A phase retrieval method, device, system and medium based on enhanced total variation regularization

Abstract

The application provides a phase retrieval method, device, system and medium based on enhanced total variation regularization, and relates to the technical field of image processing. The method comprises the following steps: constructing a non-convex optimization model for phase retrieval based on an enhanced total variation regularization model and a phase retrieval problem model; converting the non-convex optimization model into a convex optimization model by using a convex function difference algorithm; obtaining an image to be recovered, inputting the image to be recovered into the convex optimization model, iteratively solving the convex optimization model by using an alternating direction multiplier method, and obtaining a recovered image. The application can improve the definition of the recovered image.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of image processing, and particularly relates to a phase recovery method, device and system based on enhanced total variation regularization and a medium. BACKGROUND

[0002] With the rapid development of the image processing field, the phase recovery problem gradually attracts people's attention. The main purpose of phase recovery is to consider how to recover an image or a signal from the Fourier transform amplitude with severe noise.

[0003] In the image acquisition process, various factors, such as random fluctuations caused by photon impact on sensors in photodetectors, random fluctuations of electrons caused by thermal motion in resistors, defects of optical elements such as lens surface scattering, diffraction limitation or optical elements in optical systems, and background radiation, can all cause the observed image to be contaminated by noise. Gaussian noise is a common noise type in image processing, which is caused by multiple factors and has the characteristics of normal distribution. Image denoising can effectively restore the imaging effect of the image, remove or reduce the image quality degradation occurring in the process of acquiring the image, so as to achieve the improvement of the image in vision.

[0004] The reconstruction process of coherent coded diffraction imaging can be described as a phase recovery process in mathematics, and a complex domain image can be reconstructed from a diffraction pattern containing only intensity by using known measurement intensity, linear transformation and phase recovery algorithm. Due to the lens-free and interference-free optical path characteristics of coherent coded diffraction imaging, it has been widely used in the fields of optics, materials and biomedicine. In addition to the above fields, it is also applied to the phase recovery problem related to image recovery.

[0005] Phase recovery and image denoising are a challenging non-convex ill-posed problem, and the purpose is to recover a high-quality image from a noisy image. How to improve the quality of phase recovery is a very concerned problem in the field. SUMMARY

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

[0007] The embodiment of the present application provides a phase recovery method, device, system and medium based on enhanced total variation regularization, so as to improve the quality of phase recovery.

[0008] In a first aspect, the embodiment of the present application provides a phase recovery method based on enhanced total variation regularization, comprising the following steps:

[0009] S100, constructing an optimization model for phase recovery based on the phase recovery problem model and the enhanced total variation regularization model;

[0010] In some embodiments, in S100, a non-convex optimization model for phase retrieval is constructed based on the phase retrieval problem model and the enhanced total variation regularization model, including:

[0011] The enhanced total variation regularization model is denoted as Φ(u), and a specific model is

[0012] where u represents the recovered image, u∈R N×N ; α is a regularization parameter, α>0; D is a gradient operator, that is, represents a pixel of an image, and is specifically as follows:

[0013]

[0014] The phase retrieval problem model is where b represents an image to be recovered, A represents a linear operator, A∈R M×N , and M and N represent spatial dimensions.

[0015] A non-convex optimization model is constructed based on the phase retrieval problem model and the enhanced total variation regularization model:

[0016]

[0017] where λ is a positive parameter, and an encoded diffraction image measurement is used.

[0018] In S200, the non-convex optimization model is converted into a convex optimization model by using a convex function difference algorithm.

[0019] In some embodiments, in S200, the non-convex optimization model is converted into a convex optimization model by using a convex function difference algorithm, that is, The specific process is as follows:

[0020] The two convex functions are respectively: and

[0021] The principle of the convex function difference algorithm is:

[0022]

[0023] where

[0024] The convex optimization model (ETVDCA) converted according to the principle of the convex function difference algorithm is:

[0025]

[0026] where ||·||1 represents an L1 norm, and ||·||2 represents an L2 norm.

