An image multiplicative noise removal method and system

Abstract

The application discloses an image multiplicative noise removing method and system, and relates to the technical field of image processing. The method comprises the following steps: constructing a multiplicative noise removing model combined with block matching local SVD operator-based sparse regularization and total variation and fractional variation combined regularization; decomposing the multiplicative noise removing model to obtain an optimization subproblem; the optimization subproblem comprises the following steps: sparse basis updating, a subproblem for solving a sparse regularization term, a subproblem for solving a total variation and fractional variation combined regularization term, and Lagrange multiplier updating; inputting a noise image into the multiplicative noise removing model, iteratively solving the optimization subproblem, and reconstructing a denoised image according to a solving result. The application can improve the quality and usability of an image.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to a method and system for removing multiplicative noise from images. Background Technology

[0002] In coherent imaging systems, such as imaging systems and ultrasound imaging systems, multiplicative noise contamination is common. Unlike additive noise, multiplicative noise is correlated with the signal, resulting in a lower signal-to-noise ratio and more severe structural damage to images contaminated with multiplicative noise. Common denoising methods primarily focus on removing additive noise and cannot be directly applied to remove multiplicative noise.

[0003] The degradation process of multiplicative noise in a coherent imaging system can be expressed as: f = un, where u is the ideal noise-free image, n is the noise following a certain probability distribution, and f is the observed image. Here, f, u, and n are functions defined in the image domain. In various imaging systems, multiplicative noise is mostly not Gaussian noise. For example, in SAR imaging, the noise follows a gamma distribution, while in ultrasound imaging, the noise follows a Rayleigh distribution.

[0004] Denoising methods based on sparsity regularization, such as BM3D and dictionary learning, effectively remove multiplicative noise through sparse transformation, constraint, and reconstruction of images. However, their effectiveness often depends on a good sparse basis. A fixed sparse basis may result in some sparse coefficients after image transformation that are not sparsity enough. Furthermore, sparse regularization methods guide image reconstruction at a global level, ignoring the local structure of the image, which may lead to ringing artifacts in the reconstructed image, leaving artifacts in local regions.

[0005] In response to the aforementioned bottlenecks, there is an urgent need to improve sparse representation capabilities and develop new sparse regularized image denoising methods to enhance image quality and usability. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for removing multiplicative noise from images, so as to improve the quality and usability of images.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] An image multiplicative noise removal method includes:

[0009] Construct a multiplicative noise removal model that combines sparse regularization based on block-matching local SVD operators with joint regularization of total variation and fractional variation;

[0010] The multiplicative noise removal model is decomposed to obtain optimization subproblems; the optimization subproblems include: sparse basis update, subproblem for solving sparse regularization term, subproblem for solving joint regularization term of total variation and fractional variation, and Lagrange multiplier update;

[0011] The noisy image is input into the multiplicative noise removal model, the optimization sub-problem is solved iteratively, and the denoised image is reconstructed based on the solution results.

[0012] Optionally, a multiplicative noise removal model is constructed that combines sparse regularization based on block-matching local SVD operators with joint regularization of the total variation and fractional variation, specifically including:

[0013] A strictly convex fidelity term for multiplicative noise is constructed based on maximum a posteriori estimation and logarithmic transformation.

[0014] Construct a sparse regularization term based on the block-matching local SVD operator;

[0015] Construct a joint regularization term for the total variation and fractional variation based on a smooth prior;

[0016] A multiplicative noise removal model is constructed based on the strict convexity fidelity term, the sparse regularization term, and the joint regularization term of the total variation and fractional variation.

[0017] Optionally, the expression for the multiplicative noise removal model is:

[0018]

[0019] Where f is the vectorized form of the noisy image, T j For block matching local SVD operator, j = {1, 2, ..., J} is the index of the image patch, J is the total number of image patches divided by f, and μ j ω is the sparse regularization parameter, μ is the TFV regularization parameter, TFV is the discrete isotropic total variational and fractional variational joint operator, diag is the diagonalization operator, and ω is the transformation vector after logarithmic transformation of the vectorized form of the denoised image.

[0020] Optionally, the multiplicative noise removal model can be decomposed to obtain optimization sub-problems, specifically including:

[0021] By employing a variable separation method and introducing auxiliary variables, the multiplicative noise removal model is transformed into a constrained minimization optimization problem.

[0022] The augmented Lagrangian method is used to transform the constrained minimization optimization problem into an unconstrained minimization optimization problem.

[0023] The unconstrained minimization optimization problem is decomposed into optimization subproblems.

