Phase recovery method, device and system based on enhanced total variation regularization and medium

Abstract

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

Description

Technical Field

[0001] The present application relates to but is not limited to the field of image processing technology, and in particular to a phase recovery method, device, system and medium based on enhanced total variation regularization. Background Art

[0002] With the rapid development of image processing, phase recovery has gradually attracted people's attention. The main purpose of phase recovery is to consider how to recover images or signals from Fourier transform amplitudes with severe noise.

[0003] In the process of image acquisition, due to various factors, such as random fluctuations caused by photons hitting the sensor in the photodetector, resulting in shot noise, random fluctuations of electrons caused by thermal motion in the resistor, lens surface scattering, diffraction limitations or defects in optical components in the optical system, and background radiation, the observed image can be contaminated by noise. Gaussian noise is a common type of noise 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 that occurs during the image acquisition process, so as to achieve visual improvement of the image.

[0004] The reconstruction process of coherent coded diffraction imaging can be mathematically described as a phase recovery process. Using known measured intensity and linear transformation and phase recovery algorithms, complex domain images can be reconstructed from diffraction patterns containing only intensity. Due to the lens-free and interference-free optical path characteristics of coherent coded diffraction imaging, it has been widely used in optics, materials and biomedicine. In addition to the above fields, it is also used in phase recovery problems related to image recovery.

[0005] Phase recovery and image denoising is a challenging non-convex ill-posed problem, which aims to recover high-quality images from noisy images. How to improve the quality of phase recovery is a very concerned issue in the field. Summary of the invention

[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 embodiments of the present application provide a phase recovery method, device, system and medium based on enhanced total variation regularization to improve the quality of phase recovery.

[0008] In a first aspect, an 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 recovery is constructed based on the phase recovery problem model and the enhanced total variation regularization model, including:

[0011] The enhanced total variation regularization model is expressed as Φ(u), and the specific model is Where u represents the restored image, u∈R N×N ; α is the regularization parameter, α>0; D is the gradient operator, that is Represents the pixels of the image, as follows:

[0012]

[0013] The phase recovery problem model is: Where b represents the image to be restored, A represents the linear operator, A∈R M×N , M and N represent the spatial dimensions.

[0014] A non-convex optimization model is constructed based on the phase recovery problem model and the enhanced total variation regularization model:

[0015]

[0016] Here, λ is a positive parameter and coded diffraction pattern measurement is used.

[0017] S200, converting the non-convex optimization model into a convex optimization model using a convex function difference algorithm;

[0018] In some embodiments, in S200, a convex function difference algorithm is used to transform the non-convex optimization model into a convex optimization model, that is, The specific process is as follows:

[0019] The two convex functions are: and

[0020] The principle of the convex function difference algorithm is:

[0021]

[0022] in,

[0023] The convex optimization model (ETVDCA) transformed according to the convex function difference algorithm principle is:

[0024]

[0025] Among them, ||·||1 represents the L1 norm, and ||·||2 represents the L2 norm.

[0026] S300, obtaining an image to be restored, inputting the image to be restored into the convex optimization model, and solving the convex optimization model by alternating iteration using an alternating direction multiplier algorithm to obtain a restored image;

[0027] In some embodiments, in S300, an image to be restored is obtained, the image to be restored is input into the convex optimization model, and the convex optimization model is solved by alternating iteration using an alternating direction multiplier algorithm to obtain a restored image, including:

[0028] S310, initializing the number of internal and external iterations, the stopping criterion, the regularization parameter α, the penalty parameters q and ω;

[0029] S320, input the image to be restored into the convex optimization model, and solve y k ;

[0030] S330, converting the convex optimization model into the following minimization model:

[0031]

[0032] stp=Du;v=u;v∈Ω;

[0033] Among them, Ω={u|0≤u≤1}.

[0034] S340, expressing the augmented Lagrangian function of the minimization model as:

[0035]

[0036] Among them, r1 and r2 are the penalty coefficients of the quadratic term;

[0037] S350, sequentially solving to obtain a solution for minimizing v, a solution for minimizing p, and a solution for minimizing u in the minimization model, including:

[0038] The terms of the augmented Lagrangian function containing the parameter v in the minimization model are extracted according to the following formula to obtain:

[0039]

[0040] The closed-form solution of this formula is:

[0041]

[0042] The term of the augmented Lagrangian function with parameter p in the minimization model can be expanded to

[0043]

[0044] And solve the minimum value for each j value. Transform the subproblem model into another form:

[0045]

[0046] Iterate using the soft shrinkage algorithm:

[0047]

[0048] is the threshold truncation operation, defined as

[0049]

[0050] The terms of the augmented Lagrangian function containing the parameter u in the minimization model are extracted according to the following formula to obtain:

[0051]

[0052] Use the conjugate gradient descent method to solve the u optimization subproblem:

[0053]

[0054] Among them, when r1, r2, β> 0, the coefficient matrix It's very strange.

