Adaptive optical retinal image deblurring method based on non-convex total variation model

Abstract

This invention relates to the field of digital image processing technology and is an adaptive optics retinal image deblurring method based on a non-convex total variation model. The method includes: constructing an adaptive optics retinal image myopia deconvolution model; improving the adaptive optics retinal image myopia deconvolution model based on norm-based non-convex total variation regularization; constructing a constrained optimization model equivalent to the improved adaptive optics retinal image myopia deconvolution model; using the alternating direction multiplier method as the outer optimization algorithm to estimate the adaptive optics retinal image and the weights to be estimated; solving the subproblems in the alternating direction multiplier method; updating the Lagrange operator and calculating the stopping condition according to a given tolerance to obtain the updated adaptive optics retinal image myopia deconvolution model; and using the updated adaptive optics retinal image myopia deconvolution model to perform the retinal image deblurring operation.

Description

Technical Field

[0001] This invention relates to the field of digital image processing technology, and in particular to an adaptive optical retinal image deblurring method based on a non-convex total variation model. Background Technology

[0002] Retinal microvessels are the only human microvessels that can be directly observed non-invasively. Many endocrine diseases, such as hypertension and diabetes, are reflected in the retina. However, the human eye is a unique optical system, and conventional ophthalmic imaging equipment struggles to achieve high-resolution fundus imaging. Adaptive optics is a technique that can measure and correct wavefront errors in optical systems in real time, significantly improving image quality. In recent years, adaptive optics technology has been widely used in retinal microvessel imaging. This technology enables real-time measurement and control of wavefront aberrations in the human eye, obtaining high-resolution retinal cell images close to the diffraction limit of the human eye, allowing direct observation of retinal microvessels non-invasively, which has significant medical applications. However, due to the complexity of adaptive optics systems and hardware limitations, complete correction of the target is often not possible. Furthermore, the image quality of retinal images is also affected by intraocular scattering, nystagmus, and other blurring and noise during acquisition. Therefore, post-processing such as image deblurring of adaptive optics retinal images to further improve image quality is crucial for the diagnosis and analysis of ophthalmic diseases and for in-depth ophthalmic medical research.

[0003] Unlike typical deblurring problems where the point spread function (PSF) is known, the special structure of adaptive optics retinal 3D imaging means that only partial information about the PSF is known. Therefore, in adaptive optics retinal image deblurring, both the image and the PSF need to be estimated simultaneously. This leads to a relatively complex myopic (mildly blind) deconvolution problem. Furthermore, the adaptive optics retinal image deblurring problem is a large-scale ill-conditioned inverse problem. To overcome the ill-posedness of the problem and ensure the fidelity of the recovered image, a suitable regularization method is needed. Regularization is a technique that transforms an ill-posed inverse problem into a well-posed problem. Its basic idea is to replace the original ill-posed problem with a "neighboring" well-posed problem whose solution is close to the exact solution. Tikhonov regularization is a classic regularization method. Its core idea is to add a quadratic penalty term to the objective function to smooth the solution. Due to the differentiability of the penalty term, this method can often be solved efficiently through linear equations or optimization algorithms, offering advantages such as high computational efficiency and relatively simple implementation. However, Tikhonov regularization has drawbacks such as causing the recovered image to become overly smooth and making it difficult to preserve important details such as point features, fine line structures, and sharp edges.

[0004] To overcome the problems of oversmoothing and difficulty in preserving image details in the Tikhonov regularization method, Rudin et al. proposed total variation (TV) regularization. This method, as a commonly used regularization approach, has wide applications in image processing and medical imaging. Its core idea is to control the variation of the image across all its pixels, smoothing the image as much as possible within the image itself to minimize the difference between adjacent pixels, while leaving the image edges as smooth as possible. Extensive theoretical analysis and numerical experiments have shown that TV regularization can not only suppress image noise but also effectively preserve image texture and edge details. Inspired by the effectiveness of TV regularization, Chen et al. constructed a myopia deconvolution model for adaptive optics retinal images with TV regularization based on the three-dimensional structure of adaptive optics retinal imaging, and proposed an efficient alternating direction multiplier method (ADMM-LAP) based on linearized projection (LAP) for this model's structure. Unlike traditional strategies that alternately solve coupled problems, the ADMM-LAP algorithm estimates the reconstructed image and PSF simultaneously, offering advantages such as lower computational cost, faster convergence, and more accurate reconstructed image and PSF. However, this model still has certain limitations. TV regularization is based on the prior assumption that the image satisfies a piecewise constant, which often results in a very obvious staircase effect in regions outside the piecewise constant, affecting the visual quality of the reconstructed image.

