Image restoration method, device, system and medium based on image prior characteristics

Abstract

The application provides an image restoration method, device and system based on image prior characteristics and a medium, and relates to the technical field of image processing. The method comprises the following steps: determining an image restoration model based on a regularized TV model, and establishing a multivariate Cauchy function based on a Cauchy function; constructing an optimization model for image restoration based on the image restoration model and the multivariate Cauchy function; obtaining an image to be restored, inputting the image to be restored into the optimization model, and iteratively solving the optimization model by using an alternating vector multiplier method to obtain a restored image. The application can improve the definition of the restored image.

Description

Image restoration methods, devices, systems, and media based on prior image properties Technical Field

[0001] This application relates to, but is not limited to, the field of image processing technology, and in particular to an image restoration method, apparatus, system, and medium based on prior image characteristics. Background Technology

[0002] Image restoration has always been a key research area in image processing, such as medical imaging and remote sensing. In practical applications, unavoidable factors exist during image capture, leading to a certain amount of noise. Therefore, eliminating noise in acquired images has always been a focus of research.

[0003] During image acquisition, various factors, such as defocusing, diffraction, optical system aberrations, relative motion between the imaging device and the object, random atmospheric turbulence, and sensor noise, can cause blurring of the observed image. Image deblurring aims to improve the quality of blurred images, removing or mitigating the image quality degradation that occurs during the acquisition of digital images, thereby achieving visual improvement.

[0004] Magnetic resonance imaging (MRI) is widely used in the medical field due to its effective ability to depict changes in soft tissue. The main limiting factor in MRI applications is its relatively long image acquisition time. Therefore, accelerating scan speed, reducing data acquisition volume and acquisition time without compromising reconstruction quality remains a key focus.

[0005] Image deblurring and MRI reconstruction is a challenging ill-posed problem, aiming to recover high-quality images from noisy MRI images. Improving the clarity of image reconstruction has been a long-standing challenge in the field. Summary of the Invention

[0006] The following is an overview of the subject matter described in detail herein. This overview is not intended to limit the scope of the claims.

[0007] This application provides an image restoration method, apparatus, system, and medium based on prior image characteristics to improve the clarity of restored images.

[0008] In a first aspect, embodiments of this application provide an image restoration method based on prior image characteristics, comprising the following steps:

[0009] S100, the image restoration model is determined based on the regularized TV model, and the multivariate Cauchy function is established based on the Cauchy function;

[0010] S200, Based on the image restoration model and the multivariate Cauchy function, construct an optimization model for image restoration;

[0011] S300, acquire the image to be restored, input the image to be restored into the optimization model, and use the alternating vector multiplier method to iteratively solve the optimization model to obtain the restored image.

[0012] In some embodiments, S100, the determination of the image restoration model based on the regularized TV model includes:

[0013] A regularized TV model is defined, with the TV norm denoted as ||u|| TV The specific expression is ||u|| TV =∫ Ω ||Du||dx; where Du is the gradient operator, xeR, Ω∈R 2 , u represents the restored image, u∈R N×N ;

[0014] The image restoration model is determined based on the regularized TV model. The image restoration model is as follows: Where α is the regularization parameter, α > 0, f represents the image to be restored, A represents the linear operator, and f ∈ R M×N , A∈R M×N M and N represent spatial dimensions.

[0015] In some embodiments, S100, the step of establishing a multivariate Cauchy function based on the Cauchy function includes:

[0016] An improved Cauchy function is derived based on the Cauchy function; the mathematical model of the improved Cauchy function is as follows:

[0017]

[0018] Where μ and ω are the scaling parameters of the improved Cauchy function, and P M The probability density function of the improved Cauchy function distribution.

[0019]

[0020] Based on the improved Cauchy function, a multivariate Cauchy function is obtained; the multivariate Cauchy function is defined as:

[0021] In some embodiments, S200, the step of constructing an optimization model for image restoration based on the image restoration model and the multivariate Cauchy function includes:

[0022] Based on the image restoration model and the multivariate Cauchy function, an MCauchyTV model is constructed, and the MCauchyTV model is used as the optimization model for image restoration.