[0055] In order to obtain the correct solution u, it is necessary to update the Lagrange multiplier. The formula is as follows:

[0056]

[0057] S360, accumulating the number of internal and external iterations and the stopping criteria of the current generation, and determining whether a preset maximum number of iterations or a stopping criteria threshold is reached, if so, executing S370; if not, taking the solution that minimizes u as the image to be restored, and executing S320;

[0058] S370: Output the solution that minimizes u as the restored image.

[0059] In a second aspect, an embodiment of the present application further provides a phase recovery device based on enhanced total variation regularization, wherein the phase recovery device based on enhanced total variation regularization comprises:

[0060] The 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;

[0061] In the second module, the non-convex optimization model is transformed into a convex optimization model using the convex function difference algorithm;

[0062] The third module obtains the image to be restored, inputs the image to be restored into the convex optimization model, and uses the alternating direction multiplier algorithm to alternately iterate and solve the convex optimization model to obtain the restored image.

[0063] In the third aspect, an embodiment of the present application also provides a phase recovery system based on enhanced total variation regularization, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements a phase recovery method based on enhanced total variation regularization as described in the first aspect.

[0064] In a fourth aspect, an embodiment of the present application further provides a phase recovery medium based on enhanced total variation regularization, which is a computer-readable storage medium storing computer executable instructions, wherein the computer executable instructions are used to execute a phase recovery method based on enhanced total variation regularization as described in the first aspect.

[0065] The embodiments of the present application include the following beneficial effects: In the embodiments provided by the present application, the phase recovery problem model and the enhanced total variation regularization model are combined to construct a non-convex optimization model whose parameter adjustment is more flexible and more suitable for image denoising. The non-convex optimization model is converted into a convex optimization model using a convex function difference algorithm, which is conducive to solving the optimal solution of the model. The above-mentioned convex optimization model can be solved by alternating iteration using the alternating direction multiplier method to obtain a restored image. The model constructed by the present application can improve the quality of phase recovery.

[0066] Other features and advantages of the present application will be described in the following description, and partly become apparent from the description, or understood by practicing the present application. The purpose and other advantages of the present application can be realized and obtained by the structures specifically pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] The accompanying drawings are used to provide further understanding of the technical solution of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the technical solution of the present application and do not constitute a limitation on the technical solution of the present application.

[0068] Figure 1 is a flow chart of a phase recovery method based on enhanced total variation regularization provided by an embodiment of the present application;

[0069] Figure 2 This is a comparison diagram of deblurring an image with different traditional algorithms when the noise level σ=30 provided by an embodiment of the present application;

[0070] Figure 3This is a comparison diagram of an image deblurred by two novel algorithms when the noise level σ=30 provided by an embodiment of the present application;

[0071] Figure 4 is a structural diagram of a phase recovery device based on enhanced total variation regularization provided by an embodiment of the present application;

[0072] Figure 5 This is a structural diagram of a phase recovery system based on enhanced total variation regularization provided by an embodiment of the present application. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying 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.

[0074] It should be noted that, although the functional modules are divided in the device schematic diagram and the 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 above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0075] refer to Figure 1 The present application provides a phase recovery method based on enhanced total variation regularization, which comprises the following steps:

[0076] S100, constructing a non-convex optimization model for phase recovery based on the phase recovery problem model and the enhanced total variation regularization model;

[0077] In this embodiment, the phase recovery problem is expressed as the following mathematical model:

[0078]

[0079] Where A represents the fast Fourier transform (DFT) operator, b represents the observed image, u represents the restored image, and A∈R M×N , b∈R N×N ,u∈R N×N .

[0080] The enhanced total variation regularization model is denoted as Φ(u),

[0081] Where D is the discrete gradient, that is Represents the pixels of the image, as follows:

[0082]

[0083] In order to restore the optimal value u, the present application combines the phase recovery problem model and the enhanced total variation regularization model to construct a non-convex optimization model for phase recovery:

[0084]

[0085] Among them, α is the regularization parameter, ||·||2 represents the 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.