[0005] To avoid the staircase effect of TV regularization, nonconvex total variation (NTV) regularization has gained widespread attention in recent years in fields such as NMR image reconstruction and image segmentation due to its ability to enhance gradient sparsity and generate sharp edges. In 2010, Nikolova et al. found that nonconvex regularization terms outperformed convex regularization terms in preserving neat image boundaries. Therefore, they introduced a nonconvex potential function into the TV regularization term to construct the NTV model. This type of NTV model is superior to general convex regularization models in preserving sharp edges and clear contours, but unfortunately, it produces a more severe staircase effect than the TV model. To avoid this problem, Selesnick proposed a class of regularization methods based on... The nonconvex regularization method of norm construction and its application to the one-dimensional signal denoising problem is based on the idea of ​​using the minimum-maximum-concavity (MC) penalty function. Subtract its Moreau envelope from the norm. This regularization term is nonconvex and can effectively estimate larger values ​​in sparse solutions, finding wide applications in image denoising and reconstruction. Based on Selesnick's work, Liu et al. utilized a method based on... Minimax concave total variation regularity of norm (MCTV-) The anisotropic TV model was reconstructed from MR brain images. However, the anisotropic TV model is only suitable for images that exhibit a "blocky" structure, while the isotropic TV model is more suitable for natural images. Therefore, Shen et al. further constructed a TV model using the Moreau envelope function and the MC penalty function. The nonconvex regularity of norms is proposed based on Non-convex TV regularized model of norm (MCTV-) Numerical experiments show that the model can better reconstruct image textures, edges, and other details, significantly improving reconstruction performance. However, no researchers have yet investigated the deblurring problem of adaptive optics retinal images with NTV regularization.

[0006] Therefore, a method is needed to integrate MCTV- The regularization method is extended to the adaptive optics retinal image deblurring problem, and an adaptive optics retinal image deblurring model is constructed. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides an adaptive optical retinal image deblurring method based on a non-convex total variation model. The invention utilizes MCTV- The regularization method is extended to the adaptive optics retinal image deblurring problem to construct a better adaptive optics retinal image deblurring model. This effectively preserves the detailed features of the restored image and avoids staircase effects in smooth regions, resulting in a better restored image. Furthermore, MCTV- The adaptive optics retinal image deblurring problem with regularization terms can be mathematically described as a non-convex, non-smooth optimization problem with coupled objective functions and equality constraints. This invention focuses on two key issues: reducing computational cost and ensuring algorithm convergence, specifically addressing the MCTV- with non-convex total variation regularization terms. The structure of adaptive optics retinal image deblurring problem overcomes the difficulties caused by non-convexity and non-smoothness, based on the alternating direction multiplier method. A method for image deblurring with low computational cost and fast convergence was designed.

[0008] The technical means employed in this invention are as follows:

[0009] An adaptive optics retinal image deblurring method based on a non-convex total variation model includes: constructing an adaptive optics retinal image myopia deconvolution model; and based on... The non-convex total variation regularization of the norm is used to improve the adaptive optics retinal image myopia deconvolution model; a constrained optimization model equivalent to the improved adaptive optics retinal image myopia deconvolution model is constructed; the alternating direction multiplier method is used as the outer layer optimization algorithm for the adaptive optics retinal image. and the weights to be estimated Estimate the value; use the forward-backward split algorithm to solve the problem in the alternating direction multiplier method. Subproblems; the linearized projection method based on normal equations is used to solve the alternating direction multiplier method. Sub-problem: Update the Lagrange operator and calculate the stopping condition according to the given tolerance to obtain the updated adaptive optics retinal image myopia deconvolution model, and use the updated adaptive optics retinal image myopia deconvolution model to realize the deblurring operation of the retinal image.

