-7(b)As shown, this example shows the results of the average peak signal-to-noise ratio changing with the number of iterations of the plug-and-play preconditioned Krasnoselskii-Mann algorithm and the existing preconditioned ADMM algorithm in the noisy mosaic image restoration embodiment. Similarly, Figure 7(a) shows that although the preconditioned plug-and-play ADMM algorithm converges faster in the initial few steps, it quickly loses accuracy, and the results of the 40th to 50th iterations shown in Figure 7(b) indicate that the best result that the preconditioned plug-and-play ADMM algorithm can converge to is not as good as the plug-and-play preconditioned Krasnoselskii-Mann algorithm. Figure 8 The schematic diagram shows the comparison of the visual effects of the plug-and-play preconditioned Krasnoselskii-Mann algorithm and the existing preconditioned plug-and-play ADMM algorithm, MMNet algorithm, JDnDm algorithm, and DJDD algorithm in the upsampling simulation experiment of the present invention. It can be observed that Figure 8 While other methods presented suffer from residual noise or over-smoothing, the plug-and-play preconditioned Krasnoselskii-Mann algorithm best preserves image details while removing noise.

[0030] It can be seen that the present invention can improve the quality and accuracy of image restoration while reducing the number of iterations, and to a certain extent overcomes the lack of accuracy in the current field of plug-and-play image algorithms.

[0031] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable ordinary technicians in the field to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made based on the essence of the content of the present invention should be included in the protection scope of the present invention.

Claims

1. An image restoration method, characterized in that: include: Obtaining a first vector to establish an objective function of an image restoration model; the first vector is formed by stretching the image to be restored; Combined with Gaussian denoising prior, a regularization term is constructed, and the objective function is solved based on the plug-and-play preconditioned Krasnoselskii-Mann algorithm. The plug-and-play preconditioned Krasnoselskii-Mann algorithm divides the objective function into different sub-problems through fixed point theory, and introduces two preconditioned matrices, which are assigned values ​​according to the image restoration model and the convergence condition. The plug-and-play preconditioned Krasnoselskii-Mann algorithm iterates for several steps to obtain a restored image.

2. The image restoration method according to claim 1, wherein: The height of the image to be restored is , width is , stretched to the first vector , express Euclidean space, , establish the objective function of the image restoration model: ; in, , is the fidelity term of the objective function, Included in middle, is the regularization term, is the regularization parameter.

3. The image restoration method according to claim 2, characterized in that: The plug-and-play precondition Krasnoselskii-Mann algorithm is improved based on the precondition Krasnoselskii-Mann algorithm. The iterative format of the precondition Krasnoselskii-Mann algorithm is: ; in, It was carried out The restored image generated after rounds of iterations; All are preconditioned matrices; is the momentum scalar, and It is the intermediate variable of the iterative algorithm; is an auxiliary variable related to the artifact image, It was carried out The artifact image generated after rounds of iterations; Indicates about and The proximal operator of for The inverse matrix of Different, There are different ways to solve it; express The conjugate function of Indicates about and The proximal operator of for The inverse matrix of .

4. The image restoration method according to claim 3, characterized in that: , the second step of the iteration can be rewritten as: ； in, represents the unit operator, and according to the definition of the proximal operator, we get: ； The objective function minimization problem is regarded as an image The removed covariance matrix is , the denoising problem of Gaussian noise with a mean of 0, use Alternative , its iteration format is rewritten as: ； Represents a universal Gaussian denoiser, which is a denoiser for a given noisy image. The standard deviation of pixels is Gaussian noise is used for denoising, when the regularization parameter When given, the larger the diagonal element corresponding to the pixel, the greater the denoising strength. By constructing the preconditioning matrix , achieving locally adjustable image restoration.

5. The image restoration method according to claim 3, characterized in that: Preconditioning Matrix satisfy: ; The construction is: .

6. The image restoration method according to claim 3, characterized in that: The fidelity term of the objective function is established as follows: Determine the degradation process of the image; When the image restoration model is downsampling, pixel missing or mosaic array sampling, the fidelity term of the constructed objective function is: ； in, Represents the sampling matrix of the image; When the image restoration model is Poisson denoising, the fidelity term of the constructed objective function is: ; in Represents the vector inner product.

7. The image restoration method according to claim 6, characterized in that: Different The closed form solution is: When the image restoration model is downsampling, pixel missing or mosaic array sampling, The closed form solution is: ； When the image restoration model is Poisson denoising, The closed form solution is: 。 8. The image restoration method according to claim 4, wherein: The regularization parameter The specific implementation in the iteration process is: When the image restoration model is down-sampled, pixel missing, or mosaic array sampling, the regularization parameter Defined as: ， in, is the standard deviation of the actual additive noise. When there is no noise Set as , is greater than The starting standard deviation of is a hyperparameter that fixes the number of rounds, As the algorithm iterates from Gradually shrink to , when the number of iterations exceeds hour, Fixed to , When the image restoration model is Poisson denoising, the regularization parameter Defined as: .

9. The image restoration method according to claim 1, wherein: The Gaussian denoising prior uses a DRUNet convolutional neural network. The input of the DRUNet convolutional neural network is a noise image and a noise standard deviation map. The output of the DRUNet convolutional neural network is a clean image. The training process of the DRUNet convolutional neural network is as follows: During the training phase, the DRUNet convolutional neural network first In the training set of clean images, Clean pictures Randomly generate noise standard deviation plot , each diagonal element of the noise standard deviation plot is sampled as: ； in, are mutually independent random variables with values ​​in [0,1] that follow a uniform distribution; Then randomly generate noise based on the generated noise standard deviation map , and add it to the clean picture to generate the input and output of the DRUNet convolutional neural network, and then solve the network parameters according to the loss function. The loss function is: ； The Adam optimizer is used to solve the problem of minimizing the loss function and obtain a universal Gaussian denoiser. .

10. The image restoration method according to claim 3 or 4, characterized in that: Preconditioning Matrix The specific structure is: ； In super-resolution, image completion, and image demosaicing tasks, The specific structure is: , in is a hyperparameter scalar, is defined as: , in represents a two-dimensional convolution operation, The parameters are Two-dimensional Gaussian filtering, express The sampled pixel points in correspond to the set of subscripts in the restored image; In the Poisson denoising task, The specific structure is: ; Preconditioning Matrix The specific structure is: In super-resolution, image completion, and image demosaicing tasks, The specific structure is: , in, To ensure Hyperparameters of For the Poisson denoising task, The specific structure is: ; in, To ensure Hyperparameters of .

Images