[0023] The MCauchyTV model is as follows:

[0024]

[0025] Where ||·||2 represents the L2 norm.

[0026] In some embodiments, in S300, the step of inputting the image to be restored into the optimization model and solving the optimization model iteratively using the alternating vector multiplier method to obtain the restored image includes:

[0027] S310, initialize the number of iterations, stopping criterion, regularization parameter α, penalty parameter μ and ω;

[0028] S320, input the image to be restored into the optimization model, and convert the optimization model into the following minimization model:

[0029]

[0030] S330, the augmented Lagrangian function of the minimized model is expressed as:

[0031]

[0032] Where ρ is the quadratic penalty coefficient;

[0033] S340, solve sequentially to obtain the solutions for minimizing u, minimizing z, and minimizing λ in the minimization model;

[0034] S350: Accumulate the number of iterations and stopping criteria of the current generation, and determine whether the preset maximum number of iterations or the stopping criterion threshold has been reached. If yes, proceed to S360; otherwise, take the solution that minimizes u as the image to be restored and proceed to S320.

[0035] S360 outputs the solution that minimizes u as the restored image.

[0036] In some embodiments, S340, the step of sequentially solving for the solutions to minimize u, minimize z, and minimize λ in the minimization model includes:

[0037] The terms of the augmented Lagrangian function containing parameter u in the minimized model are extracted using the following formula, resulting in:

[0038]

[0039] Solving the u-optimization subproblem using Fourier diagonalization yields the solution:

[0040]

[0041] Where ⊙ denotes multiplication between components, A * Let F denote the conjugate operator of A, and F be the Fourier transform operator;

[0042] Optimize the solution of the subproblem u using the proximity operator and u k+1 This yields the z-optimization subproblem with a closed-form solution:

[0043]

[0044] This leads to the solution to the z-optimization subproblem:

[0045]

[0046] The solution to the u optimization subproblem k+1 The solution to the z-optimization subproblem k+1 Solving for the multiplier vector λ in the minimization model yields:

[0047] λ k+1 =λ k +ρ(Du k+1 -z k+1 ).

[0048] Secondly, embodiments of this application also provide an image restoration apparatus based on prior image characteristics, the image restoration apparatus based on prior image characteristics comprising:

[0049] The first module is used to determine the image restoration model based on the regularized TV model and to establish a multivariate Cauchy function based on the Cauchy function.

[0050] The second module is used to construct an optimization model for image restoration based on the image restoration model and the multivariate Cauchy function;

[0051] The third module is used to acquire the image to be restored, input the image to be restored into the optimization model, and use the alternating vector multiplier method to iteratively solve the optimization model to obtain the restored image.

[0052] Thirdly, embodiments of this application also provide an image restoration system based on prior image characteristics, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the image restoration method based on prior image characteristics as described in the first aspect.

[0053] Fourthly, embodiments of this application also provide a computer-readable storage medium storing computer-executable instructions for performing the image restoration method based on image prior characteristics as described in the first aspect.

[0054] The embodiments of this application have the following beneficial effects: In the embodiments provided in this application, the combination of image restoration model and multivariate Cauchy function constructs an optimization model with more flexible parameter adjustment, making it more suitable for image deblurring and MRI image reconstruction. The optimization model can be solved by alternating iteration using the alternating vector multiplier method, thereby obtaining the restored image. The construction of this application can improve the clarity of image restoration.

[0055] Other features and advantages of this application will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the application. The objectives and other advantages of this application may be realized and obtained by means of the structures particularly pointed out in the description, claims and drawings. Attached Figure Description

[0056] The accompanying drawings are used to provide a further understanding of the technical solutions of this application and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of this application and do not constitute a limitation on the technical solutions of this application.