[0010] Furthermore, the construction of the adaptive optics retinal image myopia deconvolution model specifically includes: constructing the adaptive optics retinal imaging process through a three-dimensional convolution model:

[0011] in, Represents a three-dimensional real object, namely the retina. Represents the three-dimensional point spread function. Represents the observed three-dimensional image. Indicates additive noise; Convert the three-dimensional convolutional model into a two-dimensional model:

[0012] in, Indicates a single depth Captured PSF, Indicates depth The observed two-dimensional image, Indicates depth Two-dimensional PSF at the location, Indicates depth Two-dimensional objects at that location, Indicates depth Additive noise at the location, Indicates the relevant weights, It is defined as; The adaptive optics retinal image myopia deconvolution model is described as follows:

[0013]

[0014] in, Indicates that it is pending recovery. Vectorization of an unknown image Indicates the weight to be estimated. For fuzzy matrices, for A known fuzzy matrix, This represents the observed blurred and noisy image. , .

[0015] Furthermore, the basis The non-convex total variation regularization of the norm improves the myopia deconvolution model of adaptive optics retinal images, specifically by defining the MC penalty function for isotropic total variation regularization. for:

[0016] in, Denotes a first-order finite difference matrix, with parameters ,function Represents the scale Moreau envelope function; [the function] Defined as:

[0017] Where, for any smoothing parameter sum vector ,function It is a convex function, and ; Construction with MCTV- Adaptive Optical Retinal Image Myopia Deconvolution Model with Regularization Terms:

[0018] in, This represents the equilibrium parameter.

[0019] Furthermore, the constrained optimization model, which is equivalent to the improved adaptive optics retinal image myopia deconvolution model, specifically includes: introducing a regularization term. ,in Represents a vector in which all components are 1, with parameters Model construction:

[0020] Introducing variables Construct a constrained optimization model:

[0021]

[0022] in, For indicator functions, that is:

[0023] in, ,in ,and , .

[0024] Furthermore, the adaptive optical retinal image and the weights to be estimated The estimation process specifically includes: inputting the adaptive optics retinal image to be repaired. The initial value of the weight to be estimated ,variable initial value Lagrange multipliers initial value ,make ; Give the augmented Lagrangian function of the constrained optimization model. :

[0025] Give Iteration format:

[0026] in, Represents the Lagrange multipliers. Represents a set Indicator functions, Represents a set Indicator functions, Indicates the penalty parameter. express The number of iterations.

[0027] Furthermore, the method of solving the alternating direction multiplier problem using the forward-backward splitting algorithm... The subproblems specifically include: solving the Alternating Direction Multiplier Method (ADMM) using the Forward-Backward Split Algorithm (FBS). Sub-problems: ; Enter the first The image obtained from the ADMM iteration ,variable Lagrange multipliers make ; Calculate the intermediate variables for the Forward-Backward Split Algorithm (FBS):

[0028] in, This represents an intermediate variable in the Forward-Backward Split Algorithm (FBS). This indicates the number of iterations in the Forward-Backward Split Algorithm (FBS).

[0029] Calculate the first Variables obtained from the FBS iteration :

[0030] in, This represents the global first-order finite difference operator.

[0031] make For a given tolerance, if If the maximum number of iterations is reached, the iteration stops, and then... Output If the iteration stopping condition is not met, then let And return the calculation .

[0032] Furthermore, the method of solving the alternating direction multiplier method using the linearized projection method based on the normal equations is employed. Sub-problems, specifically including: inputting the first... The image obtained from the ADMM iteration Weight ,make Select a summable sequence satisfy ,make ; Introduction of functions simplify Subproblem representation: , and the function Defined as: , Will The subproblem can be represented in the following equivalent form: .

[0033] Calculate the feasible index set Actively gather Non-active gathering At the current iteration point Place, let the remaining staff be ; Calculate about the variable block Jacobian matrix Regarding variable blocks Jacobian matrix : ; Calculation function gradient ,function Hessian matrix Regularization term gradient Regularization term Hessian matrix .

[0034] By projecting and restricting the above functions to a non-active set, we obtain the variable block on the non-active set. Jacobian matrix Non-active set with respect to variable block Jacobian matrix Functions on non-active sets gradient Functions on non-active sets Hessian matrix Regularization terms on non-active sets gradient Regularization term on non-active set Hessian matrix ; Calculate the left-hand side matrix of the normal equation :

[0035] Calculate the right-hand vector of the normal equation :

[0036] On non-active sets Compute update steps on non-active set variables , Compute update steps on non-active set variables :

[0037] At the current iteration point At this point, the calculation will The block of variables on the active set obtained by projecting and restricting to the active set. Jacobian matrix Actively collect variables on the block Jacobian matrix Functions on active sets gradient Actively collect regularization items gradient ; The update step on the active set variables is obtained by calculating the projected gradient descent step. :

[0038] Calculate update step Select parameters :

[0039] Calculate the update step:

[0040] Application projection Armijo line search update :

[0041] in, They represent in The projection on Represents the projected gradient. The backtracking step size is a constant and satisfies the following conditions: ; Calculate the residuals:

[0042] If the residual satisfies Then stop and output. If not satisfied, then let And return the update step computed on the non-active set variable. and .

