An edge orientation constraint based compressive sensing image reconstruction method

Abstract

The application relates to the technical field of image processing, in particular to an image reconstruction method based on edge orientation constraint. A non-convex regularization term is constructed based on edge information of an image block, an L1-TV model is combined to construct an image reconstruction model, and a mature optimization algorithm is used for solving. The model uses dynamic edge detection to locate a key structure area of an image, and correspondingly protects wavelet coefficients, so as to reduce the shrinkage deviation of large coefficients, and thus edge and texture information can be more accurately reserved.

Description

Technical Field

[0001] This invention constructs a compressed sensing reconstruction method based on edge orientation constraints, belonging to the field of image signal processing technology. Background Technology

[0002] Compressed sensing is a novel signal processing technique based on sparse priors. For a signal in a given transform basis... Signals that can be sparsely represented under (e.g., wavelet basis) ,Right now Through a measurement matrix that is independent of the transformation basis Dimensionality reduction sampling is performed, and the mathematical model is expressed as:

[0003]

[0004] in, It is a perception matrix. Candes, Tao, et al. proved that when A satisfies the RIP property, it can be derived from low-dimensional signals. The original signal was recovered without loss. Compressed sensing has enormous application potential in scenarios where complete data acquisition is difficult and sampling equipment performance is limited (such as medical imaging, remote sensing, and sensor networks).

[0005] The core of compressed sensing is solving an inverse problem based on sparsity regularization. Since directly minimizing the L0 norm (i.e., the number of non-zero elements) is an NP-hard problem, early models widely adopted L1 norm minimization.

[0006]

[0007] Among them, L1 norm It can effectively promote the sparsity of solutions. However, the L1 norm is only an approximation of the L0 norm, and its solutions are biased, and it does not always yield the sparsest true solution.

[0008] In practical applications, especially compressed sensing of natural images, obtaining ideal sparse signals is often very difficult. Although the coefficients of the image in the transform domain... It exhibits compressibility, meaning that most coefficients have small amplitudes, but they are usually not strictly zero, instead exhibiting an approximately sparse structure. Therefore, a real signal can be modeled as an ideal sparse signal. With noise The superposition, that is The presence of such noise is unavoidable. Therefore, under noise interference, the quality of compressed sensing reconstruction will significantly decrease, mainly due to the following problems. First, L1 regularization is highly sensitive to measurement noise. To fit the noisy observation vector... The optimization process will lead to a solution in the real signal In addition to the primary support set, a large number of coefficients that should be zero are incorrectly activated; this phenomenon is called "pseudo-support set expansion," which manifests as granular noise, speckles, and false textures in the reconstructed image. Secondly, the soft thresholding operator in solving the L1 regularization method applies a uniform shrinkage to all coefficients, introducing systematic amplitude bias. On the one hand, it continuously underestimates those significantly non-zero coefficients representing the main structure and contours of the image, leading to amplitude distortion of the reconstructed signal, which manifests as blurred edges and decreased contrast in the image. On the other hand, it sets almost all the non-sparse, weak components representing real details to zero, further causing a loss of detail.

[0009] The biggest problem with L1 regularized reconstruction models in practical applications is noise. Although the noise energy is small, it lacks sparsity, thus introducing unavoidable errors during the dimensionality reduction and reconstruction process of compressed sensing. To simplify the analysis, consider a linear reconstruction process. Assume the existence of an ideal linear reconstruction method. This makes the reconstruction results , will observe the signal Substituting the values, the reconstruction result can be decomposed into:

[0010]

[0011] In this ideal scenario, sparse principal components It can be perfectly reconstructed. However, for noise terms... ,when When not sparse, for The reconstruction of [the problem] is a typical underdetermined problem, and there is no method that can reconstruct it correctly. Among reconstruction methods that aim to minimize the L1 norm, the reconstruction results are... It is almost certainly a severely distorted error vector. Distorted noise. Not only did it lose realistic texture details, but it also destroyed the main outline. The accuracy of the reconstruction is compromised. Because the reconstruction coefficients deviate from the true distribution, the visual quality of the reconstructed image is significantly reduced.

[0012] Therefore, compressed sensing signal reconstruction in practical applications is essentially an underdetermined inverse problem. To address its ill-posedness, it is usually necessary to introduce effective prior knowledge to constrain the solution space.