[0086] S200, converting the non-convex optimization model into a convex optimization model using a convex function difference algorithm;

[0087] This application considers using the convex function difference algorithm to transform the non-convex optimization model into a convex optimization model, that is, The two convex functions are and

[0088] First, solve the subgradient of h(u),

[0089]

[0090] Then use the approximation h(u) at u k The first-order gradient at replaces -h(u) to obtain the convex function difference algorithm transformation model:

[0091]

[0092] Finally, the convex optimization model is obtained by combining the h(u) subgradient and convex function difference algorithm to transform the model:

[0093]

[0094] S300, obtaining an image to be restored, inputting the image to be restored into the convex optimization model, and solving the convex optimization model by alternating iteration using an alternating direction multiplier algorithm to obtain a restored image;

[0095] This application considers using the 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 transformed into an equality constrained optimization problem; specifically:

[0096] First, the solution of the convex optimization model is converted into the following minimization model:

[0097]

[0098] stp=Du;v=u;v∈Ω;

[0099] Among them, Ω={u|0≤u≤1}.

[0100] The minimization model is solved as an equality constrained optimization problem so that each subproblem has a closed-form solution.

[0101] Next, the Lagrangian multiplier vectors q, w are introduced to express the augmented Lagrangian function of the minimization model as follows:

[0102]

[0103] Among them, r1 and r2 are both quadratic penalty coefficients.

[0104] It should be noted that the Alternating Direction Method of Multipliers (ADMM) is an iterative algorithm for solving constrained optimization problems. The present application uses the Alternating Direction Method of Multipliers to solve the optimization model, and solves the above minimization model alternately in four steps.

[0105] The optimal solution is solved by using ADMM to alternately update variables, converting the original optimization problem into multiple optimization sub-problems. Multiple optimization sub-problems can be solved in multiple ways, which greatly simplifies the complexity of the original problem and can also be used for optimization problems with complex multivariate quantities.

[0106] 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.

[0107] Solve the specific content of each sub-optimization model, including:

[0108] Solve the v optimization subproblem and obtain v by iterating the v optimization subproblem. m+1 , specifically including:

[0109] The terms of the augmented Lagrangian function containing the parameter v in the minimization model are extracted according to the following formula:

[0110]

[0111] This application solves the v optimization subproblem:

[0112]

[0113] Solve p optimization subproblems and determine the solution p of p optimization subproblems m+1 , specifically including:

[0114] The terms of the augmented Lagrangian function containing the parameter p in the minimization model are extracted and expanded according to the following formula:

[0115]

[0116] And solve the minimum value for each j value. Transform the subproblem model into another form:

[0117]

[0118] Use the soft contraction algorithm to iteratively solve the p optimization subproblem:

[0119]

[0120] is the threshold truncation operation, defined as

[0121]

[0122] Solve the u optimization subproblem and determine the solution u of the u optimization subproblem m+1 , specifically including:

[0123] The terms of the augmented Lagrangian function containing the parameter u in the minimization model are extracted according to the following formula to obtain:

[0124]

[0125] Use the conjugate gradient descent method to solve the u optimization subproblem:

[0126]

[0127] Among them, when r1, r2, β> 0, the coefficient matrix It's very strange.

[0128] Solve the q,w optimization subproblem and obtain the solution q generated by the iteration of the q optimization subproblem m+1 and the solution w generated by the iteration of the w optimization subproblem m+1 , specifically including:

[0129] Substitute the solutions of the p optimization subproblem and the u optimization subproblem into the solution of the multiplier vector q for solving the equality constrained optimization problem, and substitute the solutions of the v optimization subproblem and the u optimization subproblem into the solution of the multiplier vector ω for solving the equality constrained optimization problem, and we get:

[0130]

[0131] In the embodiments provided by the present application, the enhanced total variation regularization model can effectively maintain the edge information of the image, and the non-convex optimization model constructed by combining the phase recovery problem model and the enhanced total variation regularization model is more flexible and more suitable for image noise removal and phase recovery; the non-convex optimization model is converted into a convex optimization model using a convex function difference algorithm, which is conducive to solving the optimal solution of the model; the optimization model is solved by alternating iteration using an alternating direction multiplier algorithm, and the unconstrained problem is converted into an equality constrained problem, which is equivalent to multi-block iterative optimization, thereby solving the restored image. The optimization model constructed by the present application and the corresponding solution method can improve the quality of phase recovery.