[0043] Furthermore, the step of updating the Lagrange operator and calculating the stopping condition according to the given tolerance specifically includes: updating the Lagrange operator:

[0044] Given tolerance Calculate the stopping condition:

[0045] When the stopping condition is met, the iteration stops and the output is completed. If the aforementioned stopping condition is not met, then let And return the solution in the ADMM algorithm Sub-problems.

[0046] Compared with the prior art, the present invention has the following advantages: The adaptive optical retinal image deblurring method based on a non-convex total variation model provided by this invention is based on... Non-convex total variation regularization of norm (MCTV-) It has the advantage of being able to reconstruct image textures, edges, and other details very well, thus improving reconstruction performance. This invention constructs a novel MCTV-based... The adaptive optics retinal image myopia deconvolution model can effectively preserve the detailed features of the restored image while avoiding staircase effects in smooth areas, thus improving the quality of the restored image.

[0047] The alternating direction multiplier method used in this invention ( This is a first-order optimization algorithm with advantages such as simple iterative techniques, low computational cost, and fast computation speed. This invention is based on MCTV- with non-convex total variation regularization term. The structure of the adaptive optics retinal image deblurring problem overcomes the difficulties caused by non-convexity and non-smoothness, based on... The algorithm proposes a low-computation, fast-convergence image deblurring method. During the iteration process, different efficient algorithms are used to solve the subproblems of the ADMM algorithm, enabling PSF estimation simultaneously with image deblurring, achieving high accuracy. Therefore, this invention has advantages such as simultaneous PSF estimation, effective preservation and restoration of image detail features while avoiding staircase effects in smooth regions, and high accuracy. Attached Figure Description

[0048] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of the adaptive optics retinal image deblurring method based on a non-convex total variation model in this invention.

[0050] Figure 2 This is a deblurring effect diagram of adaptive optics retinal image 1 in an embodiment of the present invention.

[0051] Figure 3 This is a diagram showing the deblurring effect of adaptive optics retinal image 2 in an embodiment of the present invention. Detailed Implementation

[0052] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. 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.

[0054] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0055] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0056] like Figure 1 As shown, this invention provides an adaptive optics retinal image deblurring method based on a non-convex total variation model, comprising: constructing an adaptive optics retinal image myopia deconvolution model; in a preferred embodiment of this invention, the adaptive optics retinal imaging process is constructed using a three-dimensional convolution model:

[0057] in, Represents a three-dimensional real object, namely the retina. Represents the three-dimensional point spread function. Represents the observed three-dimensional image. Indicates additive noise; Convert the three-dimensional convolutional model into a two-dimensional model:

[0058] in, Indicates a single depth Captured PSF, Indicates depth The observed two-dimensional image, Indicates depth Two-dimensional PSF at the location, Indicates depth Two-dimensional objects at that location, Indicates depth Additive noise at the location, Indicates the relevant weights, It is defined as; The adaptive optics retinal image myopia deconvolution model is described as follows:

[0059]

[0060] in, Indicates that it is pending recovery. Vectorization of an unknown image Indicates the weight to be estimated. For fuzzy matrices, for A known fuzzy matrix, This represents the observed blurred and noisy image. , When implementing, order , .

[0061] based on The non-convex total variation regularization of the norm improves the adaptive optics retinal image myopia deconvolution model; specifically, as a preferred embodiment of the present invention, for isotropic total variation regularization, the MC penalty function is defined. for:

[0062] in, Denotes a first-order finite difference matrix, with parameters ,function Represents the scale Moreau envelope function; [the function] Defined as:

[0063] Where, for any smoothing parameter sum vector ,function It is a convex function, and ;Implementation examples .

[0064] Construction with MCTV- Adaptive Optical Retinal Image Myopia Deconvolution Model with Regularization Terms:

[0065]

[0066] in, Indicates the balance parameter, and the implementation time command. .