[0057] Figure 1 is a flowchart of an image restoration method based on prior image characteristics provided in an embodiment of this application;

[0058] Figure 2 is a comparison of Barbara deblurred images with different Gaussian blur kernels provided in an embodiment of this application;

[0059] Figure 3 is a comparison of Brain-5 images reconstructed under a radial sampling mask according to an embodiment of this application;

[0060] Figure 4 shows the logarithmic change of the function value of the MCauchyTV model provided in one embodiment of this application with the number of iterations. 10 Line graph;

[0061] Figure 5a is a graph showing the variation of RE values ​​of Brain-5 at different sampling rates according to an embodiment of this application;

[0062] Figure 5b is a graph showing the variation of PSNR values ​​of Brain-5 at different sampling rates according to an embodiment of this application;

[0063] Figure 6 is a structural diagram of an image restoration apparatus based on prior image characteristics provided in an embodiment of this application;

[0064] Figure 7 is a structural diagram of an image restoration system based on prior image characteristics provided in an embodiment of this application. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0066] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, or the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0067] Referring to Figure 1, this application provides an image restoration method based on prior image characteristics, which includes the following steps:

[0068] S100, the image restoration model is determined based on the regularized TV model, and the multivariate Cauchy function is established based on the Cauchy function;

[0069] S200, Based on the image restoration model and the multivariate Cauchy function, construct an optimization model for image restoration;

[0070] S300, acquire the image to be restored, input the image to be restored into the optimization model, and use the alternating vector multiplier method to iteratively solve the optimization model to obtain the restored image.

[0071] In the embodiments provided in this application, the regularized TV model can effectively preserve the edge information of the image, and the determined image restoration model can also effectively preserve the edge information. A multivariate Cauchy function is established based on the heavy-tailed features of the Cauchy function, thereby improving the sparsity features and enabling accurate reconstruction of the image from highly undersampled signals, solving the problems of limited acquisition data and long acquisition time. Combining the image restoration model and the multivariate Cauchy function, the constructed optimization model parameters are more flexibly adjusted, making it more suitable for image deblurring and MRI image reconstruction. The optimization model is solved iteratively using the alternating vector multiplier method, transforming the unconstrained non-convex problem into an equality-constrained problem, equivalent to multi-block iterative optimization, thereby obtaining the restored image. The optimization model and corresponding solution method constructed in this application can improve the clarity of image restoration.

[0072] In this embodiment, the image restoration problem is represented by the following mathematical model:

[0073] f = Au + ε;

[0074] Where f represents the image to be restored, A represents the linear operator, and f∈R M×N , A∈R M×N ,u∈R N×N , ε∈R M×N , u represents the restored image, and ε represents noise.

[0075] A can be, for example, a convolution operator in image deblurring or a Fourier operator in magnetic resonance imaging (MRI) reconstruction. In fact, A is an ill-conditioned matrix, so it is difficult to recover u from f.

[0076] To recover the optimal value u, this application combines a TV (Total Variation) regularization model to determine the image restoration model, which is as follows:

[0077]

[0078] Where α is the regularization parameter, α > 0, ||u|| TV Represents the TV norm;

[0079] ||u|| TV For a regularized TV model, ||u|| TV =∫ Ω ||Du||dx;

[0080] Where Du is the gradient operator, Ω∈R 2 ,

[0081] Compared to Tikhonov regularization, the regularized TV model can effectively preserve the edge information of the image.

[0082] This application employs a sparse reconstruction method that can accurately reconstruct images from highly undersampled signals, solving the problems of limited data acquisition and long acquisition time, and can play an important role in magnetic resonance imaging.

[0083] As an improvement to the above embodiment, in S100, the step of establishing a multivariate Cauchy function based on the Cauchy function includes:

[0084] An improved Cauchy function is derived based on the Cauchy function; the mathematical model of the improved Cauchy function is as follows:

[0085]

[0086] Where μ and ω are the scaling parameters of the improved Cauchy function, p M The probability density function of the improved Cauchy function distribution.

[0087] In this embodiment, based on the heavy-tailed characteristic of the Cauchy function, this application proposes an improved Cauchy function, denoted as the MCauchy function, to further improve the sparsity feature.

[0088] Based on the improved Cauchy function, a multivariate Cauchy function is obtained; the multivariate Cauchy function is defined as: Clearly, the MCauchyTV model is non-convex.