[0013] In view of this, this application proposes a new image reconstruction method that aims to effectively suppress noise while preserving edge structure. Summary of the Invention

[0014] The main objective of this application is to provide a compressed sensing image reconstruction method based on edge orientation constraints, which aims to solve the problem of how to suppress noise during the image reconstruction process while maintaining edge structure.

[0015] To achieve the above objectives, this application provides a compressed sensing image reconstruction method combining edge non-convex regularization, the method comprising:

[0016] S10, determine the edge information of each image block to be built;

[0017] S20, Construct a non-convex regularization term based on the edge information;

[0018] S30, Construct an image reconstruction model based on the non-convex regularization term;

[0019]

[0020] S40, the image block to be reconstructed is input into the image reconstruction model, the alternating direction multiplier method is used to perform iteration, and the image reconstruction result output by the image reconstruction model is obtained after the iteration converges.

[0021] This application has at least the following beneficial effects:

[0022] 1. By dynamically updating edge information, the localization is gradually optimized during the reconstruction process, effectively avoiding misjudgment caused by fuzzy initial estimation or noise interference;

[0023] 2. Non-convex regularization is precisely applied to the wavelet coefficients corresponding to the edges to reduce the shrinkage bias of large coefficients, thereby more accurately preserving edge and texture information. This adaptive mechanism not only improves the quality of the reconstructed vision but also significantly accelerates the convergence process of the objective function, enabling the algorithm to achieve a better balance between edge preservation and noise suppression.

[0024] 3. The alternating direction multiplier method is used to solve the optimization problem efficiently, ensuring both convergence and computational efficiency;

[0025] 4. It can maintain excellent reconstruction performance even in low sampling rate and high noise environments. Experiments have shown that it can effectively alleviate the artifacts and blurring problems caused by traditional L1 regularization. Attached Figure Description

[0026] Figure 1 This is a schematic flowchart of the compressed sensing image reconstruction method based on edge orientation constraints involved in the embodiments of this application;

[0027] Figure 2 This is a comparison of the reconstruction results of the method in this application and the conventional method on the Foreman image;

[0028] Figure 3This is a comparison chart of the reconstruction results of the method in this application and the traditional method on the image Child;

[0029] Figure 4 This paper compares the performance metrics of the method in this application with those of traditional methods at different sampling rates on Foreman images.

[0030] Figure 5 This paper compares the performance of the method in this application with that of traditional methods at different sampling rates on the image child.

[0031] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0032] To better understand the above technical solutions, exemplary embodiments of this disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of this disclosure to those skilled in the art.

[0033] First Embodiment

[0034] Reference Figure 1 This embodiment provides a compressed sensing image reconstruction method (EP-CR) based on edge orientation constraints. The method, combined with the compressed sensing image reconstruction method with edge non-convex regularization, includes the following steps:

[0035] S10, determine the edge information of each image block to be built;

[0036] First, the WTMM method is used for spatial domain edge detection on the coarsely reconstructed image. The first derivative of the Gaussian function is used as a wavelet basis to construct horizontal and vertical convolution kernels to convolve the rapidly reconstructed image, calculating the gradient modulus and orientation angle pixel by pixel. Then, local maxima are searched along the gradient direction; if the current modulus is greater than its two neighbors and exceeds a threshold, a local maximum is detected. If the points are marked as candidate edge points, a binary edge map is obtained.

[0037] Next, the image is decomposed using wavelet decomposition to obtain coefficients at various scales. All wavelet coefficients are iterated through, and their corresponding support regions in the spatial domain are determined based on their scale and location. The proportion of pixels marked as edges within the support region of each coefficient is calculated; if this proportion exceeds a threshold... If the coefficient belongs to the non-low frequency subband (LL), then the coefficient is marked as "marginal correlation wavelet coefficient".

[0038] Finally, the labeled wavelet coefficients are classified according to their sub-bands and scales to construct an index set of high-frequency edge coefficients. This index structure lays the foundation for applying adaptive sparse constraints of different strengths in different frequency bands, enabling differentiated protection strategies for high-frequency and low-frequency edge coefficients.

[0039] The above process constructs an adaptive structural prior for the image through dynamic edge detection driven by coarse reconstruction. Compared with global statistical priors such as wavelet coefficient sparsity or TV, the edge prior extracted by this method is directly derived from the specific image content, which can accurately capture the geometric structural differences of individual images. This enables more targeted edge protection and feature enhancement during the regularization process, laying a key foundation for high-fidelity compressed sensing reconstruction.