[0067] A constrained optimization model equivalent to the improved adaptive optics retinal image myopia deconvolution model is constructed; in a preferred embodiment of the invention, a regularization term is introduced. ,in Represents a vector in which all components are 1, with parameters Implementation of the order Model construction:

[0068] Introducing variables Construct a constrained optimization model:

[0069]

[0070] in, For indicator functions, that is:

[0071] in, ,in ,and , .

[0072] The alternating direction multiplier method is used as the outer layer optimization algorithm for adaptive optics retinal images. and the weights to be estimated An estimation is performed; in a preferred embodiment of the present invention, the adaptive optical retinal image to be repaired is input. The initial value of the weight to be estimated ,variable initial value Lagrange multipliers initial value ,make ; Give the augmented Lagrangian function of the constrained optimization model. :

[0073] in, ,and Similarly, let for Reordering.

[0074] Give Iteration format:

[0075] in, Represents the Lagrange multipliers. Represents a set Indicator functions, Represents a set Indicator functions, Indicates the penalty parameter. express The number of iterations.

[0076] The forward-backward split algorithm is used to solve the problem in the alternating direction multiplier method. Subproblems; in specific implementation, as a preferred embodiment of the present invention, the Forward-Backward Split Algorithm (FBS) is used to solve the Alternating Direction Multiplier Method (ADMM). Sub-problems: ; Enter the first The image obtained from the ADMM iteration ,variable Lagrange multipliers make When implementing, order .

[0077] Calculate the intermediate variables for the Forward-Backward Split Algorithm (FBS):

[0078] in, This represents an intermediate variable in the Forward-Backward Split Algorithm (FBS). This indicates the number of iterations in the Forward-Backward Split Algorithm (FBS).

[0079] Calculate the first Variables obtained from the FBS iteration :

[0080] in This represents the global first-order finite difference operator.

[0081] make For a given tolerance, if If the maximum number of iterations is reached, the iteration stops, and then... Output If the iteration stopping condition is not met, then let And return the calculation In implementation, order The maximum number of iterations is 100.

[0082] The linearized projection method based on the normal equations is used to solve the problem in the alternating direction multiplier method. Sub-problem; In specific implementation, as a preferred embodiment of the present invention, the input of the first... The image obtained from the ADMM iteration Weight ,make Select a summable sequence satisfy ,make ; during implementation, order For random Pixel image, ,in It is to satisfy The random selection constant, .

[0083] To simplify Subproblem representation, function definition : , And define the function : , Will The subproblem can be represented in the following equivalent form: .

[0084] Calculate the feasible index set Actively gather Non-active gathering At the current iteration point Place, let the remaining staff be ; Calculate about the variable block Jacobian matrix Regarding variable blocks Jacobian matrix : ; Calculation function gradient ,function Hessian matrix Regularization term gradient Regularization term Hessian matrix .

[0085] By projecting and restricting the above functions to a non-active set, we obtain the variable block on the non-active set. Jacobian matrix Non-active set with respect to variable block Jacobian matrix Functions on non-active sets gradient Functions on non-active sets Hessian matrix Regularization terms on non-active sets gradient Regularization term on non-active set Hessian matrix ; Calculate the left-hand side matrix of the normal equation :

[0086] Calculate the right-hand vector of the normal equation :

[0087] On non-active sets Compute update steps on non-active set variables , Compute update steps on non-active set variables :

[0088] At the current iteration point At this point, the calculation will The block of variables on the active set obtained by projecting and restricting to the active set. Jacobian matrix Actively collect variables on the block Jacobian matrix Functions on active sets gradient Actively collect regularization items gradient ; The update step on the active set variables is obtained by calculating the projected gradient descent step. :

[0089] Calculate update step Select parameters :

[0090] Calculate the update step:

[0091] Application projection Armijo line search update :

[0092] in, They represent in The projection on Represents the projected gradient. The backtracking step size is a constant and satisfies the following conditions: ; during implementation, order .

[0093] Calculate the residuals:

[0094] If the residual satisfies Then stop and output. If not satisfied, then let And return the update step computed on the non-active set variable. and .

[0095] The Lagrange operator is updated, and the stopping condition is calculated according to a given tolerance to obtain the updated adaptive optics retinal image myopia deconvolution model. The updated adaptive optics retinal image myopia deconvolution model is then used to perform deblurring of the retinal image. Specifically, in a preferred embodiment of this invention, the Lagrange operator is updated as follows:

[0096] Given tolerance Calculate the stopping condition:

[0097] When implementing, When the stopping condition is met, the iteration stops and the output is completed. If the aforementioned stopping condition is not met, then let And return the solution in the ADMM algorithm Sub-problems.

