Multi-scale image restoration method based on accelerated near-end stochastic gradient
By employing a multi-scale image restoration method based on accelerated proximal stochastic gradients, and utilizing discrete cosine transform and cross-layer attention mechanisms to optimize the image, the problems of low efficiency and insufficient feature utilization in large-scale image restoration are solved, achieving efficient image sharpness and detail preservation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-10
- Publication Date
- 2026-03-13
AI Technical Summary
Existing technologies are computationally inefficient in large-scale image restoration and fail to fully utilize multi-scale features, leading to imbalances such as structural blurring or residual noise in the restored images.
A multi-scale image restoration method based on accelerated proximal stochastic gradients is adopted. The image is decomposed by multi-scale tight frame filter bank induced by discrete cosine transform. An optimization model containing data fidelity term, multi-scale sparse regularization term and global smoothing term is constructed. A dual cyclic gradient optimization framework is adopted and the sparse weights are dynamically adjusted through cross-layer attention mechanism. Finally, a clear image is reconstructed through inverse tight frame transform.
It effectively improves image restoration efficiency and quality, achieves differentiated optimization of low-frequency structure and high-frequency details, and ensures the clarity and detail preservation of restored images.
Smart Images
Figure CN121660937A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of digital image processing and optimization algorithm technology, and more specifically to a multi-scale image restoration method based on accelerated proximal stochastic gradients. Background Technology
[0002] In the field of image restoration, multi-scale balanced sparse modeling methods have become the mainstream technology due to their ability to hierarchically represent image structural features. However, their traditional solution schemes, relying on direct iteration of fixed-point equations, exhibit significant iterative efficiency bottlenecks when dealing with images of millions of pixels. Current machine learning algorithms such as SGD have demonstrated high efficiency in large-scale data optimization through improvement strategies like variance reduction and adaptive step size. However, these algorithms face the core challenge of insufficient decoupling of multi-scale features in image restoration scenarios. Existing methods struggle to accurately adapt to the differentiated optimization needs of low-frequency structure and high-frequency details in images, leading to imbalances such as structural blurring or residual noise in restored images. Current technologies lack targeted optimization for the multi-scale characteristics of images, making it difficult to achieve efficiency breakthroughs while ensuring restoration quality.
[0003] Therefore, how to solve the problems of low computational efficiency and insufficient utilization of multi-scale features in traditional algorithms in large-scale image restoration is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0004] In view of this, the present invention provides a multi-scale image restoration method based on accelerated proximal stochastic gradients to solve the above problems.
[0005] To achieve the above objectives, the present invention adopts the following technical solution: This invention discloses a multi-scale image restoration method based on accelerated proximal stochastic gradients, comprising: Step 1: Perform normalization preprocessing on the noisy and blurred image, and decompose the image into high and low frequency coefficients of each layer using a multi-scale tight frame filter bank induced by discrete cosine transform to obtain the sample set; Step 2: Construct a multi-scale optimization model that includes data fidelity terms, multi-scale sparse regularization terms, and global smoothing terms; Step 3: The parameters of the multi-scale optimization model are iteratively updated using a dual-loop gradient optimization framework. During the iterative update, a hierarchical multi-scale block update strategy is adopted, and the sparse weights are dynamically adjusted through a cross-layer attention mechanism. Step 4: When the rate of change of the objective function of the multi-scale optimization model meets the threshold or reaches the maximum number of iterations, stop the iterative optimization and reconstruct a clear image through inverse tight frame transformation.
[0006] Furthermore, the original sharp image is blurred and noise-processed using a degradation model to obtain the noisy and blurred image. The degradation model is represented as follows: ; in, This represents a noisy and blurred observation image; Represents the Gaussian blur kernel; Represents the original, clear image; Indicates Gaussian white noise; The preprocessing involves normalizing the image pixel values to the [0, 1] range using linear scaling. The method of decomposing the image into high- and low-frequency coefficients at each level using a multi-scale tight-frame filter bank induced by discrete cosine transform is specifically as follows: a tight-frame filter bank induced by discrete cosine transform is constructed through cascading. The multi-scale decomposition structure is used to extract high- and low-frequency components of the image layer by layer, and the tight-frame coefficients of each layer are obtained, which are expressed as: ;in, Indicates the first Layer coefficient, Indicates the first Multi-scale transformation operator, .