[0089] It should be noted that, for certain values ​​of μ and ω, the multivariate Cauchy function... It is closer to the L0 norm. Furthermore, the proximity operator of the multivariate Cauchy function lies between soft and hard thresholding. In other words, the multivariate Cauchy function... It is more sensitive to the characteristics of the data tails. In summary, the multivariate Cauchy function... It exhibits good heavy-tailed characteristics, making it more suitable for sparse image restoration models. Furthermore, the multivariate Cauchy function... It can also maintain the convexity of the objective function, which is an advantage over the original Cauchy function.

[0090] Finally, the image restoration model is combined with the multivariate Cauchy function to construct the MCauchyTV model. This MCauchyTV model is then used as the optimization model, and its expression is as follows:

[0091]

[0092] Where α is the regularization parameter, ||·||² represents the L2 norm, μ and ω are the scaling parameters of the multivariate Cauchy function, and u is the restored image, u∈R. n f is the image to be recovered, Du is the gradient operator, and A is the linear operator.

[0093] This application considers using the efficient alternating vector multiplier method with variable splitting to solve the proposed optimization model (MCauchyTV model). By introducing a variable z, the unconstrained nonconvex problem of solving the MCauchyTV model is transformed into an equality-constrained optimization problem; specifically:

[0094] First, the optimization model is transformed into the following minimization model:

[0095]

[0096] The solution minimizes the model as an equality-constrained optimization problem, ensuring that each subproblem has a closed-form solution.

[0097] Next, we introduce the Lagrange multiplier vector λ, and express the augmented Lagrange function of the minimized model as:

[0098]

[0099] Where ρ is the quadratic penalty coefficient.

[0100] It should be noted that the Alternating Direction Method of Multipliers (ADMM) is an iterative algorithm for solving constrained optimization problems. This application utilizes the Alternating Direction Method of Multipliers with variable splitting to solve the optimization model, solving the aforementioned minimization model in three alternating steps.

[0101] The optimal solution is obtained by using ADMM to alternately update variables, which transforms the original optimization problem into multiple subproblems. These subproblems can be solved in various ways, greatly simplifying the complexity of the original problem. It can also be used for optimization problems with complex multivariate variables.

[0102] Specifically, it can be divided into three subproblems: the u-optimization subproblem, the z-optimization subproblem, and the λ-optimization subproblem. The u-optimization subproblem mainly includes data fitting terms and total variational regularization terms; the z-optimization subproblem mainly includes MCauchyTV terms and total variational regularization terms; the λ-optimization subproblem only has total variational regularization terms, specifically including:

[0103] 1. Solve the optimization subproblem u to obtain the restored image u generated in this iteration. k+1= (Dx, Dy), where Dx is the difference of image u in the horizontal direction, and Dy is the difference of image u in the horizontal direction. Substitute these values ​​into the z-optimization subproblem to solve the z-optimization subproblem.

[0104] 2. Solve the z-optimization subproblem, and convert u from the u-optimization subproblem to u. k+1 Substitute soft contraction to solve for z k+1 = (Zx, Zy), where Zx represents the soft contraction value updated in the horizontal direction, and Zy represents the soft contraction value updated in the vertical direction. Substitute these values ​​into the λ-optimization subproblem to solve the λ-optimization subproblem.

[0105] 3. Solve the λ optimization subproblem, and use the u optimization subproblem and z optimization subproblem to obtain u k+1 and z k+1 Solve for the Lagrange multipliers and solve for λ. k+1 = (λx, λy), where λx represents the update of the multiplier vector in the horizontal direction, and λy represents the update of the multiplier vector in the vertical direction.

[0106] The steps to solve each sub-optimization model include:

[0107] (1) Solve the optimization subproblem u, which mainly includes the data fitting term and the total variation regularization term, and obtain u by iteratively generating u from the optimization subproblem u. k+1 Specifically, it includes:

[0108] The terms of the augmented Lagrangian function containing parameter u in the minimization model are extracted using the following formula:

[0109]

[0110] Mainly includes data fitting terms and total variational regularization term Based on the optimality condition and the diagonalizable matrix, this application utilizes Fourier diagonalization to solve the optimization subproblem u:

[0111]

[0112] Where ⊙ denotes multiplication between components, A * Let F denote the conjugate operator of A, and F be the Fourier transform operator.