[0024] Optionally, the expression for the optimization subproblem is:

[0025]

[0026]

[0027]

[0028]

[0029] Among them, T j,k For the block-matching local SVD operator in the k-th iteration, M j,k Let be the low-rank matrix of the k-th iteration. Let α be the auxiliary variable for the k-th iteration. j As an auxiliary variable, ω k Let ω be the transformation vector for the k-th iteration. k-1 Let be the transformation vector for the (k-1)th iteration. Let Lagrange multipliers be the multipliers for the k-th iteration. Let f be the Lagrange multiplier for the (k-1)th iteration, f be the vectorized form of the noisy image, ω be the transformation vector after logarithmic transformation of the vectorized form of the denoised image, vec be the matrix vectorization operator, diag be the diagonalization operator, TFV be the discrete isotropic total variational and fractional variational joint operator, and μ be the Lagrange multiplier for the (k-1)th iteration. j η is the sparse regularization parameter, μ is the TFV regularization parameter, η is the step size parameter for the transformation vector iteration, δ is the step size parameter for the Lagrange multiplier iteration, j = {1,2,...,J} is the index of the image patch, J is the total number of image patches divided by f, and k is the iteration number.

[0030] Optionally, the noisy image is input into the multiplicative noise removal model to iteratively solve the optimization sub-problem, and the denoised image is reconstructed based on the solution results, specifically including:

[0031] The noisy image is acquired and vectorized and logarithmically transformed to obtain the initial transformation vector.

[0032] The optimization subproblem is iteratively solved based on the initial transformation vector to obtain the solution result;

[0033] The solution is subjected to inverse logarithmic transformation and vector matrix rearrangement to obtain a denoised image.

[0034] Optionally, the optimization subproblem is solved iteratively based on the initial transformation vector to obtain the solution result, specifically including:

[0035] Non-local similarity block matching is performed on the transformation vector of the (k-1)th iteration to obtain the low-rank matrix of the k-th iteration; where k is a positive integer starting from 1, when k=1, the transformation vector of the (k-1)th iteration is the initial transformation vector, and the Lagrange multipliers and auxiliary variables of the (k-1)th iteration are all preset values.

[0036] Based on the low-rank matrix of the k-th iteration and the transformation vector of the (k-1)-th iteration, a sparse basis update is performed to obtain the block-matching local SVD operator of the k-th iteration.

[0037] Based on the block matching local SVD operator of the k-th iteration, the transformation vector of the (k-1)-th iteration, the Lagrange multipliers of the (k-1)-th iteration, and the auxiliary variable of the (k-1)-th iteration, the linear Bregman algorithm is used to solve the subproblem used to solve the sparse regularization term, and the auxiliary variable of the k-th iteration is obtained.

[0038] Based on the auxiliary variable of the k-th iteration, the block matching local SVD operator of the k-th iteration, and the Lagrange multiplier of the (k-1)-th iteration, the gradient descent method is used to solve the subproblem used to solve the joint regularization term of the total variation and fractional variation, and the transformation vector of the k-th iteration is obtained.

[0039] Based on the transformation vector of the k-th iteration, the block matching local SVD operator of the k-th iteration, the auxiliary variable of the k-th iteration, and the Lagrange multiplier of the (k-1)-th iteration, the Lagrange multiplier is updated to obtain the Lagrange multiplier of the k-th iteration.

[0040] Determine whether the stopping condition is met based on the transformation vector of the k-th iteration and the transformation vector of the (k-1)-th iteration.

[0041] If not satisfied, update the value of k and return to the step of performing nonlocal similarity block matching on the transformation vector of the (k-1)th iteration to obtain the low-rank matrix of the kth iteration;

[0042] If the conditions are met, the transformation vector of the kth iteration is determined as the solution result.

[0043] An image multiplicative noise removal system, comprising:

[0044] The model building module is used to build a multiplicative noise removal model that combines sparse regularization based on block matching local SVD operators with joint regularization of total variation and fractional variation.

[0045] The problem decomposition module is used to decompose the multiplicative noise removal model to obtain optimization sub-problems; the optimization sub-problems include: sparse basis update, sub-problem for solving sparse regularization term, sub-problem for solving joint regularization term of total variation and fractional variation, and Lagrange multiplier update;

[0046] The iterative solution module is used to input the noisy image into the multiplicative noise removal model, iteratively solve the optimization sub-problem, and reconstruct the denoised image based on the solution results.