[0098] Example For two real adaptive optics retinal images, the result of using this invention to deblur the adaptive optics retinal images is as follows: Figure 2 , Figure 3 As shown. Figure 2 (a) Figure 3 (a) is a real image. Figure 2 (b) Figure 3 (b) is a blurred, noisy image. Figure 2 (c) Figure 3 (c) is the image obtained by deblurring using the present invention. Table 1 shows the MCTV- using the present invention. Model and Comparison Model TV- Numerical results obtained by deblurring these two real adaptive optics retinal images.

[0099] from Figure 2 and Figure 3 As can be seen, this invention can effectively preserve the detailed features of the restored image and avoid stair-step effects in smooth areas while achieving adaptive optical retinal image deblurring, thus obtaining high-quality restored images and improving the efficiency of subsequent ophthalmic disease diagnosis and analysis. As shown in Table 1, compared with TV- Compared to the model, the MCTV- proposed in this invention The model achieves lower relative errors in reconstructed images and estimated parameters, and higher signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM). This indicates that the present invention can obtain more accurate reconstructed images and estimated parameters than existing models.

[0100] Table 1

[0101] In Table 1, Represents the relative error of the image, where This represents the image obtained by deblurring using the present invention. Represents a real image. This represents the relative error of the parameter, where This represents the estimated parameters obtained by the present invention. This represents the actual parameters. Represents the signal-to-noise ratio, where This represents the image obtained by deblurring using the present invention. Represents the observed image, This indicates its average intensity value. Represents the peak signal-to-noise ratio, where I and K are The image, This represents the maximum value of the color of a point in the image. Represents structural similarity, where and They represent and The average value, and They represent and variance express and covariance, constant and , Indicates the dynamic range of pixel values; parameter selection is as follows. .

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive optical retinal image deblurring method based on a non-convex total variation model, characterized in that, include: Construct an adaptive optics retinal image myopia deconvolution model; based on The non-convex total variation regularization of the norm improves the adaptive optics retinal image myopia deconvolution model; Construct a constrained optimization model equivalent to the improved adaptive optics retinal image myopia deconvolution model; The alternating direction multiplier method is used as the outer layer optimization algorithm for adaptive optics retinal images. and the weights to be estimated Make an estimate; The forward-backward split algorithm is used to solve the problem in the alternating direction multiplier method. Sub-problems; The linearized projection method based on the normal equations is used to solve the problem in the alternating direction multiplier method. Sub-problems; The Lagrange operator is updated and the stopping condition is calculated according to the given tolerance to obtain the updated adaptive optics retinal image myopia deconvolution model. The updated adaptive optics retinal image myopia deconvolution model is then used to perform the deblurring operation on the retinal image.

2. The adaptive optical retinal image deblurring method based on a non-convex total variation model according to claim 1, characterized in that, The construction of the adaptive optics retinal image myopia deconvolution model specifically includes: Constructing an adaptive retinal imaging process using a 3D convolutional model: in, Represents a three-dimensional real object, namely the retina. Represents the three-dimensional point spread function. Represents the observed three-dimensional image. Indicates additive noise; Convert the three-dimensional convolutional model into a two-dimensional model: in, Indicates a single depth Captured PSF, Indicates depth The observed two-dimensional image, Indicates depth Two-dimensional PSF at the location, Indicates depth Two-dimensional objects at that location, Indicates depth Additive noise at the location, Indicates the relevant weights, It is defined as; The adaptive optics retinal image myopia deconvolution model is described as follows: in, Indicates that it is pending recovery. Vectorization of an unknown image Indicates the weight to be estimated. For fuzzy matrices, for A known fuzzy matrix, This represents the observed blurred and noisy image. , .

3. The adaptive optical retinal image deblurring method based on a non-convex total variation model according to claim 2, characterized in that, The basis Non-convex total variation regularization of the norm improves the myopia deconvolution model of adaptive optics retinal images, specifically including: For isotropic total variation regularization, define the MC penalty function. for: in, Denotes a first-order finite difference matrix, with parameters ,function Represents the scale Moreau envelope function; [the function] Defined as: Wherein, for any smoothing parameter sum vector ,function It is a convex function, and ; Construction with MCTV- Adaptive Optical Retinal Image Myopia Deconvolution Model with Regularization Terms: in, This represents the equilibrium parameter.