[0027] S300, obtaining an image to be recovered, inputting the image to be recovered into the convex optimization model, and obtaining a recovered image by alternately and iteratively solving the convex optimization model by using an alternating direction multiplier algorithm;

[0028] In some embodiments, in S300, obtaining an image to be recovered, inputting the image to be recovered into the convex optimization model, and obtaining a recovered image by alternately and iteratively solving the convex optimization model by using an alternating direction multiplier algorithm, comprises:

[0029] S310, initializing an inner-outer iteration number, a stopping criterion, a regularization parameter a, a penalty parameter q and w;

[0030] S320, inputting the image to be recovered into the convex optimization model, and solving y k ;

[0031] S330, converting the convex optimization model into the following minimization model:

[0032]

[0033] s.t.p = Du; v = u; v e Q;

[0034] wherein, Q = {u | 0 < u < 1}.

[0035] S340, representing an augmented Lagrangian function of the minimization model as:

[0036]

[0037] wherein, r1 and r2 are both quadratic penalty coefficients;

[0038] S350, sequentially solving the solution of minimizing v, the solution of minimizing p and the solution of minimizing u in the minimization model, comprising:

[0039] According to the following formula, the term of the augmented Lagrangian function containing the parameter v in the minimization model is extracted to obtain:

[0040]

[0041] The closed solution of the formula is:

[0042]

[0043] The term of the augmented Lagrangian function containing the parameter p in the minimization model can be expanded as

[0044]

[0045] and respectively solve the minimum value for each j value. Let Transform the sub-problem model into another form:

[0046]

[0047] Iterate using the soft shrinkage algorithm:

[0048]

[0049] is a threshold truncation operation, defined as

[0050]

[0051] Extract the term containing the parameter u in the augmented Lagrangian function of the minimization model according to the following formula to obtain:

[0052]

[0053] Solve the u optimization sub-problem using the conjugate gradient descent method:

[0054]

[0055] where, r1, r2, β>0, the coefficient matrix is non-singular.

[0056] In order to obtain the correct solution u, it is necessary to update the Lagrange multiplier. Its formula is as follows:

[0057]

[0058] S360, accumulate the number of internal and external iterations of the current generation and the stopping criterion, determine whether the maximum number of iterations or the stopping criterion threshold is reached, if so, execute S370; if not, the solution of minimizing u is taken as the image to be restored, and S320 is executed;

[0059] S370, output the solution of minimizing u as the restored image.

[0060] In a second aspect, the embodiments of the present application also provide a phase recovery device based on enhanced total variation regularization, and the phase recovery device based on enhanced total variation regularization comprises:

[0061] A first module constructs a non-convex optimization model for phase recovery based on the phase recovery problem model and the enhanced total variation regularization model;

[0062] A second module converts the non-convex optimization model into a convex optimization model using a convex function difference algorithm;

[0063] The third module acquires an image to be recovered, inputs the image to be recovered into the convex optimization model, and obtains a recovered image by alternately and iteratively solving the convex optimization model by using an alternating direction multiplier method.

[0064] In a third aspect, an embodiment of the present application further provides a phase retrieval system based on enhanced total variation regularization, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the phase retrieval method based on enhanced total variation regularization when executing the computer program.

[0065] In a fourth aspect, an embodiment of the present application further provides a phase retrieval medium based on enhanced total variation regularization, which is a computer readable storage medium, and stores computer executable instructions for executing the phase retrieval method based on enhanced total variation regularization.

[0066] The embodiment of the present application has the following beneficial effects: in the embodiment provided by the present application, the phase retrieval problem model and the enhanced total variation regularization model are combined to construct a non-convex optimization model, and the parameter adjustment of the non-convex optimization model is more flexible and more suitable for image denoising. The non-convex optimization model is converted into a convex optimization model by using a convex function difference algorithm, which is beneficial to solving the optimal solution of the model. The convex optimization model can be solved by using the alternating direction multiplier method, so that a recovered image is obtained. The model constructed by the present application can improve the quality of phase retrieval.