[0113] (2) Solve the z-optimization subproblem, which mainly involves the MCauchyTV term and the total variational regularization term, and determine the solution z of the z-optimization subproblem. k+1 Specifically, it includes:

[0114] Since the proximity operator of the multivariate Cauchy function has a closed-form solution, it can be used to solve the z-optimization subproblem.

[0115] Based on the solutions of the proximity operator and the u-optimization subproblem, a solution with a closed form is obtained:

[0116]

[0117] The solution to the z-optimization subproblem is approximately obtained as follows:

[0118]

[0119] (3) Solve the λ optimization subproblem, which mainly involves the total variational regularization term, and obtain the solution λ generated by the iteration of the λ optimization subproblem. k+1 Specifically, it includes:

[0120] Substituting the solutions to the u-optimization subproblem and the z-optimization subproblem into the solution to the multiplier vector λ of the equality-constrained optimization problem, we obtain:

[0121] λ k+1 =λ k +ρ(Du k+1 -z k+1 );

[0122] This application employs Fast Fourier Transform and proximity operator to solve subproblems alternately, which greatly reduces the time complexity.

[0123] To recover blurred images and MRI images, the iteration count, stopping criterion, regularization parameter α, penalty parameter μ, and ω are first initialized. Then, the image to be recovered is input into the optimization model, and the optimization model is solved. After each solution is completed, the iteration count of the current generation is accumulated once, and the stopping criterion of the current generation is calculated. The steps of solving the minimization model are continued iteratively until the preset maximum number of iterations or the stopping criterion threshold is reached. The solution of the u optimization subproblem is then output as the recovered image.

[0124] In one embodiment, the maximum number of iterations is preset to 250, and the stopping criterion threshold is preset tol = 1 × 10⁻⁶. -6 Scan the dimensions (m, n) of the noisy image, where m is the length and n is the width.

[0125] As an optional embodiment, in S300, the method further includes: outputting evaluation index parameters for evaluating the restored image, the evaluation index parameters including relative error RE and peak signal-to-noise ratio PSNR;

[0126]

[0127]

[0128] In this embodiment, the restored image u is evaluated using relative error (RE) and peak signal-to-noise ratio (PSNR). k+1 The quality.

[0129] The following describes two classic image processing experiments conducted using the model proposed in the embodiments of this application: image deblurring and MRI reconstruction. The efficiency and feasibility of the MCauchyTV model were verified.

[0130] First, a blurred image and an MRI image are acquired. Simulated noise is added to the image according to the type of image data to be restored, resulting in the image to be restored.

[0131] In some embodiments, three MRI images of different parts of the human body are selected. It should be noted that image deblurring can use classic images of different sizes. In one embodiment, barbara is used as the original image, denoted as u, with an image size of 512×512. After determining the original image, the original image to be restored is loaded.

[0132] It should be noted that image deblurring simulates the generation of blur noise using two different filters (averaging filter and Gaussian low-pass filter). MRI images, on the other hand, have different sampling patterns added (radial sampling mask, random sampling mask, and horizontal Cartesian sampling mask). Finally, random noise with a standard deviation of 0.001 is added as the image to be restored for comparison experiments.

[0133] In one embodiment, different Gaussian blur kernels ([3,3],10); ([15,15],10); ([21,21],10) are selected to simulate and generate blur noise, blurring the barbara image. The blurred image is denoted as f. The purpose of this embodiment is to recover the image u based on the blurred image f.