[0047] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0048] The image multiplicative noise removal method provided by this invention first constructs a multiplicative noise removal model that combines sparse regularization based on block-matching local SVD operators with joint regularization of total variation and fractional variation. Second, the multiplicative noise removal model is decomposed to obtain optimization sub-problems, including: sparse basis update, a sub-problem for solving the sparse regularization term, a sub-problem for solving the joint regularization term of total variation and fractional variation, and Lagrange multiplier update. Finally, the noisy image is input into the multiplicative noise removal model, the optimization sub-problems are iteratively solved, and the denoised image is reconstructed based on the solution results. Compared with other classic methods in the same field, this invention has stronger denoising capabilities and overall structure preservation capabilities, and further enhances the ability to preserve special structures such as similar textures. It is more suitable for images contaminated by high-intensity multiplicative noise, and can improve image quality and usability. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 A flowchart of the image multiplicative noise removal method provided by the present invention;

[0051] Figure 2 A detailed flowchart of the image multiplicative noise removal method provided by the present invention;

[0052] Figure 3 The original image provided for the embodiments of the present invention;

[0053] Figure 4 The noise image provided in the embodiments of the present invention;

[0054] Figure 5 This is a Synimage denoised image provided in an embodiment of the present invention;

[0055] Figure 6 This is a Barbara-denoised image provided in an embodiment of the present invention. Detailed Implementation

[0056] 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.

[0057] The purpose of this invention is to provide a method and system for removing multiplicative noise from images, so as to improve the quality and usability of images.

[0058] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] This invention provides a method for removing multiplicative noise from images, such as... Figure 1 and Figure 2 As shown, the method includes:

[0060] Step S1: Construct a multiplicative noise removal model based on the joint sparse regularization of the block-matching local SVD operator and the joint regularization of the total variation and fractional variation, namely the BMSVD-TFV regularization model.

[0061] Step S1.1: Construct a strictly convex fidelity term for multiplicative noise based on maximum a posteriori estimation and logarithmic transformation.

[0062] The fidelity term is used to constrain the similarity between the denoised image and the original noisy image. This invention focuses on multiplicative noise that follows a gamma distribution. Gamma multiplicative noise follows a gamma distribution with a mean of 1 and a variance of 1 / L, and its probability density function is as follows:

[0063]

[0064] Where x represents the gray value of a pixel, Γ is the gamma function, and L > 0 is the noise level parameter, where a smaller L indicates a stronger noise. The globally strictly convex fidelity term corresponding to multiplicative gamma noise is:

[0065] H(ω,f)=||ω+fe -ω ||2;

[0066] Where ω = lnu, u is the vectorized form of the ideal noise-free image, and f is the vectorized form of the observed image. Here, f and u are functions defined on the image domain. After vectorization, it becomes Indicates the image size.

[0067] Step S1.2: Construct a sparse regularization term based on the block matching local SVD operator.

[0068] Image vectorization is obtained Divide image f into J image patches of size h×1. Perform similarity block matching on the image patch at position j. Construct a low-rank matrix M by stacking multiple vectorized similar image patches of image f at position j. j :

[0069]

[0070] in, It extracts a matrix, where all elements are either 0 or 1. Represents the i-th vectorized similar image patch corresponding to image patch j, h refers to the size of image patch f at j, and I j This represents the number of vectorized similar image patches of the image patch at location j. Performing an SVD transformation on the matrix yields:

[0071]

[0072] in, It is a diagonal matrix, U j ∈R h×h and Let be the orthogonal matrix obtained by SVD transformation. The equation is derived using the properties of the Kronecker product:

[0073]

[0074] Where vec is a matrix vectorization operator, for example It is the operator for the Kronecker product. For V j The i-th component. Therefore, the mathematical definition of the block-matching local SVD operator is:

[0075]

[0076] Therefore, we get:

[0077]

[0078] This is the sparse regularization term.

[0079] Step S1.3: Construct a joint regularization term based on the total variation and fractional variation of smooth priors.

[0080] We introduce a joint regularization term for the total variation and fractional variation based on a smooth prior, where TFV is a discrete joint operator of the total variation and fractional variation:

[0081]

[0082] Where 0≤c1≤1, 0≤c2≤1 represent the weights of the total variation term and the fractional variation term, and c1+c2=1, ‖·‖ 2,1 Defined as: when hour, And D x D y These are 1-dimensional first-order difference operators in the x and y directions, respectively. And D x,v D y,v These are 1D v-order difference operators in the x and y directions, respectively. For an N×N matrix... When i,j < 1 or i,j > N, let ω(i,j) = 0:

[0083]

[0084] in, Let Z be the binomial coefficient, and Z be the difference parameter to be set. When z ≥ v + 1, Defined as: Γ is the gamma function.

[0085] Step S1.4: Construct a multiplicative noise removal model based on the strict convexity fidelity term, the sparse regularization term, and the joint regularization term of the total variation and fractional variation.