[0040] S20, construct a non-convex regularization based on the edge information, wherein the expression is:

[0041]

[0042] in, Control the sparsity promotion intensity.

[0043] In this embodiment, non-convex regularization is applied to the coefficients. When the value is small, it has strong compression capability, effectively bringing noise or redundancy coefficients close to zero; while... When the value is large, the penalty effect weakens, thus asymptotically and unbiasedly preserving image edges. This property makes it particularly suitable for sparsity promotion of edge-related wavelet coefficients.

[0044] It should be noted that, from the perspective of image representation, edge structures in the wavelet domain are mainly represented by sparse coefficients with larger amplitudes in the high-frequency subbands, while smooth or textured regions that are not edges correspond to a large number of coefficients with smaller amplitudes. Based on this prior knowledge, the non-convex optimization process is mainly applied to the wavelet coefficients related to edges in the high-frequency subbands, while the low-frequency coefficients are kept unchanged or only moderately constrained by the data fidelity term.

[0045] To balance the sparsity performance of non-convex regularization with the advantages of convexity in optimization problems (such as global optimum, convergence reliability, and simplified parameter selection), it is necessary to ensure that the objective function is strictly convex globally. According to relevant theories, this is achieved when the following conditions are met: When the objective function is strictly convex, it can fully leverage the strong sparsity-inducing ability of the non-convex penalty while maintaining the numerical stability and efficient convergence of the optimization process.

[0046] S30, Construct an image reconstruction model based on the non-convex regularization term;

[0047] S40, the image block to be reconstructed is input into the image reconstruction model, the alternating direction multiplier method is used to perform iteration, and the image reconstruction result output by the image reconstruction model is obtained after the iteration converges.

[0048] In each ADMM iteration, the algorithm performs the following key steps: First, a temporary image is reconstructed based on the current wavelet coefficient estimates. Then, the wavelet modulus maxima method is used to dynamically detect and accurately locate edge regions in the image. This edge detection process is continuously optimized with each iteration, gradually distinguishing between real edge structures and noise interference. Subsequently, the algorithm applies a scale-adaptive non-convex penalty function to the wavelet coefficients corresponding to the identified edge regions. The unique feature of this function is that it applies a strong contraction to small-amplitude coefficients to suppress noise, while applying a near-zero penalty to large-amplitude coefficients. This effectively avoids the systematic amplitude underestimation problem caused by traditional L1 regularization, ensuring that important edge and texture information is accurately preserved.

[0049] In the technical solution provided in this embodiment, non-convex regularization is constructed based on the edge information of image blocks, and a reconstruction model is constructed by combining L1 and TV regularization. This allows the algorithm to fit non-edge regions without overfitting noise in order to compensate for the deviation of edge regions, thereby more effectively suppressing pseudo-undulations and noise in non-edge regions.

[0050] Second Embodiment

[0051] Based on any embodiment, in this embodiment, the image reconstruction model includes L1 regularization and TV regularization in addition to the non-convex regularization term, resulting in the following expression for the image reconstruction model:

[0052]

[0053] in, For measurement data, For the perception matrix, It is wavelet transform. These are wavelet coefficients. It is the set of indices of all high-frequency subbands in the image wavelet decomposition, where L is the number of wavelet decomposition levels. It is a set of indices for high-frequency coefficients at the edges. It is a set Different scales Index on This is the regularization parameter.

[0054] This is the fidelity term, which measures the performance of wavelet coefficients. Reconstructed signal Compared with actual observation data The squared error between the two values. Minimizing this term ensures that the reconstruction results do not deviate from the actual measurements, preventing structural distortion caused by over-regularization.

[0055] This is an L1 regularization term applied to the wavelet coefficients. By imposing sparsity constraints, it causes most insignificant wavelet coefficients to shrink to zero. This effectively suppresses noise and irrelevant details, thereby promoting a sparse representation of the signal globally.

[0056] This is a TV regularization term that operates in the image space. It takes an isotropic form and is defined as follows:

[0057]

[0058] in, and These are the gradients in the horizontal and vertical directions, respectively. This regularization term effectively suppresses oscillations in abrupt regions by penalizing the image gradient, thereby maintaining the continuity of the intensity distribution in smooth regions, while allowing limited gradient changes at structural locations such as edges to preserve key image structural information.