[0134] Figure 2 shows a comparison of Barbara-deblurred images with different Gaussian blur kernels. Each row corresponds to a different Gaussian blur kernel: ([3, 3], 10); ([15, 15], 10); ([21, 21], 10). It can be seen that the image restored based on the MCauchyTV model is superior to those restored by other methods in both numerical value and quality, with better detail. The image deblurred by the TV method has obvious granular spots and poor image continuity; the image restored by the CPS method has a step error, which illustrates the importance of method selection in the experiment; although the CauchyTV method achieves good results, it does not handle details well.

[0135] Figure 3 shows a comparison of Brain-5 images (PSNR(dB)) reconstructed under an 8% radial sampling mask. The four methods in the MRI reconstruction model demonstrate good performance and have certain application value. Numerical analysis shows that the method using the MCauchyTV model is more effective than the TV method, MCTV method, SCADTV method, and CauchyTV method.

[0136] As shown in Figure 4, Figure 4 plots the logarithmic changes in the function values ​​of the MCauchyTV model with the number of iterations. 10 As shown in Figure 4, the function value decreases with increasing iteration count and eventually flattens out. This result demonstrates that the MCauchyTV model provided in this application has convergence.

[0137] As shown in Figures 5a and 5b, the performance parameters of Brain-5 vary under different sampling rates. Figure 5a shows that the RE value decreases with increasing sampling rate for all methods, while Figure 5b shows that the PSNR value increases with increasing sampling rate. Overall, the MCauchyTV method outperforms the TV, MCTV, SCADTV, AtanTV, and CauchyTV methods.

[0138] Referring to Table 1, by comparing the experimental results of all methods in Table 1, it is easy to find that the CauchyTV index proposed in this application has been significantly improved, and the overall experimental results are better.

[0139] Table 1: Experimental results of each method;

[0140]

[0141]

[0142] The two experiments above verify that the MCauchyTV model provided in this application can significantly improve upon existing non-convex TV methods, MCTV methods, SCADTV methods, AtanTV methods, CauchyTV methods, and CPS methods. The MCauchyTV model has obvious advantages in both numerical and visual aspects.

[0143] Additionally, referring to FIG6, in one embodiment, an image restoration apparatus based on prior image characteristics is also provided, the image restoration apparatus based on prior image characteristics includes;

[0144] The first module 100 is used to acquire electroencephalogram (EEG) signals; wherein the EEG signals are obtained by sampling signals from multiple electrode channels at a set sampling rate when the subject is performing a motor imagery task.

[0145] The second module 200 is used to perform bandpass filtering on the EEG signal using a filter bank to obtain multiple frequency band signals. For each frequency band signal, multiple sliding time windows are used to extract a corresponding number of single-trial data to obtain multiple single-trial data.

[0146] The third module 300 is used to extract the spatial and graphical features from each trial data, fuse the spatial and graphical features of each trial data to obtain time-frequency-spatial-graphical features, and use the time-frequency-spatial-graphical features as features extracted from the EEG signal.

[0147] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0148] Additionally, referring to FIG7, an embodiment of this application also provides an image restoration system based on image prior characteristics, the system comprising: a memory 11, a processor 12, and a computer program stored on the memory 11 and executable on the processor 12.

[0149] The processor 12 and the memory 11 can be connected via a bus or other means.

[0150] The non-transient software program and instructions required to implement the image restoration method based on image prior characteristics in the above embodiments are stored in memory 11. When executed by processor 12, the image restoration method based on image prior characteristics in the above embodiments is executed.

[0151] Furthermore, one embodiment of this application provides a computer-readable storage medium storing computer-executable instructions that are executed by a processor or controller, for example, by a processor in the above-described electronic device embodiment, causing the processor to perform the image restoration method based on image prior characteristics in the above-described embodiment.