[0007] Furthermore, the objective function of the multi-scale optimization model is: ; Among them, the data fidelity item is To ensure a proper fit between the restored image and the observed data, For fuzzy matrices, For multi-scale compact frame transformation operators; multi-scale sparse regularization term is Dynamically adjust sparse weights through a cross-layer attention mechanism Strengthen constraints on high-frequency details. Here are the sparse regularization parameters; the global smoothing term is... To suppress overfitting and ensure iterative stability, This is the global smoothing parameter.
[0008] Furthermore, the dual-loop gradient optimization framework is used to iteratively update the parameters of the multi-scale optimization model. The specific steps are as follows: First, perform initialization settings and configure the update frequency. Small batch sample size Initial point Simple moving average quantity Initial step ,function ,parameter Acceleration parameters and probability distribution Set the low-frequency component update probability and high-frequency component update probability ,satisfy ; Based on the set parameters and outer loop variables, execute the outer loop to determine the first... The final step size obtained from the outer loop. , This represents the maximum number of iterations in the outer loop. According to the set parameters, the first The outer loop obtains the final step size and global reference point, the inner loop is executed, and the outer loop variables are updated. This represents the number of times the inner loop executes. , The total number of iterations of the inner loop, each iteration... The inner loop executes the outer loop once.
[0009] Furthermore, the execution of the outer loop specifically includes: Step 301: Let Establish global reference points The formula is: ;in For the first The global reference point of the outer loop. For the first Gradient of each sample; Step 302: Dynamically adjust the step size using the BB step size strategy, specifically as follows: If the objective function is strongly convex, the step size is: ; If the objective function is non-convex, the step size is: ;in These are stabilization parameters used for stabilizing the BB step size in non-convex problems; Step 303: Calculate the current step size using the moving average technique: like ,but ; like ,but or ; like ,but or ,in ;in and It is the baseline step size calculated using the moving average technique; To calculate the r-th order average using the first s step sizes, To calculate the r-th order average using the most recent c step sizes; No. The final step size obtained from the second outer loop is: ;in This represents the acceleration parameter, a positive constant, used to calculate the step size of the overall scaling moving average. Represents the total number of iterations in the inner loop; It is a function, specifically in the form of .
[0010] Furthermore, the execution of the inner loop specifically includes: Step 311: Based on structural entropy Dynamic adjustment and The formula is: , ; in, Represents the scaling factor, controlling the structural entropy. Update probability and The impact; Step 312: Select a sub-batch of size b from the sample set. The formula for calculating the stochastic gradient with variance compensation is as follows: ; in, Let represent the stochastic gradient estimate with variance compensation in the s-th outer loop and the k-th inner loop. This represents the current iteration point of the s-th outer loop and the k-th inner loop; Step 313: Perform near-end mapping update, the specific formula is as follows: ; in, This represents the estimated image coefficients after the s-th outer loop iteration and the (k+1)-th inner loop iteration. This represents the combination of regularization terms in a multi-scale optimization model. Define the near-end mapping. The input parameters for near-end mapping; Step 314: Perform Nesterov momentum acceleration, the specific formula is as follows: ,in The momentum coefficient; Step 315: Update the outer loop variable: .
[0011] Furthermore, the hierarchical multi-scale block update strategy specifically involves updating low-frequency components with larger step sizes. and high update probability Accelerate global convergence by using smaller step sizes for high-frequency components. High and low new probabilities Combine sparse regularization terms to suppress noise.
[0012] Furthermore, the dynamic adjustment of sparse weights through a cross-layer attention mechanism specifically involves: First, the image is decomposed into its components using a tight-frame transform. Layer, calculate the variance of the coefficients in each layer. ; Then, the inner product normalization formula is used. Calculate the first Layers and Cross-layer correlation ; Finally, through the formula Dynamically adjust sparse weights; where It is the strength of the global fundamental constraints. Control the range of attention adjustment. It is the maximum value of the variance across all layers.
[0013] Furthermore, the process of reconstructing a clear image through inverse compact frame transformation specifically involves: Collect optimized multi-scale tight frame coefficients for each layer ,in Indicates the optimized first... Layer coefficient, The total number of layers; the image is synthesized through inverse tight-frame transformation: ,in, for The image is transposed; the reconstructed image is then denormalized to restore pixel values to their original range, resulting in the final clear image. .