[0086] First, the strictly convex fidelity term based on logarithmic transformation constructed in step S1.1 is introduced. Then, the sparse regularization term based on block-matching local SVD operator constructed in step S1.2 is introduced. Finally, the TFV regularization term based on smooth prior constructed in step S1.3 is introduced. With the introduction of these three terms, a multiplicative noise removal model combining sparse regularization and TFV regularization based on block-matching local SVD operator is proposed (hereinafter referred to as the BMSVD-TFV regularization model or multiplicative noise removal model):

[0087]

[0088] Where f is the vectorized form of the noisy image, T j For block matching local SVD operator, j = {1, 2, ..., J} is the index of the image patch, J is the total number of image patches divided by f, and μ j ω is the sparse regularization parameter, μ is the TFV regularization parameter, TFV is the discrete isotropic total variational and fractional variational joint operator, diag is the diagonalization operator used to transform a vector into a diagonal matrix, and ω is the transformation vector after logarithmic transformation of the vectorized form of the denoised image.

[0089] The first, second, and third terms in the model correspond to the strictly convex fidelity term, the sparse regularization term, and the TFV regularization term in the transform domain, respectively. The first term, the fidelity term in the transform domain, is derived through MAP estimation and logarithmic transform. It is obtained by multiplying the fidelity terms of each image patch with the block-matching local SVD operator and then summing the results. The second term, the sparse regularization term, removes noise by controlling the sparsity of the transform coefficients of ω. This is achieved through the sparse basis T... j As ω is continuously updated, its transformation coefficients will become increasingly sparse. μ≥0 and μ j ≥0 represents the regularization parameter, indicating the weight coefficient of this term. Here, the l0 norm is chosen as the measure of the sparse regularization term to achieve a stronger denoising effect than the l1 norm. Finally, the third term in the model is the TFV regularization term in the spatial domain, which can reduce artifacts introduced by sparse regularization.

[0090] Step S2: Decompose the multiplicative noise removal model to obtain optimization subproblems; the optimization subproblems include: sparse basis update, subproblem for solving sparse regularization term, subproblem for solving joint regularization term of total variation and fractional variation, and Lagrange multiplier update.

[0091] Step S2.1: Using the variable separation method and introducing auxiliary variables, the multiplicative noise removal model is transformed into a constrained minimization optimization problem.

[0092] Apply the variable separation method and introduce auxiliary variables and auxiliary variable matrix The model is transformed into an equivalent constrained minimization optimization problem:

[0093]

[0094] stα j =T j ω,j=1,2,…,J.

[0095] Step S2.2: Using the augmented Lagrangian method, the constrained minimization optimization problem is transformed into an unconstrained minimization optimization problem.

[0096] By introducing the augmented Lagrangian method, the constrained minimization optimization problem described above is transformed into an unconstrained minimization optimization problem:

[0097]

[0098] Where, λ j Let be the Lagrangian multiplier, where the superscript k represents the value of the variable at the k-th step of the iteration, i.e., the iteration number, and η and δ are both step size parameters, representing the step size of the iteration update.

[0099] Step S2.3: Decompose the unconstrained minimization optimization problem to obtain optimization subproblems.

[0100] The optimization problem can be decomposed into the following subproblems through alternating iterations:

[0101]

[0102] In each outer iteration, the sparse basis is updated by matching similar blocks. The sparse basis T in the iteration... j It can be represented as:

[0103]

[0104] Among them, the left singular matrix And right singular matrix From the corresponding SVD:

[0105]

[0106] in:

[0107]

[0108] Thus, sparse base U j,k and V j,k The outer loop is updated in each iteration. This update process makes the transformation coefficients sparser, thus achieving better denoising results.

[0109] The final iterative process can be reduced to the steps of sparse basis update, subproblem for solving sparse regularization term, subproblem for solving TFV regularization term, and updating Lagrangian multipliers. The expressions for each of the above subproblems are as follows:

[0110]

[0111]

[0112]

[0113]

[0114] Among them, T j,k For the block-matching local SVD operator in the k-th iteration, M j,k Let be the low-rank matrix of the k-th iteration. Let α be the auxiliary variable for the k-th iteration. j As an auxiliary variable, ω k Let ω be the transformation vector for the k-th iteration. k-1Let be the transformation vector for the (k-1)th iteration. Let Lagrange multipliers be the multipliers for the k-th iteration. Let f be the Lagrange multiplier for the (k-1)th iteration, f be the vectorized form of the noisy image, ω be the transformation vector after logarithmic transformation of the vectorized form of the denoised image, vec be the matrix vectorization operator, diag be the diagonalization operator, TFV be the discrete isotropic total variational and fractional variational joint operator, and μ be the Lagrange multiplier for the (k-1)th iteration. j η is the sparse regularization parameter, μ is the TFV regularization parameter, η is the step size parameter for the transformation vector iteration, δ is the step size parameter for the Lagrange multiplier iteration, j = {1,2,...,J} is the index of the image patch, J is the total number of image patches divided by f, and k is the iteration number.

