An Adaptive Restoration Method for Poisson Noise Images

Abstract

The present invention relates to an adaptive restoration method for Poisson noise images. Based on the forward-backward algorithm, intermediate variables are introduced, and the Poisson noise image restoration optimization problem is decomposed into two alternately iterative sub-problems, and a clear restored image is obtained through alternating iteration. The present invention relies on the forward-backward algorithm to construct a plug-and-play numerical solution framework, and embeds a genetic algorithm in the alternating iteration process, solves the problem of adaptive selection of parameters in each iteration, and provides an infrared image adaptive restoration framework with a simple framework, strong applicability, good effect, easy engineering implementation, and high adaptability.

Description

Technical Field

[0001] The present invention relates to the technical field of aerospace engineering image processing, and particularly relates to an adaptive restoration method for Poisson noise images. Background Art

[0002] Currently, there are a huge number of detection satellites in space at home and abroad, including space-based remote sensing satellites, infrared warning satellites, and aerial photography satellites, etc. However, during the in-orbit operation of satellites, due to the influence of random noise, optical diffraction, and camera optical axis jitter on the imaging system, the image data detected by the space-based satellite camera payload appears blurred, which causes a decline in imaging quality, seriously affecting the high-resolution imaging ability and high-precision mapping ability of space-based satellites. In order to improve the clarity and quality of imaging, it is necessary to restore or deblur the images.

[0003] Image restoration or deblurring is one of the most basic problems in image processing, and its main principle is to reconstruct the original data from a noisy and blurred image. Currently, the main research is focused on additive Gaussian noise. However, in practical applications, especially for electronic noise, the noise signal often follows a Poisson distribution. Poisson noise image restoration is a typical non-linear imaging problem, and it is relatively difficult to solve directly. For the solution of the image restoration model, currently, the more commonly used frameworks include the Alternating Direction Method of Multipliers (ADMM), the Forward Backward Splitting (FBS), etc. Among them, the forward-backward algorithm can avoid matrix inversion when solving non-linear problems, and has fewer parameters, which can reduce the workload of manual parameter tuning. Therefore, the forward-backward solution framework has obvious advantages in solving non-linear problems such as Poisson noise restoration.

[0004] In addition, in the problem of Poisson image restoration, the selection of the regularization parameter will significantly affect the restoration effect. How to select the appropriate parameter is the key. Currently, it mainly relies on manual confirmation based on experience and lacks self-adaptability. Therefore, a genetic algorithm is tried to construct an image quality evaluation function combined with the characteristics of image pixel distribution, and adaptively select the regularization parameter to make the restoration result optimal. The Genetic Algorithm (GA) was proposed by John holland in the 1970s and is a method of searching for the optimal solution by simulating the natural evolution process. The genetic algorithm has strong global search ability and is not easily trapped in local optima, etc. It is an efficient random search algorithm and has been widely used in the fields of image processing, adaptive control, and machine learning. According to the existing problems in the process of Poisson noise image restoration, such as difficult non-linear solution and complex manual selection of parameters, it is necessary to design an easily implemented image adaptive restoration method. Summary of the Invention

[0005] To solve the existing technical problems, the present invention provides an adaptive restoration method for Poisson noise images.

[0006] The specific content of the present invention is as follows: An adaptive restoration method for Poisson noise images, based on the forward-backward algorithm, introducing an intermediate variable, decomposing the Poisson noise image restoration optimization problem into two alternately iterative sub-problems, and obtaining a clear restored image through alternating iteration, including the following steps:

[0007] (1) Define the Poisson noise restoration optimization model based on the maximum a posteriori estimation:

[0008]

[0009] (2) Based on the forward-backward algorithm, introduce an intermediate variable z, and convert the above optimization model into the following alternating iteration problem:

[0010]

[0011] where 0 < γ < 2 / L represents the iteration step size, L is the Lipschitz constant of, and

[0012]

[0013]

[0014] (3) Select the initial parameters γ, u 0 , regularization function

[0015] (4) Substitute the parameters γ and u k-1 , and solve for the intermediate variable z k ;

[0016] (5) Based on the intermediate variable z k , rely on the genetic algorithm to complete the automatic optimization of the regularization parameter τ k and u k in each iteration process;

[0017] (6) Alternately iterate steps (4) and (5) to complete the solution of the optimal solution u * ;

[0018] where, is the estimated value after alternating iteration, u is the image to be restored or the original image, <·,·> is the inner product operator, 1 is a column or row vector with all element values being 1, K is the blurring function, g is the observed data or the blurred image, log is the logarithmic function, τ is the regularization parameter, non-negative, is a data fidelity term, is a regular function; k is the number of alternating cycle iterations; * is the conjugate complex number, I is the identity matrix, is the convolution operator.

[0019] Furthermore, in step (4), the solution of z k can be quickly solved based on the Fourier transform.

[0020] Furthermore, in step (5), the optimization solution model of u k can be regarded as a denoising problem with a noise level of based on the definition of the approximate mapping operator, and the corresponding solution strategy is selected to generate the restored image after denoising based on the regular term .