[0014] As can be seen from the above technical solution, compared with the prior art, this invention provides a multi-scale image restoration method based on accelerated proximal stochastic gradients. It preprocesses noisy and blurred images using standardization, decomposes the image into high- and low-frequency coefficients at each layer using a multi-scale tight-frame filter bank induced by discrete cosine transform, constructs an optimization model to balance structure fidelity, detail sparsity, and overall smoothness, and employs a dual-loop gradient optimization framework. The outer loop dynamically adjusts the step size using full-sample gradients combined with a Barzilai-Borwein (BB) step size strategy, while the inner loop calculates stochastic gradients with variance compensation using a non-uniform sampling strategy to counteract noise. A hierarchical multi-scale block update strategy is implemented, dynamically adjusting the sparse weights of each layer through a cross-layer attention mechanism. When the rate of change of the objective function meets a threshold or reaches the maximum number of iterations, a clear image is reconstructed through inverse tight-frame transformation. This invention effectively improves image restoration efficiency and quality by differentially optimizing low-frequency structure and high-frequency details. Attached Figure Description
[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0016] Figure 1 This is a schematic diagram of the overall process of the present invention.
[0017] Figure 2 This is a schematic diagram of the dual-loop gradient optimization framework provided by the present invention. Detailed Implementation
[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0019] This invention discloses a multi-scale image restoration method based on accelerated proximal stochastic gradients, such as... Figure 1 As shown, it includes: Step 1: Perform normalization preprocessing on the noisy and blurred image, and decompose the image into high and low frequency coefficients of each layer using a multi-scale tight frame filter bank induced by discrete cosine transform to obtain the sample set; Step 2: Construct a multi-scale optimization model that includes data fidelity terms, multi-scale sparse regularization terms, and global smoothing terms; Step 3: Use a dual-loop gradient optimization framework to iteratively update the parameters of the multi-scale optimization model; during the iterative update, a hierarchical multi-scale block update strategy is adopted, and the sparse weights are dynamically adjusted through a cross-layer attention mechanism. Step 4: When the rate of change of the objective function of the multi-scale optimization model meets the threshold or reaches the maximum number of iterations, stop the iterative optimization and reconstruct a clear image through inverse tight frame transformation.
[0020] In one specific embodiment, a degradation model is used to blur and noise the original sharp image, resulting in a noisy and blurred image. The degradation model is represented as follows: ; in, This represents a noisy and blurred observation image; Indicates the Gaussian blur kernel (size) Standard deviation ); Represents the original, clear image; Gaussian white noise (standard deviation) ); Preprocessing involves linearly scaling and normalizing the image pixel values to the [0, 1] range; that is, the pixel values... Mapped to .
[0021] The image is decomposed into high- and low-frequency coefficients at each level using a multi-scale compact frame filter bank induced by discrete cosine transform. Specifically, a compact frame filter bank induced by discrete cosine transform is constructed through cascading. The multi-scale decomposition structure is used to extract high- and low-frequency components of the image layer by layer, and the tight-frame coefficients of each layer are obtained, which are expressed as: ;in, Indicates the first Layer coefficient, Indicates the first Multi-scale transformation operator, .
[0022] In a specific embodiment, the objective function of the multi-scale optimization model is: ; Among them, the data fidelity item is To ensure a proper fit between the restored image and the observed data, For fuzzy matrices, For multi-scale compact frame transformation operators; multi-scale sparse regularization term is Dynamically adjust sparse weights through a cross-layer attention mechanism Strengthen constraints on high-frequency details. Here are the sparse regularization parameters; the global smoothing term is... To suppress overfitting and ensure iterative stability, This is a global smoothing parameter. Adjust it... and It collaboratively optimizes the low-frequency structural integrity, high-frequency detail sparsity, and global smoothness of images in a multi-scale space, thereby achieving high-quality restoration of noisy and blurred images.