[0115] Step S3: Input the noisy image into the multiplicative noise removal model, iteratively solve the optimization sub-problem, and reconstruct the denoised image based on the solution results.

[0116] To solve the optimization subproblems in the four iterative steps obtained in step S2, the known variables must first be input into the BMSVD-TFV regularization model.

[0117] Step S3.1: Image logarithmic transformation, i.e., acquiring the noisy image and performing vectorization and logarithmic transformation to obtain the initial transformation vector. In subsequent iterations, the iteration number k is a positive integer starting from 1. When k = 1, the transformation vector of the (k-1)th iteration is the initial transformation vector, and the Lagrange multipliers and auxiliary variables of the (k-1)th iteration are both preset values.

[0118] To introduce operators and construct the fidelity term in the BMSVD-TFV regularization model, the image is vectorized and logarithmically transformed, as mathematically expressed below:

[0119] f = vec(F);

[0120] ω 0 =aln(f+b);

[0121] Where F represents the input digital matrix image, i.e., the noisy image, a is the scale parameter, b is the offset parameter (b≥1), and ω 0 This is the initial transformation vector obtained after vectorizing and logarithmically transforming F.

[0122] Step S3.2: Similarity block matching, that is, performing non-local similarity block matching on the transformation vector of the (k-1)th iteration to obtain the low-rank matrix of the kth iteration.

[0123] Perform non-local similarity block matching on the image. For each image patch, find similar image blocks p. ij ω k-1i = 1, 2, ..., I j j = 1, 2, ..., J is obtained through the formula:

[0124]

[0125] Construct as a 2D low-rank matrix M j,k The corresponding extraction matrix is: P ij i = 1, 2, ..., I j , j = 1, 2, ..., J.

[0126] Step S3.3: Sparse basis update, that is, perform sparse basis update based on the low-rank matrix of the k-th iteration and the transformation vector of the (k-1)-th iteration to obtain the block matching local SVD operator of the k-th iteration.

[0127] Through operator T j,k Construct a sparse basis. Avoid the interference with operator T using the following formula. j,k Direct calculation:

[0128]

[0129]

[0130]

[0131] Step S3.4: Solve the subproblem for solving the sparse regularization term, i.e., based on the block matching local SVD operator of the k-th iteration, the transformation vector of the (k-1)-th iteration, the Lagrange multiplier of the (k-1)-th iteration, and the auxiliary variable of the (k-1)-th iteration, use the linear Bregman algorithm to solve the subproblem for solving the sparse regularization term, and obtain the auxiliary variable of the k-th iteration.

[0132] The following subproblems are solved using the linear Bregman algorithm:

[0133]

[0134] The solution process is as follows:

[0135]

[0136] Where, p k It refers to the continuous convex function part of the objective function in the linear Bregman algorithm. The gradient at step k, θ is the gradient of the smooth convex part of the objective function in the linear Bregman algorithm. denoted as g(α) j ),exist The linear approximation parameters of the first-order Taylor expansion, i.e. For a hard thresholding operator that processes each element individually:

[0137]

[0138] Step S3.5: Solve the subproblem for solving the TFV regularization term, that is, based on the auxiliary variable of the k-th iteration, the block matching local SVD operator of the k-th iteration, and the Lagrange multiplier of the (k-1)-th iteration, use the gradient descent method to solve the subproblem for solving the joint regularization term of the total variation and fractional variation, and obtain the transformation vector of the k-th iteration.

[0139] The following subproblems are solved using gradient descent:

[0140]

[0141] The iterative scheme is as follows:

[0142]

[0143] in This represents the matrix obtained after rearranging ω into a vector matrix, where τ > 0 is the step size parameter, and l = 1, 2, ..., N represents the vector representation of ω. k The element index is in the array, where array is the vector-matrix rearrangement operator and div is the integer division operator.

[0144] Step S3.6: Lagrangian multiplier update, i.e., based on the transformation vector of the k-th iteration, the block matching local SVD operator of the k-th iteration, the auxiliary variable of the k-th iteration, and the Lagrangian multiplier of the (k-1)-th iteration, perform Lagrangian multiplier update to obtain the Lagrangian multiplier of the k-th iteration; determine whether the stopping condition is met based on the transformation vector of the k-th iteration and the transformation vector of the (k-1)-th iteration; if not, update the value of k and return to step S3.2; if met, determine the transformation vector of the k-th iteration as the solution result.