[0067] Other features and advantages of the present application will be illustrated in the following description, and some will become apparent from the description, or will be understood through implementation of the present application. The purpose and other advantages of the present application can be achieved and obtained by the structure specifically indicated in the description, claims and drawings. BRIEF DESCRIPTION OF DRAWINGS

[0068] The accompanying drawings are used to provide a further understanding of the technical solutions of the present application, and constitute a part of the specification, and are used to explain the technical solutions of the present application together with the embodiments of the present application, and do not constitute a limitation to the technical solutions of the present application.

[0069] Figure 1 is a flowchart of a phase retrieval method based on enhanced total variation regularization provided by an embodiment of the present application;

[0070] Figure 2 is a comparison diagram of deblurring images by different traditional algorithms in the case of noise level σ = 30 provided by an embodiment of the present application;

[0071] Figure 3is a comparison chart of deblurring images with two new algorithms in the case of noise level σ = 30 provided by an embodiment of the present application;

[0072] Figure 4 is a structural diagram of an apparatus for phase retrieval based on enhanced total variation regularization provided by an embodiment of the present application;

[0073] Figure 5 is a structural diagram of a system for phase retrieval based on enhanced total variation regularization provided by an embodiment of the present application. DETAILED DESCRIPTION

[0074] In order to make the purposes, technical solutions and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0075] It should be noted that although the functional modules are divided in the apparatus schematic diagram, and the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a manner different from the module division in the apparatus or the order in the flowchart. The terms "first", "second", etc. in the specification, claims or above-described drawings are used to distinguish similar objects, and do not necessarily describe a specific order or sequence.

[0076] Reference Figure 1 The present application provides a method for phase retrieval based on enhanced total variation regularization, which comprises the following steps:

[0077] S100, constructing a non-convex optimization model for phase retrieval based on the phase retrieval problem model and the enhanced total variation regularization model;

[0078] In this embodiment, the phase retrieval problem is represented as a mathematical model as follows:

[0079]

[0080] wherein A represents a discrete Fourier transform (DFT) operator, b represents an observed image, u represents a recovered image, A ∈ R M×N , b ∈ R N×N , u ∈ R N×N .

[0081] The enhanced total variation regularization model is represented as Φ(u),

[0082] wherein D is a discrete gradient, i.e. represents a pixel of an image, and is specifically as follows:

[0083]

[0084] To restore the optimal value u, the application combines the phase recovery problem model and the enhanced total variation regularization model to construct a non-convex optimization model for phase recovery:

[0085]

[0086] Wherein, α is a regularization parameter, ||·||2 represents L2 norm, λ is a positive parameter, u is the restored image, u∈R n , Du is the gradient operator, and A represents the fast Fourier transform (DFT) operator.

[0087] S200, using a convex function difference algorithm to convert the non-convex optimization model into a convex optimization model;

[0088] The application considers using a convex function difference algorithm to convert the non-convex optimization model into a convex optimization model, that is, The two convex functions are And

[0089] First, the sub-gradient of h(u) is solved,

[0090]

[0091] Then, the first-order gradient of h(u) at u k is used to replace -h(u) to obtain the convex function difference algorithm conversion model:

[0092]

[0093] Finally, the convex optimization model is obtained by combining the sub-gradient of h(u) and the convex function difference algorithm conversion model:

[0094]

[0095] S300, obtaining an image to be restored, inputting the image to be restored into the above convex optimization model, and using an alternating direction multiplier algorithm to alternately iterate and solve the convex optimization model to obtain a restored image;

[0096] The application considers using an alternating direction multiplier method to solve the proposed convex optimization model. By introducing two variables p and v, the unconstrained problem of solving the convex optimization model is converted into an equality constraint optimization problem; specifically:

[0097] First, the solution of the convex optimization model is converted into the following minimization model:

[0098]

[0099] s.t.p = Du; v = u; v e Q;

[0100] where Q = {u | 0 < u < 1}.

[0101] Solving the minimization model is an equality constraint optimization problem, and each sub-problem has a closed-form solution.