[0059] In the technical solution provided in this embodiment, the TV regularization term is updated in the image domain after performing an inverse transform on the wavelet coefficients, and the Chambolle dual algorithm is used to effectively suppress artifacts and noise in the piecewise smooth region; the L1 regularization term processes the wavelet coefficients through the classic soft threshold function to further enhance the sparsity of the coefficients. After a preset number of iterations and convergences, the reconstruction results of each image block are stitched together into a complete reconstructed image, and appropriate post-processing is performed. The final output reconstructed image maintains high objective quality indicators while exhibiting significant advantages in terms of sharp edges and clear textures, effectively overcoming the edge blurring and artifact problems commonly found in traditional compressed sensing reconstruction methods, thus verifying the effectiveness and advancement of the proposed method.

[0060] Third Embodiment

[0061] Based on any embodiment, this embodiment provides a method for performing iterations using the Alternating Direction Multiplier Method (ADMM). The ADMM decomposes a complex optimization problem into multiple simpler subproblems. Specifically:

[0062] S41, by introducing auxiliary variables Refactor the problem into an equivalent constraint form:

[0063]

[0064] in, It is the gradient operator. Representing element-wise multiplication. Constructing the augmented Lagrangian function:

[0065]

[0066] in, As dual variables, This is the penalty parameter.

[0067] S42, update wavelet coefficients using the conjugate gradient method:

[0068]

[0069] This quadratic programming problem can be solved efficiently using the conjugate gradient method. The corresponding equation is: ,in express It is in diagonal matrix form.

[0070] S43, Update the L1 regularization term using a soft threshold:

[0071]

[0072] This problem has a closed-ended solution, which can be achieved using a soft threshold function: The soft threshold operator is defined as follows: .

[0073] S44, Update the TV regularization term using the Chambolle dual algorithm:

[0074]

[0075] This problem is equivalent to the total variational denoising problem in the image domain, and can be solved using the Chambolle dual algorithm:

[0076]

[0077]

[0078] in, As dual variables, This is the step size parameter.

[0079] S45, through an inner loop, introduces an auxiliary variable and iteratively updates the edge-aware regularization auxiliary variable:

[0080]

[0081] This problem is solved using an inner loop, introducing an auxiliary variable. and Iterative updates:

[0082]

[0083]

[0084]

[0085] in, It represents the number of iterations in the inner loop.

[0086] S46, Update the dual variable:

[0087]

[0088]

[0089]

[0090] Verification Implementation Examples

[0091] Based on the method provided in any of the above embodiments, in this embodiment, as follows: Figure 2As shown, compressed sensing reconstruction was performed on the Foreman test images at a 50% sampling rate. The performance of SPGL, L1-TV, Non-convex, and the proposed EP-CR method was compared across three dimensions: the complete image, the 64x64 block image, and the error image. The results are as follows: In the first row, the complete image, using the original image as a baseline, shows clear character outlines, rich textures in clothing folds and background details, and no artifacts or blurring. The SPGL reconstruction image exhibits significant grain noise, slightly blurred edges, loss of textures such as clothing folds, and poor visual smoothness. While L1-TV suppresses some noise, smooth areas such as the background wall show a stepped effect, and the character's facial outline is blurred. Non-convex noise suppression is better than the previous two, with slightly improved edge clarity, but still some loss of detail and poor texture integrity. EP-CR is closest to the original image, with sharp edges, complete texture details, no obvious noise artifacts, and the highest visual fidelity. The second row shows the 64x64 block image focusing on local details. The original image blocks show clear eyelashes and skin texture. The SPGL block exhibits significant noise, with almost complete loss of skin texture around the eyes and chaotic pixel fluctuations at the edges; the L1-TV block shows a smooth transition but blurry details, with some pixels exhibiting blocky artifacts that disrupt the continuity of the local structure; the Non-convex block improves details but still shows a slight shift in the eye contour and insufficient texture fineness; the EP-CR block accurately restores local features, with clear eyelashes and facial lines, natural pixel transitions, and high consistency with the original image. The third row shows the error maps between the reconstruction method and the original image patch (the higher the brightness, the greater the deviation): The SPGL error map is bright overall, with dense error pixels, and a large number of high-deviation pixels in both edge and smooth areas. The deviation is more significant in areas with complex textures such as clothing folds; The L1-TV error map has lower brightness, but there are still high-deviation pixels in the edge areas due to regularization shrinkage, and the error in the smooth area is distributed in blocks at the pixel transitions; The Non-convex error map has further reduced brightness, with sparse pixel distribution, and there are still a few high-deviation pixels in weak edge areas. The deviation control is better than the previous two, but it is not optimal; The EP-CR error map is the darkest, with very few and scattered pixels. Only a few noise-sensitive areas have slight deviations, and the deviations in each area are at a very low level. The difference between the reconstructed value and the original value is the smallest.