4. The adaptive optical retinal image deblurring method based on a non-convex total variation model according to claim 3, characterized in that, The constrained optimization model, which is equivalent to the improved adaptive optics retinal image myopia deconvolution model, specifically includes: Introducing regularization terms ,in Represents a vector in which all components are 1, with parameters Model construction: Introducing variables Construct a constrained optimization model: in, For indicator functions, that is: in, ,in ,and , .

5. The adaptive optical retinal image deblurring method based on a non-convex total variation model according to claim 4, characterized in that, The adaptive optics retinal image and the weights to be estimated The estimation includes: Input the adaptive optics retina image to be repaired. The initial value of the weight to be estimated ,variable initial value Lagrange multipliers initial value ,make ; Give the augmented Lagrangian function of the constrained optimization model. : Give Iteration format: in, Represents the Lagrange multipliers. Represents a set Indicator functions, Represents a set Indicator functions, Indicates the penalty parameter. express The number of iterations.

6. The adaptive optical retinal image deblurring method based on a non-convex total variation model according to claim 1, characterized in that, The forward-backward splitting algorithm is used to solve the alternating direction multiplier method. Sub-problems, specifically including: The Forward-Backward Split Algorithm (FBS) is used to solve the Alternating Direction Multiplier Method (ADMM). Sub-problems: ； Enter the first Image obtained from ADMM iteration ,variable Lagrange multipliers make ; Calculate the intermediate variables for the Forward-Backward Split Algorithm (FBS): in, This represents an intermediate variable in the Forward-Backward Split Algorithm (FBS). This indicates the number of iterations in the Forward-Backward Split Algorithm (FBS). Calculate the first Variables obtained from the FBS iteration : in, This represents the global first-order finite difference operator; make For a given tolerance, if If the maximum number of iterations is reached, the iteration stops, and then... Output If the iteration stopping condition is not met, then let And return the calculation .

7. The adaptive optical retinal image deblurring method based on a non-convex total variation model according to claim 6, characterized in that, The method employs a linearized projection method based on normal equations to solve the alternating direction multiplier method. Sub-problems, specifically including: Enter the first Image obtained from ADMM iteration Weight ,make Select a summable sequence satisfy ,make ; Introduction of functions simplify Subproblem representation: and the function Defined as: Will The subproblem can be represented in the following equivalent form: Calculate the feasible index set Actively gather Non-active gathering At the current iteration point Place, let the remaining staff be ; Calculate about the variable block Jacobian matrix Regarding variable blocks Jacobian matrix : Calculation function gradient ,function Hessian matrix Regularization term gradient Regularization term Hessian matrix ; Function By projecting and restricting to a non-active set, we obtain the variable block on the non-active set. Jacobian matrix Non-active set with respect to variable block Jacobian matrix Functions on non-active sets gradient Functions on non-active sets Hessian matrix Regularization terms on non-active sets gradient Regularization term on non-active set Hessian matrix ; Calculate the left-hand side matrix of the normal equation : Calculate the right-hand vector of the normal equation : On non-active sets Compute update steps on non-active set variables , Compute update steps on non-active set variables : At the current iteration point At this point, the calculation will The block of variables on the active set obtained by projecting and restricting to the active set. Jacobian matrix Actively collect variables on the block Jacobian matrix Functions on active sets gradient Actively collect regularization items gradient ; The update step on the active set variables is obtained by calculating the projected gradient descent step. : Calculate update step Select parameters : Calculate the update step: Application projection Armijo line search update : in, They represent in Projection on Represents the projected gradient. The constant is given, and the backtracking step size satisfies the following conditions: ; Calculate the residuals: If the residual satisfies Then stop and output. If not satisfied, then let And return the update step computed on the non-active set variable. and .

8. The adaptive optical retinal image deblurring method based on a non-convex total variation model according to claim 7, characterized in that, The process of updating the Lagrange operator and calculating the stopping condition based on a given tolerance specifically includes: Update the Lagrange operator: Given tolerance Calculate the stopping condition: When the stopping condition is met, the iteration stops and the output is completed. If the aforementioned stopping condition is not met, then let And return the solution in the ADMM algorithm Sub-problems.

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