[0102] Then, the Lagrange multiplier vector q, w is introduced, and the augmented Lagrangian function of the minimization model is expressed as:

[0103]

[0104] where r1 and r2 are both quadratic penalty coefficients.

[0105] It should be noted that the Alternating Direction Method of Multipliers (ADMM) is an iterative algorithm for solving optimization problems with constraints. The present application uses the Alternating Direction Method of Multipliers to solve the optimization model, which is solved in four steps by alternately solving the above minimization model.

[0106] The optimal solution is solved by alternately updating the variables using ADMM, which converts the original optimization problem into multiple optimization sub-problems, which can be solved in multiple ways, greatly simplifying the complexity of the original problem, and can also be used for optimization problems with complex multiple variables.

[0107] Specifically, it can be divided into four sub-problems: v optimization sub-problem, p optimization sub-problem, u optimization sub-problem and q, w optimization sub-problem.

[0108] The specific content of solving each sub-optimization model includes:

[0109] Solving the v optimization sub-problem, obtaining the v optimization sub-problem iteration v m+1 , specifically including:

[0110] The term containing the parameter v in the augmented Lagrangian function of the minimization model is extracted according to the following formula:

[0111]

[0112] The present application solves the v optimization sub-problem:

[0113]

[0114] Solving the p optimization sub-problem, determining the solution p m+1 of the p optimization sub-problem, specifically including:

[0115] The term of the augmented Lagrange function containing parameter p in the minimization model is extracted and expanded according to the following formula:

[0116]

[0117] And the minimum value is solved for each j value respectively. Let The sub-problem model is transformed into another form:

[0118]

[0119] The soft shrinkage algorithm is used to solve the p optimization sub-problem iteratively:

[0120]

[0121] Is a threshold truncation operation, defined as

[0122]

[0123] Solve the u optimization sub-problem to determine the solution u of the u optimization sub-problem m+1 , specifically including:

[0124] The term of the augmented Lagrange function containing parameter u in the minimization model is extracted according to the following formula, and

[0125]

[0126] The conjugate gradient descent method is used to solve the u optimization sub-problem:

[0127]

[0128] Where, r1, r2, β>0, the coefficient matrix is non-singular.

[0129] Solve the q, w optimization sub-problem to get the solution q m+1 of the q optimization sub-problem generated by iteration and the solution w m+1 of the w optimization sub-problem generated by iteration, specifically including:

[0130] The solution of the p optimization sub-problem and the u optimization sub-problem is substituted into the solution of the multiplier vector q of the equality constraint optimization problem, and the solution of the v optimization sub-problem and the u optimization sub-problem is substituted into the solution of the multiplier vector ω of the equality constraint optimization problem, to get:

[0131]

[0132] In the embodiments provided in this application, the enhanced total variational regularization model can effectively preserve the edge information of the image. Combining the phase retrieval problem model with the enhanced total variational regularization model results in a more flexible non-convex optimization model, which is more suitable for image noise removal and phase retrieval. The non-convex optimization model is transformed into a convex optimization model using the convex function difference algorithm, which is beneficial for finding the optimal solution. The optimization model is solved iteratively using the alternating direction multiplier algorithm, transforming the unconstrained problem into an equality-constrained problem, equivalent to multi-block iterative optimization, thereby obtaining the recovered image. The optimization model and corresponding solution method constructed in this application can improve the quality of phase retrieval.

[0133] In some embodiments, the maximum number of iterations in the inner loop is preset to 20, the maximum number of iterations in the outer loop is preset to 20, and the stopping criterion threshold is preset tol = 1 × 10. -10 Scan the dimensions (n1, n2) of the noisy image, where n1 is the length and n2 is the width.

[0134] As an optional embodiment, in S300, the method further includes: outputting evaluation index parameters for evaluating the restored image, the evaluation index parameters including structural similarity index SSIM and signal-to-noise ratio SNR;

[0135]

[0136] In this embodiment, the reconstructed image u is evaluated using the structural similarity index SSIM and the signal-to-noise ratio SNR. m+1 The quality.