[0145] The Lagragian multipliers are calculated using the following formula:

[0146]

[0147] Check if the stopping condition is met ||ω k -ω k-1 || / ||ω k-1 ||≤ε, where ε is a constraint parameter for precision. If the constraint is not met, return to step S3.2.

[0148] Step S3.7: Exponential restoration of the image, that is, performing inverse logarithmic transformation and vector matrix rearrangement on the solution result to obtain a denoised image.

[0149] The image is exponentially restored and rearranged to obtain the final denoised image U, as shown in the following formula:

[0150] u = e ω / a -b;

[0151]

[0152] in, This is the vector obtained after performing an inverse logarithmic transformation on the transformed vector obtained from the solution. The denoised image is obtained after vector matrix rearrangement of u, where array is the vector matrix rearrangement operator.

[0153] This invention proposes an image multiplicative noise removal method based on block-matching local SVD operator sparse regularization. The key feature is the introduction of the block-matching local SVD operator as a sparse basis and joint denoising with a TFV regularization term. A better sparse representation is obtained by updating the sparse basis derived from the local SVD operator, and the TFV regularization term helps reduce artifacts caused by sparse regularization. Alternating sparse regularization and TFV regularization can improve the removal effect of multiplicative noise. A specific embodiment is provided below to verify the above technical effects.

[0154] In this embodiment, let the original image be as follows: Figure 3 As shown, images Synimage and Barbara are included. Multiplicative gamma noise of L=10 is added to both, resulting in noisy images as shown. Figure 4 As shown, the specific steps for image denoising using the image multiplicative noise removal method provided by this invention are as follows:

[0155] (1) Establish a multiplicative noise removal model based on block-matching local SVD operator and TFV regularization (BMSVD-TFV regularization model):

[0156]

[0157] Where f is the vectorized form of the initial noisy image, and T j For block matching local SVD operator, j = {1, 2, ..., J} is the index of the image patch, μ ≥ 0 and μ j ≥0 is the regularization parameter, and TFV is the discrete isotropic total variational and fractional variational joint operator.

[0158] (2) Determine the optimization sub-problem of the BMSVD-TFV regularization model, i.e., the algorithm iteration steps are as follows:

[0159]

[0160]

[0161]

[0162]

[0163] in, λ is an auxiliary variable. j ,j=1,2,...,J are Lagrangian multipliers, and the superscript k represents the value of the variable at the k-th step of iteration.

[0164] (3) Solve the optimization subproblem of the BMSVD-TFV regularization model.

[0165] For a noisy image (Synimage) with dimensions of 256×256, set the logarithmic transform parameters a=40, b=25, and the image patch size parameter... Image patch quantity parameter I j =10, TFV regularization parameter μ=2, c1=0.5, c2=0.5, v=1.2, sparsity regularization parameter μ j =100.

[0166] For the noisy image Barbara, with dimensions of 512×512, set the logarithmic transform parameters a=40, b=25, and the image patch size parameter... Image patch quantity parameter I j =50, TFV regularization parameter μ=2, c1=0.5, c2=0.5, Z=20, v=1.2, sparsity regularization parameter μ j =600.

[0167] S3.1 Logarithmic transformation of the image.

[0168] For images Synimage images have N = 256, while Barbara images have N = 512. According to the mathematical expression:

[0169] f = vec(F);

[0170] ω 0 =40ln(f+25);

[0171] Perform logarithmic transformations on the images Synimage and Barbara respectively to obtain ω. 0 .

[0172] S3.2 Similar block matching.

[0173] According to the formula Calculate M j,k The extraction matrix P is constructed by non-local similar block matching. ij i = 1, 2, ..., Ij .

[0174] S3.3 Sparse Base Update.

[0175] Based on the formula:

[0176]

[0177]

[0178] calculate U j,k and V j,k . Sparse base U j,k and V j,k The outer ring was updated in all iterations. For the Synimage image, the outer ring iterations were 20, and for the Barbara image, they were 15.

[0179] S3.4 is used to solve the subproblem of solving the sparse regularization term.

[0180] Based on the formula:

[0181]

[0182] renew Where p k It refers to the continuous convex function part of the objective function in the linear Bregman algorithm. The gradient at step k, θ is the gradient of the smooth convex part of the objective function in the linear Bregman algorithm. denoted as g(α) j ),exist The linear approximation parameters of the first-order Taylor expansion, i.e. For a hard thresholding operator that processes each element individually:

[0183]

[0184] S3.5 is used to solve the subproblem of the TV regularization term.