[0023] In one specific embodiment, a dual-loop gradient optimization framework is used to iteratively update the parameters of the multi-scale optimization model, such as... Figure 2 As shown, the specific steps are as follows: First, perform initialization settings and configure the update frequency. Small batch sample size Initial point Simple moving average quantity Initial step ,function ,parameter Acceleration parameters and probability distribution Set the low-frequency component update probability and high-frequency component update probability ,satisfy ; Based on the set parameters and outer loop variables, execute the outer loop to determine the first... The final step size obtained from the outer loop. , This represents the maximum number of iterations in the outer loop. According to the set parameters, the first The outer loop obtains the final step size and global reference point, the inner loop is executed, and the outer loop variables are updated. This represents the number of times the inner loop executes. , The total number of iterations of the inner loop, each iteration... The inner loop executes the outer loop once.
[0024] In a specific embodiment, executing the outer loop specifically includes: Step 301: Let Establish global reference points The formula is: ;in For the first The global reference point of the outer loop. For the first Gradient of each sample; Step 302: Dynamically adjust the step size using the BB step size strategy, specifically as follows: If the objective function is strongly convex, the step size is: ; If the objective function is non-convex, the step size is: ;in These are stabilization parameters used for stabilizing the BB step size in non-convex problems; Step 303: Calculate the current step size using the moving average technique: like ,but ; like ,but or ; like ,but or ,in ;in and It is the baseline step size calculated using the moving average technique; To calculate the r-th order average using the first s step sizes, To calculate the r-th order average using the most recent c step sizes; No. The final step size obtained from the second outer loop is: ;in This represents the acceleration parameter, a positive constant, used to calculate the step size of the overall scaling moving average. Represents the total number of iterations in the inner loop; It is a function, specifically in the form of .
[0025] In a specific embodiment, executing the inner loop specifically includes: Step 311: Based on structural entropy Dynamic adjustment and The formula is: , ; in, Represents the scaling factor, controlling the structural entropy. Update probability and The impact; and The non-uniform sampling strategy is dynamically determined by structural entropy: high-frequency regions are sampled with lower probability. The selected areas are used for fine-grained noise reduction with small step sizes, while the low-frequency region is denoised with a higher probability. The selected method uses a large step size to quickly restore the overall structure, thereby achieving the purpose of hierarchical optimization.
[0026] Step 312: Select a sub-batch of size b from the sample set. The formula for calculating the stochastic gradient with variance compensation is as follows: ; in, Let represent the stochastic gradient estimate with variance compensation in the s-th outer loop and the k-th inner loop. This represents the current iteration point of the s-th outer loop and the k-th inner loop; Step 313: Perform near-end mapping update, the specific formula is as follows: ; in, This represents the estimated image coefficients after the s-th outer loop iteration and the (k+1)-th inner loop iteration. This represents the combination of regularization terms in a multi-scale optimization model. Define the near-end mapping The input parameters for near-end mapping; Step 314: Perform Nesterov momentum acceleration, the specific formula is as follows: ,in The momentum coefficient; Step 315: Update the outer loop variable: .
[0027] In a specific embodiment, a hierarchical multi-scale block update strategy is adopted, specifically: low-frequency components (structural layer, With a larger step size and high update probability Accelerate global convergence; high-frequency components (detail layer, With smaller step size High and low new probabilities Combine sparse regularization terms to suppress noise.
[0028] In a specific embodiment, the sparse weights are dynamically adjusted through a cross-layer attention mechanism, specifically as follows: First, the image is decomposed into its components using a tight-frame transform (such as DCT or wavelet transform). Layer, calculate the variance of the coefficients in each layer. High-frequency layers (textures, edges) have larger variances due to larger coefficient fluctuations; low-frequency layers (outlines, backgrounds) have smaller variances due to flatter coefficients, which is used to depict the "activity of layers".
[0029] Then, the inner product normalization formula is used. Calculate the first Layers and Cross-layer correlation This measures the correlation between features (the result is between 0 and 1; the closer the value is to 1, the closer the features are between layers, such as edge layers and texture layers; the closer the value is to 0, the weaker the correlation, such as noise layers and structure layers), and this is used to describe the "intimacy of layers".
[0030] Finally, through the formula Dynamically adjust sparse weights; where It is the strength of the global fundamental constraints. Control the range of attention adjustment. It is the maximum value of the variance across all layers (used for normalization to ensure...). (in the range of 0 to 1), when the high-frequency layer is due to big, High leads to When significantly increased, This strengthens the sparsity constraints on high-frequency layers (by leveraging the difference between real details, which have "large variance and strong correlation," and noise, which has "large variance but weak correlation," to precisely suppress noise and preserve details); while low-frequency layers, due to... Small, even if there are connections between layers, after adjustment It maintains a low intensity to avoid blurring of the outline and other structures due to excessive constraints, ultimately achieving a layered optimization effect of "precise noise reduction of high-frequency details and stable preservation of low-frequency structures".