[0137] The following describes two image comparison experiments conducted based on the model proposed in the embodiments of this application: comparison with classical algorithms and comparison with two novel algorithms. The efficiency and feasibility of the proposed convex optimization model (ETVDC A) are verified.

[0138] First, images with different levels of Gaussian noise are acquired. Then, an error reduction algorithm is used to add simulated noise to the images to obtain the images to be restored.

[0139] In some embodiments, a publicly available dataset containing eighteen distinct images is used. In some embodiments, the original image is denoted as u, and its image size is 512×512. After the original image is determined, the original image to be recovered is loaded.

[0140] In some embodiments, different Gaussian noise levels are selected to simulate images being contaminated by Gaussian noise, namely σ = 5, 10, 30. The purpose of this embodiment is to recover image u from image F after Gaussian noise contamination.

[0141] like Figure 2 As shown,Figure 2 For comparison with the recovery results of different nine classical algorithms under the noise level of σ = 30, the original image is image 12, and the specific algorithms are RAAR algorithm, RAF algorithm, RWF algorithm, TAF algorithm, CDA algorithm, HIO algorithm, TWF algorithm, WF algorithm and TVDCA algorithm. It can be seen that the image recovered based on the ETVDCA is better in quality than the image recovered by other methods, and the detail effect is better.

[0142] As shown in Figure 3 , Figure 3 For comparison with the recovery results of TFBDCA algorithm and TVDCA algorithm under the noise level of σ = 30, the original image is image 02, and the ETVDCA method has good effect and certain application value. It can be seen through observation that the method using the ETVDCA model is more effective than the TFBDCA method and the TVDCA method.

[0143] Table 1 shows the average values of the indexes of eighteen images recovered by different algorithms under noise levels σ = 5, 10 and 30 respectively. The above experiments verify that the ETVDCA model provided by the present application can be significantly improved, and compared with the existing RAAR method, RAF method, RWF method, TAF method, CDA method, HIO method, TWF method, WF method and ETVDCA method, the method using ETVDCA has obvious superiority in numerical value and vision.

[0144] Table 1: Experimental results of each method under different noise levels;

[0145]

[0146] Referring to Table 1, by comparing the experimental results of all methods in Table 1, it can be easily found that the ETVDCA index proposed in the present application is significantly improved compared with other algorithms, and the comprehensive experimental results are better.

[0147] In addition, with reference to Figure 4 In some embodiments, an enhanced total variation regularization based phase recovery device is also provided, and the enhanced total variation regularization based phase recovery device comprises:

[0148] A first module constructs a non-convex optimization model for phase recovery based on the phase recovery problem model and the enhanced total variation regularization model;

[0149] A second module converts the non-convex optimization model into a convex optimization model by using a convex function difference algorithm;

[0150] The third module acquires an image to be recovered, inputs the image to be recovered into the convex optimization model, and obtains a recovered image by iteratively solving the convex optimization model by using an alternating direction multiplier method.

[0151] The apparatus embodiments described above are merely illustrative, and units described as separate components can or can not be physically separate, i.e., can be located in one place or distributed over multiple network units. Part or all of the modules can be selected according to actual needs to achieve the purpose of the embodiment.

[0152] In addition, with reference to Figure 5 One embodiment of the present application further provides a phase retrieval system based on enhanced total variation regularization, which comprises a memory 11, a processor 12 and a computer program stored in the memory 11 and executable on the processor 12.

[0153] The processor 12 and the memory 11 can be connected by a bus or other means.

[0154] The non-transitory software program and instructions required for implementing the phase retrieval method based on enhanced total variation regularization in the above embodiment are stored in the memory 11, and when executed by the processor 12, the phase retrieval method based on enhanced total variation regularization in the above embodiment is executed.

[0155] In addition, one embodiment of the present application further provides a phase retrieval medium based on enhanced total variation regularization, which is a computer readable storage medium, and the computer readable storage medium stores computer executable instructions, which are executed by a processor or a controller, for example, a processor in the above electronic device embodiment, so that the above processor executes the phase retrieval method based on enhanced total variation regularization in the above embodiment.