[0185] Based on the formula:

[0186]

[0187] Calculate ω k .

[0188] S3.6 Lagrangian multiplier update.

[0189] Formula used:

[0190]

[0191] Calculate the Lagragian multipliers. Check if the stopping condition ||ω is satisfied. k -ω k-1 || / ||ω k-1 ||≤ε. Set ε=10 -5 If the condition is not met, return to step S3.2.

[0192] Exponential restoration of the S3.7 image.

[0193] Based on the formula:

[0194] u = e ω / a -b;

[0195]

[0196] Let ω = ω k , where a = 40, b = 25, thus reconstructing the denoised image U.

[0197] The above steps are used to denoise the noisy image, and the denoising result is as follows: Figure 5 and Figure 6 As shown in Table 1, the comparison method is the LogBM3D model. The method is quantitatively compared by introducing two evaluation indicators, PSNR and SSIM. The results show that the method proposed in this invention is superior to the comparison method in terms of image denoising ability and overall image structure preservation ability.

[0198] Table 1 Image denoising results

[0199]

[0200] In summary, traditional denoising methods based on sparse regularization use a fixed sparse basis, which may lead to insufficient sparsity of the transformed coefficients in some images. Sparse regularization methods typically guide image reconstruction at a global level but neglect local image structure, potentially resulting in artifacts in local regions of the reconstructed image. This invention introduces a block-matching local operator as the sparse basis, continuously updating the derived local basis vectors to obtain a good sparse basis. It also introduces a regularization term for joint denoising, thereby removing artifacts and reconstructing local details in the image. Compared to other classic methods in the field, this invention has stronger denoising capabilities and overall structure preservation, further enhancing its ability to preserve special structures such as similar textures. It is more suitable for images contaminated by high-intensity multiplicative noise, improving image quality and usability.

[0201] To implement the above method and achieve the corresponding functions and technical effects, an image multiplicative noise removal system is provided below, which includes:

[0202] The model building module is used to construct a multiplicative noise removal model that combines sparse regularization based on block-matching local SVD operators with joint regularization of total variation and fractional variation.

[0203] The problem decomposition module is used to decompose the multiplicative noise removal model to obtain optimization sub-problems; the optimization sub-problems include: sparse basis update, sub-problem for solving sparse regularization term, sub-problem for solving joint regularization term of total variation and fractional variation, and Lagrange multiplier update.

[0204] The iterative solution module is used to input the noisy image into the multiplicative noise removal model, iteratively solve the optimization sub-problem, and reconstruct the denoised image based on the solution results.

[0205] 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 systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0206] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for removing multiplicative noise from images, characterized in that, include: A multiplicative noise removal model is constructed by jointly using sparse regularization based on block-matching local SVD operators and joint regularization of total variation and fractional variation. Specifically, this includes: constructing a strictly convex fidelity term for multiplicative noise based on maximum a posteriori estimation and logarithmic transformation; constructing a sparse regularization term based on block-matching local SVD operators; constructing a joint regularization term of total variation and fractional variation based on smooth priors; and constructing a multiplicative noise removal model based on the strictly convex fidelity term, the sparse regularization term, and the joint regularization term of total variation and fractional variation. The multiplicative noise removal model is decomposed to obtain optimization subproblems, specifically including: using a variable separation method and introducing auxiliary variables to transform the multiplicative noise removal model into a constrained minimization optimization problem; using an augmented Lagrangian method to transform the constrained minimization optimization problem into an unconstrained minimization optimization problem; and decomposing the unconstrained minimization optimization problem to obtain optimization subproblems. The optimization subproblems include: sparse basis update, subproblem for solving sparse regularization terms, subproblem for solving joint regularization terms of total variation and fractional variation, and Lagrange multiplier update; The noisy image is input into the multiplicative noise removal model, the optimization subproblem is solved iteratively, and the denoised image is reconstructed based on the solution results. Specifically, this includes: acquiring the noisy image and performing vectorization and logarithmic transformation to obtain an initial transformation vector; iteratively solving the optimization subproblem based on the initial transformation vector to obtain a solution result; and performing inverse logarithmic transformation and vector-matrix rearrangement on the solution result to obtain the denoised image.

2. The image multiplicative noise removal method according to claim 1, characterized in that, The expression for the multiplicative noise removal model is: ； in, This is the vectorized form of the noisy image. For block matching local SVD operators, For the index of the image slice, for The total number of image slices divided, For sparse regularization parameters, For TFV regularization parameters, It is a discrete joint operator of isotropic total variation and fractional variation. For diagonalization operators, The transformed vector is the result of a logarithmic transformation of the vectorized form of the denoised image.