[0031] In one specific embodiment, the termination criterion is: real-time monitoring of the rate of change of the objective function. ( The optimization is terminated when the threshold is reached, or when the maximum number of iterations is reached.
[0032] A clear image is obtained by reconstructing it through inverse compact frame transformation, specifically as follows: Collect optimized multi-scale tight frame coefficients for each layer ,in Indicates the optimized first... Layer coefficient, The total number of layers; the image is synthesized through inverse tight-frame transformation: ,in, for The image is transposed; the reconstructed image is then denormalized to restore pixel values to their original range, resulting in the final clear image. .
[0033] The optimized coefficients are obtained by iteratively solving a "multi-scale optimization model." The objective function of this model defines the conditions that a sharp image should satisfy. We use an accelerated proximal stochastic gradient method to iteratively optimize this model. In each iteration, the coefficient estimates for all scales are updated by calculating the gradient and performing proximal mapping. This process effectively imposes sparsity constraints to suppress noise and preserve details. When the iteration converges, the final set of coefficients is the optimized set of coefficients for each layer, which is used for subsequent image reconstruction.
[0034] The iteration process primarily updates the model's "optimization variables," namely the complete "multi-scale image coefficients." The initial point is an initial estimate of these coefficients (e.g., obtained directly from the decomposition of a blurred image). Within a dual-loop framework, the algorithm continuously updates and refines these coefficient values using stochastic gradients, proximal mapping, and momentum acceleration techniques, gradually approximating the optimal solution and thus achieving coarse-to-fine image restoration.
[0035] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.
[0036] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A multi-scale image restoration method based on accelerated proximal stochastic gradients, characterized in that, include: Step 1: Perform normalization preprocessing on the noisy and blurred image, and decompose the image into high and low frequency coefficients of each layer using a multi-scale tight frame filter bank induced by discrete cosine transform to obtain the sample set; Step 2: Construct a multi-scale optimization model that includes data fidelity terms, multi-scale sparse regularization terms, and global smoothing terms; Step 3: The parameters of the multi-scale optimization model are iteratively updated using a dual-loop gradient optimization framework. During the iterative update, a hierarchical multi-scale block update strategy is adopted, and the sparse weights are dynamically adjusted through a cross-layer attention mechanism. Step 4: When the rate of change of the objective function of the multi-scale optimization model meets the threshold or reaches the maximum number of iterations, stop the iterative optimization and reconstruct a clear image through inverse tight frame transformation.
2. The multi-scale image restoration method based on accelerated proximal stochastic gradients according to claim 1, characterized in that, The original sharp image is blurred and noise-treated using a degradation model to obtain the noisy and blurred image. The degradation model is expressed as follows: ; in, This represents a noisy and blurred observation image; Represents the Gaussian blur kernel; Represents the original, clear image; Indicates Gaussian white noise; The preprocessing involves normalizing the image pixel values to the [0, 1] range using linear scaling. The method of decomposing the image into high- and low-frequency coefficients at each level using a multi-scale tight-frame filter bank induced by discrete cosine transform is specifically as follows: a tight-frame filter bank induced by discrete cosine transform is constructed through cascading. The multi-scale decomposition structure is used to extract high- and low-frequency components of the image layer by layer, and the tight-frame coefficients of each layer are obtained, which are expressed as: ;in, Indicates the first Layer coefficient, Indicates the first Multi-scale transformation operator, .
3. The multi-scale image restoration method based on accelerated proximal stochastic gradients according to claim 2, characterized in that, The objective function of the multi-scale optimization model is: ； Among them, the data fidelity item is To ensure a proper fit between the restored image and the observed data, For fuzzy matrices, For multi-scale compact frame transformation operators; multi-scale sparse regularization term is Dynamically adjust sparse weights through a cross-layer attention mechanism Strengthen constraints on high-frequency details. Here are the sparse regularization parameters; the global smoothing term is... To suppress overfitting and ensure iterative stability, This is the global smoothing parameter.