[0156] Those skilled in the art can understand that all or part of the steps in the disclosed method and the system can be implemented by software, firmware, hardware and suitable combinations thereof. Some or all of the physical components can be implemented by processor (CPU, DSP or MPU) software, or hardware or ASIC. The software is stored in a readable storage medium, including storage (RAM, ROM, EEPROM, flash memory, CD-ROM, DVD, magnetic tape, magnetic disk) and communication medium (signal). In addition, the communication medium usually contains computer readable instructions, data structures, program modules and other data as a carrier wave or other modulated data signal of transmission mechanism. In short, these media and storage technologies collectively constitute the data storage and communication foundation of the computer system, making the storage and transmission of information possible.

[0157] The above describes the preferred embodiments of the present application, but the present application is not limited to the above-described embodiments, and those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the present application, and these equivalent modifications or replacements are all included in the scope defined by the claims of the present application.

Claims

1. A phase retrieval method based on enhanced total variation regularization, characterized in that, The method comprises the following steps: S100, constructing a non-convex optimization model for phase retrieval based on a phase retrieval problem model and an enhanced total variation regularization model; The enhanced total variation regularization model is: The enhanced total variation regularization model is represented as Φ(u), and the specific expression is wherein u represents the recovered image, u e R N×N ; a is a regularization parameter, a > 0; D is a discrete gradient; The phase recovery problem model is: wherein b represents an image to be recovered, A represents a linear operator, A ∈ R M ×N M, N represent spatial dimensions; The non-convex optimization model is: Wherein, λ is a positive parameter; S200, converting the non-convex optimization model into a convex optimization model by using a convex function difference algorithm; comprising: The non-convex optimization model is converted into a convex optimization model ETVDCA by using a convex function difference algorithm DCA, and the ETVDCA model is used as a convex optimization model for phase retrieval; m u inF(u) = g(u) - h(u), where both convex functions are and The principle of the convex function difference algorithm is: wherein, k denotes the number of outer loop iterations; The convex optimization model ETVDCA converted according to the principle of the convex function difference algorithm is: Wherein, ||·||1 represents an L1 norm, and ||·||2 represents an L2 norm; S300, obtaining an image to be recovered, inputting the image to be recovered into the convex optimization model, and solving the convex optimization model by using an alternating direction multiplier algorithm to obtain a recovered image; In S300, an image to be recovered is obtained, the image to be recovered is input into the convex optimization model, and the convex optimization model is solved by using an alternating direction multiplier algorithm to obtain a recovered image, comprising: S310, initializing the number of inner and outer iterations, a stopping criterion, a regularization parameter α, a penalty parameter q and ω; S320, input the image to be recovered into a convex optimization model, solve y k ; S330, converting the convex optimization model into the following minimization model: Wherein, Ω = {u|0≤u≤1}; S340, solving by using an alternating direction multiplier method ADMM, and representing an augmented Lagrange function of the minimization model as: Wherein, r1 and r2 are both quadratic term penalty coefficients; S350, sequentially solving to obtain a solution of minimizing v, a solution of minimizing p and a solution of minimizing u in the minimization model, comprising: According to the following formula, the term of the augmented Lagrange function containing the parameter v in the minimization model is extracted to obtain: Wherein, m is the number of inner loop iterations; The closed solution of the formula is: The term of the augmented Lagrange function containing the parameter p in the minimization model can be expanded as and solve for the minimum value for each j value, respectively; let Transform the subproblem model into another form: Iterate by using a soft shrinkage algorithm: is a threshold cut-off operation defined as According to the following formula, the term of the augmented Lagrange function containing the parameter u in the minimization model is extracted to obtain: Solve the u optimization sub-problem by using a conjugate gradient descent method; In order to obtain a correct solution u, update the Lagrange multiplier; S360, accumulating the number of inner and outer iterations and the stopping criterion of the current generation, determining whether the maximum number of iterations or the stopping criterion threshold set in advance is reached, if yes, executing S370; if not, taking the solution of minimizing u as the image to be recovered, and executing S320; S370, outputting the solution of minimizing u as the recovered image.

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