3. The image multiplicative noise removal method according to claim 1, characterized in that, The expression for the optimization subproblem is: ； ； ； ； in, For the block-matching local SVD operator in the k-th iteration, Let be the low-rank matrix of the k-th iteration. Let this be the auxiliary variable for the k-th iteration. As an auxiliary variable, Let be the transformation vector for the k-th iteration. Let be the transformation vector for the (k-1)th iteration. Let Lagrange multipliers be the multipliers for the k-th iteration. For the (k-1)th iteration, This is the vectorized form of the noisy image. The transformed vector is the result of a logarithmic transformation on the vectorized form of the denoised image. For matrix vectorization operators, For diagonalization operators, It is a discrete joint operator of isotropic total variation and fractional variation. For sparse regularization parameters, For TFV regularization parameters, The step size parameter is used for iterating the transformation vector. Let be the step size parameter for the Lagrange multiplier iteration. For the index of the image slice, for The total number of image slices divided, This represents the number of iterations.

4. The image multiplicative noise removal method according to claim 1, characterized in that, The optimization subproblem is iteratively solved based on the initial transformation vector to obtain the solution result, which specifically includes: Non-local similarity block matching is performed on the transformation vector of the (k-1)th iteration to obtain the low-rank matrix of the k-th iteration; where k is a positive integer starting from 1, when k=1, the transformation vector of the (k-1)th iteration is the initial transformation vector, and the Lagrange multipliers and auxiliary variables of the (k-1)th iteration are all preset values. Based on the low-rank matrix of the k-th iteration and the transformation vector of the (k-1)-th iteration, a sparse basis update is performed to obtain the block-matching local SVD operator of the k-th iteration. Based on the block matching local SVD operator of the k-th iteration, the transformation vector of the (k-1)-th iteration, the Lagrange multipliers of the (k-1)-th iteration, and the auxiliary variable of the (k-1)-th iteration, the linear Bregman algorithm is used to solve the subproblem used to solve the sparse regularization term, and the auxiliary variable of the k-th iteration is obtained. Based on the auxiliary variable of the k-th iteration, the block matching local SVD operator of the k-th iteration, and the Lagrange multiplier of the (k-1)-th iteration, the gradient descent method is used to solve the subproblem used to solve the joint regularization term of the total variation and fractional variation, and the transformation vector of the k-th iteration is obtained. Based on the transformation vector of the k-th iteration, the block matching local SVD operator of the k-th iteration, the auxiliary variable of the k-th iteration, and the Lagrange multiplier of the (k-1)-th iteration, the Lagrange multiplier is updated to obtain the Lagrange multiplier of the k-th iteration. Determine whether the stopping condition is met based on the transformation vector of the k-th iteration and the transformation vector of the (k-1)-th iteration. If not satisfied, update the value of k and return to the step of performing nonlocal similarity block matching on the transformation vector of the (k-1)th iteration to obtain the low-rank matrix of the kth iteration; If the conditions are met, the transformation vector of the kth iteration is determined as the solution result.

5. An image multiplicative noise removal system, characterized in that, include: The model building module is used to construct a multiplicative noise removal model that combines sparse regularization based on block-matching local SVD operators and joint regularization of total variation and fractional variation. Specifically, it includes: constructing a strictly convex fidelity term for multiplicative noise based on maximum a posteriori estimation and logarithmic transformation; constructing a sparse regularization term based on block-matching local SVD operators; constructing a joint regularization term of total variation and fractional variation based on smooth priors; and constructing a multiplicative noise removal model based on the strictly convex fidelity term, the sparse regularization term, and the joint regularization term of total variation and fractional variation. The problem decomposition module is used to decompose the multiplicative noise removal model to obtain optimization subproblems. Specifically, it includes: using a variable separation method and introducing auxiliary variables to transform the multiplicative noise removal model into a constrained minimization optimization problem; using an augmented Lagrangian method to transform the constrained minimization optimization problem into an unconstrained minimization optimization problem; and decomposing the unconstrained minimization optimization problem to obtain optimization subproblems. The optimization subproblems include: sparse basis update, subproblem for solving sparse regularization terms, subproblem for solving joint regularization terms of total variation and fractional variation, and Lagrange multiplier update; The iterative solution module is used to input the noisy image into the multiplicative noise removal model, iteratively solve the optimization subproblem, and reconstruct the denoised image based on the solution results. Specifically, it includes: acquiring the noisy image and performing vectorization and logarithmic transformation to obtain an initial transformation vector; iteratively solving the optimization subproblem based on the initial transformation vector to obtain the solution result; and performing inverse logarithmic transformation and vector-matrix rearrangement on the solution result to obtain the denoised image.

Images