[0132] In some embodiments, the maximum number of iterations of the inner loop is preset to 20, the maximum number of iterations of the outer loop is preset to 20, and the stopping criterion threshold is preset to tol=1×10 -10 , scan the noisy image with size (n1, n2), where n1 is the length and n2 is the width.

[0133] As an optional embodiment, in S300, the method further includes: outputting evaluation index parameters for evaluating the restored image, the evaluation index parameters including a structural similarity index SSIM and a signal-to-noise ratio SNR;

[0134]

[0135] In this embodiment, the restored image u is evaluated by the structural similarity index SSIM and the signal-to-noise ratio SNR. m+1 quality.

[0136] The following are two image comparison experiments conducted based on the model proposed in the embodiment of the present application, namely, comparison with the classical algorithm and comparison with two new algorithms, and verify the efficiency and feasibility of the convex optimization model (ETVDC A).

[0137] First, images with different levels of Gaussian noise are obtained, and simulated noise is added to the images using an error reduction algorithm to obtain images to be restored.

[0138] In some embodiments, a set of public data sets is used, which includes eighteen different images. In some embodiments, the original image is recorded as u, and its image size is 512×512. After the original image is determined, the original image to be restored is loaded.

[0139] In some embodiments, different Gaussian noise levels are selected to simulate that an image is contaminated by Gaussian noise, σ=5, 10, 30 respectively. The purpose of this embodiment is to restore the image u based on the image F contaminated by Gaussian noise.

[0140] like Figure 2 As shown, Figure 2 The following is a comparison chart of the restoration results of nine different classic algorithms under the noise level of σ=30. The original image used is image 12. 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 restored based on the ETVDCA is better in quality than the images restored by other methods, and the detail effect is better.

[0141] like Figure 3 As shown, Figure 3 This is a comparison of the restoration results of the TFBDCA algorithm and the TVDCA algorithm at a noise level of σ = 30. The original image used is image 02. The ETVDCA method has a good effect and has certain application value. It can be seen from the observation that the method using the ETVDCA model is more effective than the TFBDCA method and the TVDCA method.

[0142] Table 1 shows the average values ​​of the indicators of eighteen images restored by different algorithms at noise levels σ = 5, 10, and 30. The above experiments verify that the ETVDCA model provided by this application can significantly improve the numerical and visual performance of the existing RAAR method, RAF method, RWF method, TAF method, CDA method, HIO method, TWF method, WF method, and ETVDCA method.

[0143] Table 1: Experimental results of various methods under different noise conditions;

[0144]

[0145] Referring to Table 1, by comparing the experimental results of all the methods in Table 1, it is easy to find that the ETVDCA index proposed in this application has been significantly improved compared with other algorithms, and the comprehensive experimental results are better.

[0146] In addition, refer to Figure 4 In some embodiments, a phase recovery device based on enhanced total variation regularization is further provided. A phase recovery device based on enhanced total variation regularization includes:

[0147] The 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;

[0148] In the second module, the non-convex optimization model is transformed into a convex optimization model using the convex function difference algorithm;

[0149] The third module obtains the image to be restored, inputs the image to be restored into the convex optimization model, and uses the alternating direction multiplier algorithm to alternately iterate and solve the convex optimization model to obtain the restored image.

[0150] The device embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separated, that is, they may be located in one place or distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0151] In addition, refer to Figure 5 An embodiment of the present application also provides a phase recovery system based on enhanced total variation regularization, which includes: a memory 11, a processor 12, and a computer program stored in the memory 11 and executable on the processor 12.

[0152] The processor 12 and the memory 11 may be connected via a bus or other means.

[0153] The non-transient software program and instructions required to implement a phase recovery method based on enhanced total variation regularization in the above embodiment are stored in the memory 11. When executed by the processor 12, a phase recovery method based on enhanced total variation regularization in the above embodiment is executed.

[0154] In addition, an embodiment of the present application also provides a phase recovery medium based on enhanced total variation regularization, which is a computer-readable storage medium. The computer-readable storage medium stores computer executable instructions, and the computer executable instructions are executed by a processor or controller, for example, by a processor in the above-mentioned electronic device embodiment, so that the above-mentioned processor can execute a phase recovery method based on enhanced total variation regularization in the above-mentioned embodiment.