[0092] like Figure 3As shown, the performance of different methods was compared across three dimensions—complete image, local detail, and error image—based on Child image reconstruction experiments. In the complete image, the original image has sharp contours and natural texture; SPGL exhibits grainy noise and loss of detail; L1-TV shows a staircase effect and blurred edges; Non-convex noise suppression is better but still has artifacts; EP-CR is closest to the original image, with complete details and clear contours. In the local detail analysis, SPGL shows significant block noise, L1-TV blocks have smooth transitions leading to block artifacts, Non-convex blocks still have slight contour shifts, while EP-CR blocks accurately restore details with natural transitions. In the error image, SPGL has widespread and high-brightness errors, L1-TV shows significant deviations in edge regions, Non-convex errors are reduced but still have deviations at weak edges, and EP-CR has the darkest error with minimal deviation. In summary, EP-CR outperforms other methods in both visual effect and error control, achieving the best reconstruction performance.

[0093] like Figure 4 As shown, in Foreman image compressed sensing reconstruction, based on the provided performance comparison data analysis, EP-CR exhibits significant advantages in all key indicators. This invention will analyze it from two dimensions: Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). Regarding PSNR, EP-CR maintains a leading position across all sampling rates, particularly in the low-to-medium sampling rate range (30%-70%). This indicates that EP-CR can more effectively utilize limited observation data, and its unique edge protection mechanism plays a crucial role in situations of insufficient information. Analysis of the SSIM index further verifies the superiority of this invention, with EP-CR consistently maintaining the highest level. This phenomenon demonstrates that EP-CR not only performs excellently in numerical accuracy but also has significant advantages in preserving image structural information, edge sharpness, and visual naturalness. The significant improvement in structural similarity directly reflects the improved visual perception quality of this method.

[0094] like Figure 5 As shown, in Child image compressed sensing reconstruction, based on the provided performance comparison data, EP-CR demonstrates significant advantages in all key indicators. Regarding PSNR, EP-CR maintains its leading position even under low sampling rate conditions, indicating that the introduced edge guidance mechanism and global non-convex constraint play a crucial role in situations with insufficient information. Analysis of the SSIM indicator further confirms the algorithm's superiority; EP-CR not only excels in numerical accuracy but also performs exceptionally well in preserving image structural information, edge sharpness, and visual naturalness.

[0095] However, EP-CS is a priori-guided iterative optimization method, and its effectiveness depends on sufficient measurements to support a preliminary coarse structure reconstruction. When the sampling rate is below 0.3, insufficient measurement information leads to poor reconstruction results, resulting in poor overall performance of the proposed algorithm. Conversely, in the scenario with a sampling rate of 0.9, the signal is already close to ideal sparsity in the wavelet domain. In this case, introducing too much prior information can limit the reconstruction performance. Therefore, we observed that the SPGL method actually outperforms other methods that use prior constraints in terms of PSNR / SSIM.

[0096] A deeper analysis reveals the reasons for the performance gap. Traditional SPGL algorithms rely solely on L1 sparsity constraints, offering insufficient edge protection. While the L1-TV combination introduces spatial continuity constraints, the trade-off between the two often results in blurred edges. Basic global non-convex methods enhance the preservation of large coefficients but lack targeted protection for edge structures. In contrast, EP-CR's innovation lies in its organic combination of dynamic edge detection and adaptive non-convex penalty—edge detection ensures accurate localization of key structures, while non-convex constraints provide differentiated protection for these structures, avoiding over-smoothing and suppressing artifacts. In summary, EP-CR, through the synergistic effect of multiple regularization terms and intelligent guidance from edge priors, achieves a significant improvement in reconstruction quality under a wide range of sampling conditions, demonstrating stronger practical value, particularly in low-sampling scenarios, providing an effective solution for compressed sensing image reconstruction.