[0021] Furthermore, in the solution process of step (5), a genetic algorithm inner loop is embedded. The regularization parameter τ is used as a variable to dynamically determine the optimal regularization parameter for each alternating iteration, and the restored result corresponding to the optimal regularization parameter is output.

[0022] Furthermore, in the solution process of step (5), the value range of τ is set as [τ min , τ max , and the population size, binary coding length, crossover probability, and mutation probability are designed.

[0023] Furthermore, in the solution process of step (5), a quality evaluation function based on the local structure tensor is constructed as the fitness function of the genetic algorithm to evaluate the clarity and deblurring effect of the restored result of each iteration. The quality evaluation function based on the local structure tensor includes the following steps:

[0024] (1) Divide the image into R×R sub-regions equally;

[0025] (2) Calculate the local gradient vector matrix of each sub-region;

[0026] (3) Based on the local gradient vector matrix, calculate the covariance matrix, and perform singular value decomposition on the covariance matrix to obtain the eigenvalues a1 and a2;

[0027] (4) Calculate the local quality metric of each sub-region through the eigenvalues a1 and a2;

[0028] (5) Sum the local quality metrics of each point in the image to obtain the quality evaluation result of the image.

[0029] Furthermore, the genetic algorithm inner loop includes:

[0030] In the solution process of step (5), denote the optimal regularization parameter calculated in the k-th alternating iteration as τ k and uk , take τ k as the initial parameter for the (k + 1)-th alternating iteration, and perform binary encoding on τ k to form the initial population

[0031] For each individual in the population , perform binary decoding calculation

[0032] According to , calculate the fitness function of each individual to obtain the fitness value of each individual, and determine the position of the individual with the optimal fitness value in the population;

[0033] Sort all individuals in the population in descending order of fitness value, and select the top 80% of the individuals as the optimal individuals;

[0034] Perform crossover and mutation operations on the selected optimal individuals, calculate the new fitness values corresponding to each optimal individual respectively, determine the new positions of the optimal individuals, and form a new population

[0035] Through multiple operations such as selection, crossover, and mutation, output the optimal individual of this inner loop iteration and

[0036] By repeating the above steps until the end of the inner loop of the (k + 1)-th alternating iteration, and at the same time output the optimal individual u of the inner loop of the (k + 1)-th alternating iteration k+1 and τ k+1 .

[0037] Advantages of the present invention: The present invention relies on the forward-backward algorithm to construct a plug-and-play numerical solution framework, and embeds a genetic algorithm in the alternating iteration process, solves the problem of adaptive selection of parameters in each iteration, and provides an infrared image adaptive restoration framework with a simple framework, strong applicability, good effect, easy engineering implementation, and high adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The following further clarifies the specific embodiments of the present invention with reference to the accompanying drawings.

[0039] Figure 1 is a schematic diagram of the adaptive restoration solution framework of the present invention;

[0040] Figure 2 is a schematic diagram of genetic operations: crossover and mutation. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] Combined with Figure 1 and Figure 2, the adaptive restoration method for Poisson noise images of the present invention is based on the forward-backward algorithm, introduces intermediate variables, decomposes the Poisson noise image restoration optimization problem into two alternately iterative sub-problems, and obtains a clear restored image through alternating iteration.

[0042] In this application, the definitions of variables and symbols involved are shown in Table 1.

[0043] Table 1 Definitions of Variables and Symbols

[0044]

[0045] To solve the existing problem of Poisson noise image restoration, which has the problems of complex solution process caused by non-linearity and the need for manual adjustment of regularization parameters, the present invention provides a parameter adaptive adjustment image restoration solution framework with strong adaptability of the model, which can meet the problems of image restoration or deblurring with different regularization terms.

[0046] To achieve the above object, the present invention provides a plug-and-play parameter adaptive restoration method, including the following steps:

[0047] <Step 1> Define the Poisson noise restoration optimization model based on the maximum a posteriori estimation:

[0048]

[0049] Among them, is the data fidelity term, is the regularization function;

[0050] <Step 2> Introduce the intermediate variable z. Based on the forward-backward solution framework, the optimization model in <Step 1> can be converted into the following iterative model:

[0051]

[0052] where 0 < γ < 2 / L represents the iteration step size, L is the Lipschitz constant of, and The proximity mapping operator is defined as:

[0053]

[0054] Alternating iteration solution strategy:

[0055] Solve <Step 2>, set the initial value u 0 , substitute it into the optimization model, and alternately iterate (1-1) and (1-2). When a certain stopping condition is met, obtain the restored image. The alternating iteration process is:

[0056]

[0057] For the solution of model (1-1), the iteration step size γ can essentially be regarded as the iteration step size of the gradient descent method. The selection of its value only affects the convergence speed but does not affect the restoration effect. Therefore, in application, γ is set as a fixed value that can ensure convergence and is directly calculated;

[0058] For the solution of model (1-2), since the selection of the regularization parameter τ will affect the restoration effect, this patent considers embedding a genetic algorithm inner loop in each alternating iteration process. The regularization parameter τ is used as a genetic variable to dynamically determine the optimal regularization parameter for each alternating iteration and output the restoration result corresponding to the optimal regularization parameter;

[0059] According to the definition of the approximate mapping operator, model (1-2) can be regarded as a denoising problem with a noise level of Based on the regularization term Select the corresponding solution strategy to obtain the restored image after denoising;

[0060] Models (1-1) and (1-2) are alternately iterated. When the termination condition is satisfied, the best restoration result u * .