[0155] It will be appreciated by those skilled in the art that all or part of the steps and systems in the disclosed methods may be implemented by software, firmware, hardware, and appropriate combinations thereof. Some or all of the physical components may 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, tape, disk) and communication media (signals). In addition, the communication medium typically contains computer-readable instructions, data structures, program modules and other data, as well as carriers or other modulated data signals as transmission mechanisms. In short, these media and storage technologies together constitute the data storage and communication basis of computer systems, making the preservation and transmission of information possible.

[0156] The above is a specific description of the preferred implementation of the present application, but the present application is not limited to the above-mentioned implementation mode. Technical personnel familiar with the field can also make various equivalent deformations or substitutions without violating the spirit of the present application. These equivalent deformations or substitutions 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 following steps are involved: S100, constructing a non-convex optimization model for phase recovery based on the phase recovery problem model and the enhanced total variation regularization model; S200, converting the non-convex optimization model into a convex optimization model using a convex function difference algorithm; S300, obtaining an image to be restored, inputting the image to be restored into the convex optimization model, and using an alternating direction multiplier algorithm to alternately iterate and solve the convex optimization model to obtain a restored image.

2. The phase recovery method based on enhanced total variation regularization according to claim 1, characterized in that: In S100, a non-convex optimization model for phase recovery is constructed based on the phase recovery problem model and the enhanced total variation regularization model; The enhanced total variation regularization model is: The enhanced total variation regularization is expressed as Φ(u), and the specific expression is Among them, u represents the restored image, u∈R N×N ; α is the regularization parameter, α>0; D is the discrete gradient, that is Represents the pixels of the image, as follows The phase recovery problem model is: Where b represents the image to be restored, A represents the linear operator, A∈R M ×N , M and N represent the spatial dimensions. A non-convex optimization model for phase recovery is constructed based on the enhanced total variation regularization model and the phase recovery problem model: where λ is a positive parameter, b is the observed image, A is a linear operator, and coded diffraction image measurement is applied.

3. The phase recovery method based on enhanced total variation regularization according to claim 2, characterized in that: In S200, the non-convex optimization model is converted into a convex optimization model using a convex function difference algorithm, including: 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 recovery; The non-convex optimization model is transformed into a convex optimization model through the convex function difference algorithm, that is, The two convex functions are and The principle of convex function difference algorithm is: in, The convex optimization model (ETVDCA) transformed according to the convex function difference algorithm principle is: Among them, ||·||1 represents the L1 norm, and ||·||2 represents the L2 norm.

4. A phase recovery method based on enhanced total variation regularization according to claim 3, characterized in that : In S300, an image to be restored is obtained, the image to be restored is input into the convex optimization model, and the convex optimization model is solved by alternating iteration using an alternating direction multiplier algorithm to obtain a restored image, including: S310, initializing the number of internal and external iterations, the stopping criterion, the regularization parameter α, the penalty parameters q and ω; S320, input the image to be restored into the convex optimization model, and solve y k . S330, converting the convex optimization model into the following minimization model: stp=Du;v=u;v∈Ω; Where Ω={u|0≤u≤1} S340, expressing the augmented Lagrangian function of the minimization model as: Among them, r1 and r2 are the penalty coefficients of the quadratic term; S350, sequentially solving to obtain a solution for minimizing v, a solution for minimizing p, and a solution for minimizing u in the minimization model, including: The terms of the augmented Lagrangian function containing the parameter v in the minimization model are extracted according to the following formula to obtain: The closed-form solution of this formula is: The term of the augmented Lagrangian function with parameter p in the minimization model can be expanded to And solve the minimum value for each j value. Transform the subproblem model into another form: Iterate using the soft shrinkage algorithm: is the threshold truncation operation, defined as The terms of the augmented Lagrangian function containing the parameter u in the minimization model are extracted according to the following formula to obtain: Use the conjugate gradient descent method to solve the u optimization subproblem: Among them, when r1, r2, β> 0, the coefficient matrix It's very strange. In order to obtain the correct solution u, it is necessary to update the Lagrange multiplier. The formula is as follows: S360, accumulating the number of internal and external iterations and the stopping criteria of the current generation, and determining whether a preset maximum number of iterations or a stopping criteria threshold is reached, if so, executing S370; if not, taking the solution that minimizes u as the image to be restored, and executing S320; S370: Output the solution that minimizes u as the restored image.

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