[0097] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0098] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A compressed sensing image reconstruction method based on edge orientation constraints, characterized in that, The reconstruction method includes the following steps: S10, determine the edge information of each image block to be built; S20, Construct a non-convex regularization term based on the edge information; S30, Construct an image reconstruction model based on the non-convex regularization term; S40, input the image block to be reconstructed into the image reconstruction model, perform iteration using the alternating direction multiplier method, and obtain the image reconstruction result output by the image reconstruction model after the iteration converges; S10 includes: S11, perform fast coarse reconstruction of the signal to be reconstructed; S12, the modulus maxima method is used for spatial domain edge detection on the coarsely reconstructed image. The first derivative of the Gaussian function is used as a wavelet basis to construct a convolution kernel to convolve the rapidly reconstructed image. Gradient modulus and orientation angle are calculated pixel-by-pixel. Then, local modulus maxima are searched along the gradient direction. If the current modulus is greater than its two neighboring values ​​and exceeds a threshold, the local modulus is considered. If the points are marked as candidate edge points, a binary edge map is obtained. S13, perform wavelet decomposition on the image to obtain coefficients at each scale. Iterate through all wavelet coefficients and determine their corresponding support regions in the spatial domain based on their scale and location. Calculate the proportion of pixels marked as edges within the support region of each coefficient. If this proportion is greater than a threshold... If the coefficient belongs to a non-low-frequency sub-band, then the coefficient is marked as an edge-correlated wavelet coefficient; S14, construct the edge coefficient index, classify the marked wavelet coefficients according to their sub-band and scale, and construct the edge high-frequency coefficient index set E; The model in S20 is represented as follows: Based on the aforementioned edge information, an edge non-convex regularization term is constructed. This term does not act on all coefficients, but rather selectively and precisely applies to the set of edge coefficients in the high-frequency subbands corresponding to the edge regions. It focuses only on the edge and structural information most important to visual perception, providing asymptotically unbiased contraction at large coefficient values, thereby avoiding a systematic underestimation of significant edge structures. This non-convex function is defined as follows: ； Among them, parameters Controlling the sparsity promotion strength, although the function is non-convex, its strict convexity can be guaranteed by satisfying certain conditions, when the parameters satisfy... When this condition is met, the strict convexity of the function can be guaranteed. The model in S30 is represented as follows: ； in, For measurement data, For the perception matrix, It is wavelet transform. These are wavelet coefficients. It is the set of indices of all high-frequency subbands in the image wavelet decomposition, where L is the number of wavelet decomposition levels. It is a set of indices for high-frequency coefficients at the edges. It is a set Different scales Index on For regularization parameters; This is the fidelity term, which measures the wavelet coefficients. Reconstructed signal Compared with actual observation data Minimizing this term, which represents the squared error between the two values, is to ensure that the reconstruction results do not deviate from the actual measured values ​​and to prevent structural distortion caused by excessive regularization. It is the L1 regularization term, which imposes a global sparsity constraint in the wavelet domain and is mainly used for noise suppression and background smoothing. Since natural images are sparsity under wavelet transform, the L1 norm, as a sparsity penalty for convex relaxation, will cause small coefficients to be compressed to zero, which effectively filters out noise and weak texture details scattered across the entire frequency band. This is the TV regularization term, which imposes a piecewise smoothness constraint in the image space. It is primarily used to maintain edge sharpness and smooth homogeneous regions, aiming to promote the piecewise smoothness of the image. It suppresses oscillations in abrupt regions by penalizing the image gradient and is defined in an isotropic form. ； in, and These are the gradients in the horizontal and vertical directions, respectively. The model ensures data consistency through a fidelity term, utilizes L1 and TV regularization to leverage the sparsity and piecewise smoothness characteristics of the transform domain and spatial domain respectively, and introduces edge non-convex regularization to precisely optimize the initial solution, thereby enhancing the ability to preserve edge information. Ultimately, it achieves a balance between denoising, smoothing, and detail preservation.

2. The method according to claim 1, characterized in that, The method in S40 is as follows: S41 reconstructs the problem into an equivalent constraint form by introducing auxiliary variables, and constructs an augmented Lagrangian function. S42 updates the wavelet coefficients using the conjugate gradient method; S43 updates L1 regularization using a soft threshold; S44 updates TV regularization using the Chambolle dual algorithm; S45 achieves non-convex regularization of inner iterative loop edges; S46 updates auxiliary variables.

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