[0152] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0153] The above is a detailed description of the preferred embodiments of this application. However, this application is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. An image restoration method based on prior image properties, characterized in that, The steps include: S100, determining an image restoration model based on a regularized TV model, and establishing a multivariate Cauchy function based on the Cauchy function; wherein: the TV norm in the regularized TV model is represented as... The specific expression is Where Du is the gradient operator. ， ， u represents the restored image. The image restoration model is as follows: Where α is the regularization parameter, α>0, f represents the image to be restored, and A represents the linear operator. ， M and N represent spatial dimensions; the multivariate Cauchy function is constructed using the following improved Cauchy function: the mathematical model of the improved Cauchy function is... Where μ and ω are the scaling parameters of the improved Cauchy function; The probability density function of the improved Cauchy function distribution. The multivariate Cauchy function is defined as follows: ， S200, Based on the image restoration model and the multivariate Cauchy function, construct the MCauchyTV model, and use the MCauchyTV model as the optimization model for image restoration; the MCauchyTV model is: ;in, S300: Obtain the image to be restored, input the image to be restored into the optimization model, and use the alternating vector multiplier method to iteratively solve the optimization model to obtain the restored image.

2. The image restoration method based on prior image characteristics according to claim 1, characterized in that, In step S300, the step of inputting the image to be restored into the optimization model and solving the optimization model iteratively using the alternating vector multiplier method to obtain the restored image includes: S310, initializing the number of iterations, stopping criterion, regularization parameter α, scale parameter μ, and ω as penalty parameters; S320, inputting the image to be restored into the optimization model and converting the optimization model into the following minimization model: ,satisfy S330, the augmented Lagrangian function of the minimized model is expressed as: ; where ρ is the quadratic penalty coefficient and λ is the Lagrange multiplier vector; S340, solve sequentially to obtain the solutions for minimizing u, minimizing z, and minimizing λ in the minimization model; S350, accumulate the iteration count and stopping criterion of the current generation, and determine whether the preset maximum iteration count or stopping criterion threshold has been reached. If yes, execute S360; if no, use the solution for minimizing u as the image to be restored, and execute S320; S360, output the solution for minimizing u as the restored image.

3. The image restoration method based on prior image characteristics according to claim 2, characterized in that, In S340, the step of sequentially solving to obtain the minimized model is described. Solution, minimization Solution and minimization The solution includes: minimizing the parameters in the model according to the following formula. The terms of the augmented Lagrangian function are extracted to obtain: Solving using Fourier diagonalization Optimize the subproblem to obtain Optimize the solution to the subproblem: Where D is the gradient operator, the superscript T denotes transpose, and ⊙ denotes multiplication between components. Let A be the conjugate operator, and F be the Fourier transform operator; using the Cauchy nearest neighbor operator and Optimize the solution of the subproblem We obtain a solution with a closed form. Optimization subproblems: ; and thus obtain Optimize the solution to the subproblem: Where prox represents the proximity operator; based on Optimize the solution of the subproblem Solution to the z-optimization subproblem Solving for the multiplier vector in the minimization model The solution yields: = + ( － )。 4. An image restoration device based on prior image characteristics, characterized in that, The image restoration device based on prior image characteristics includes: a first module, used to determine an image restoration model based on a regularized TV model and to establish a multivariate Cauchy function based on a Cauchy function; wherein: the TV norm in the regularized TV model is represented as... The specific expression is Where Du is the gradient operator. ， Ω∈R², u represents the restored image. The image restoration model is as follows: Where α is the regularization parameter, α>0, f represents the image to be restored, and A represents the linear operator. ， M and N represent spatial dimensions; the multivariate Cauchy function is constructed using the following improved Cauchy function: the mathematical model of the improved Cauchy function is... Where μ and ω are the scaling parameters of the improved Cauchy function; The probability density function for the improved Cauchy function. The multivariate Cauchy function is defined as follows: ， The second module is used to construct an MCauchyTV model based on the image restoration model and the multivariate Cauchy function, and to use the MCauchyTV model as the optimization model for image restoration; the MCauchyTV model is as follows: ;in, The first module represents the L2 norm; the second module is used to acquire the image to be restored, input the image to be restored into the optimization model, and use the alternating vector multiplier method to iteratively solve the optimization model to obtain the restored image.

5. An image restoration system based on prior image properties, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the computer program, it implements the image restoration method based on image prior characteristics as described in any one of claims 1 to 3.

6. A computer-readable storage medium storing computer-executable instructions for performing the image restoration method based on image prior characteristics as described in any one of claims 1 to 3.

Images