4. The multi-scale image restoration method based on accelerated proximal stochastic gradients according to claim 1, characterized in that, The dual-loop gradient optimization framework is used to iteratively update the parameters of the multi-scale optimization model. The specific steps are as follows: First, perform initialization settings and configure the update frequency. Small batch sample size Initial point Simple moving average quantity Initial step ,function ,parameter Acceleration parameters and probability distribution Set the low-frequency component update probability and high-frequency component update probability ,satisfy ; Based on the set parameters and outer loop variables, execute the outer loop to determine the first... The final step size obtained from the outer loop. , This represents the maximum number of iterations in the outer loop. According to the set parameters, the first The outer loop obtains the final step size and global reference point, the inner loop is executed, and the outer loop variables are updated. This represents the number of times the inner loop executes. , The total number of iterations of the inner loop, each iteration... The inner loop executes the outer loop once.
5. The multi-scale image restoration method based on accelerated proximal stochastic gradients according to claim 4, characterized in that, The execution of the outer loop specifically includes: Step 301: Let Establish global reference points The formula is: ;in For the first The global reference point of the outer loop. For the first Gradient of each sample; Step 302: Dynamically adjust the step size using the BB step size strategy, specifically as follows: If the objective function is strongly convex, the step size is: ; If the objective function is non-convex, the step size is: ;in These are stabilization parameters used for stabilizing the BB step size in non-convex problems; Step 303: Calculate the current step size using the moving average technique: like ,but ; like ,but or ; like ,but or ,in ;in and It is the baseline step size calculated using the moving average technique; To calculate the r-th order average using the first s step sizes, To calculate the r-th order average using the most recent c step sizes; No. The final step size obtained from the second outer loop is: ;in This represents the acceleration parameter, a positive constant, used to calculate the step size of the overall scaling moving average. Represents the total number of iterations in the inner loop; It is a function, specifically in the form of .
6. The multi-scale image restoration method based on accelerated proximal stochastic gradients according to claim 5, characterized in that, The execution of the inner loop specifically includes: Step 311: Based on structural entropy Dynamic adjustment and The formula is: ， ； in, Represents the scaling factor, controlling the structural entropy. Update probability and The impact; Step 312: Select a sub-batch of size b from the sample set. The formula for calculating the stochastic gradient with variance compensation is as follows: ; in, Let represent the stochastic gradient estimate with variance compensation in the s-th outer loop and the k-th inner loop. This represents the current iteration point of the s-th outer loop and the k-th inner loop; Step 313: Perform near-end mapping update, the specific formula is as follows: ; in, This represents the estimated image coefficients after the s-th outer loop iteration and the (k+1)-th inner loop iteration. This represents the combination of regularization terms in a multi-scale optimization model. Define the near-end mapping. The input parameters for near-end mapping; Step 314: Perform Nesterov momentum acceleration, the specific formula is as follows: ,in The momentum coefficient; Step 315: Update the outer loop variable: .
7. The multi-scale image restoration method based on accelerated proximal stochastic gradients according to claim 5, characterized in that, The hierarchical multi-scale block update strategy is specifically as follows: low-frequency components are updated with larger step sizes. and high update probability Accelerate global convergence by using smaller step sizes for high-frequency components. High and low new probabilities Combine sparse regularization terms to suppress noise.
8. The multi-scale image restoration method based on accelerated proximal stochastic gradients according to claim 3, characterized in that, The dynamic adjustment of sparse weights through a cross-layer attention mechanism is specifically as follows: First, the image is decomposed into its components using a tight-frame transform. Layer, calculate the variance of the coefficients in each layer. ; Then, the inner product normalization formula is used. Calculate the first Layers and Cross-layer correlation ; Finally, through the formula Dynamically adjust sparse weights; in It is the strength of the global fundamental constraints. Control the range of attention adjustment. It is the maximum value of the variance across all layers.
9. The multi-scale image restoration method based on accelerated proximal stochastic gradients according to claim 1, characterized in that, The process of reconstructing a clear image through inverse compact frame transform specifically involves: Collect optimized multi-scale tight frame coefficients for each layer ,in Indicates the optimized first... Layer coefficient, The total number of layers; the image is synthesized through inverse tight-frame transformation: ,in, for The image is transposed; the reconstructed image is then denormalized to restore pixel values to their original range, resulting in the final clear image. .