[0061] Adaptive solution of model (1-2) based on the genetic algorithm inner loop:

[0062] Set the value range of τ as [τ min , τ max , and design parameters such as population size, binary coding length, crossover probability, and mutation probability;

[0063] Construct a quality evaluation function based on the local structure tensor as the fitness function of the genetic algorithm to evaluate the clarity and deblurring effect of the restoration result of each iteration.

[0064] Denote the optimal regularization parameter calculated in the k-th alternating iteration as τ k and u k . Take τ k as the initial parameter for the (k + 1)-th alternating iteration, and perform binary coding on τ k to form the initial population

[0065] For each individual in the population perform binary decoding calculation

[0066] According to calculate the fitness function of each individual to obtain the fitness values of each individual, and determine the position of the individual with the optimal fitness value in the population;

[0067] Sort all individuals in the population from largest to smallest according to the fitness value, and select the top 80% of the individuals as excellent individuals;

[0068] Perform crossover and mutation operations on the selected optimal individuals, calculate the new fitness values corresponding to each optimal individual respectively, determine the new positions of the optimal individuals, and form a new population

[0069] Output the optimal individual of this inner loop iteration and

[0070] Repeat the above steps until the end of the inner loop of the (k + 1)-th alternating iteration, and at the same time output the optimal individual u of the inner loop of the (k + 1)-th alternating iteration k+1 and τ k+1 。

[0071] The quality evaluation function based on the local structure tensor includes: ① Divide the image into R×R sub-regions equally; ② Calculate the local gradient vector matrix of each sub-region; ③ Based on the local gradient vector matrix, calculate the covariance matrix, and perform singular value decomposition on the covariance matrix to obtain the eigenvalues a1 and a2; ④ Calculate the local quality measure of each sub-region through the eigenvalues a1 and a2; ⑤ Sum the local quality measures of each sub-region of the image to obtain the quality evaluation result of the image

[0072] The following is an example to illustrate the adaptive restoration method of this application, including the following steps

[0073] (10) Initial parameter setting

[0074] (11) As Figure 1 shown in the flowchart of the infrared image adaptive restoration method based on the genetic algorithm, select the original image u with a resolution of 256×256

[0075] (12) Select the image blur function H as a Gaussian filter, set the filter size to 9×9, and the standard deviation to 2; perform convolution operation on the original image u with the blur function H, adjust the image pixel range to between [0, 100], and then add Poisson noise to form the blurred image g

[0076] (13) Select the regularization term as the Hessian function where is the second derivative operator

[0077] (20) Solve z based on the fast Fourier transform k

[0078] (21) Set u 0 =g, and the value range of the parameter γ is between 0.01 - 0.55

[0079] (22) Calculate where It can be directly calculated by Fourier transform:

[0080] (30) Solve for u based on the genetic algorithm k

[0081] (31) Determine the genetic system, including a population size of 100, a binary coding length of 10, a crossover probability of 0.6, a mutation probability of 0.001, determine the range of the regularization parameter τ to be [0, 100], and the number of inner loop iterations of the genetic algorithm to be 100;

[0082] (32) Initialize the population and randomly generate the initial population Form an initial population with individual elements being 0 or 1 and a size of 100×10;

[0083] (33) Decode each individual in the initial population to obtain the decoded regularization parameter set as and substitute each element in the decoded regularization parameter set and z 1 into formula (3) respectively, and select the alternating direction multiplier method for solution to obtain

[0084] (34) Calculate the fitness function corresponding to each individual in the population U' based on the local structure tensor 0 specifically including the following steps;

[0085] 【1】Divide the image into 256 sub-regions equally, and each sub-region contains 16×16 pixel points;

[0086] 【2】Calculate the local gradient vector matrix of each sub-region and obtain the covariance matrix of each local gradient vector matrix;

[0087] 【3】Perform singular value decomposition on the covariance matrix to obtain the eigenvalues a1 and a2 of the covariance matrix of each sub-region;

[0088] 【4】Calculate the local quality measure of each sub-region based on the eigenvalues of the covariance matrix of each sub-region;

[0089] 【5】Sum the local quality measures of the 256 sub-regions to obtain the quality evaluation result of the restored image, that is, the fitness value of the restored image;

[0090] (35) Use the selection operator to select the 80 individuals with the optimal fitness function values from the initial population and perform crossover and mutation operations on them to form new individuals;

[0091] (36) Determine whether the individuals of the new population meet the pre-defined termination criteria. If not, return to step (0009) and perform a loop according to the same steps until the pre-set number of iterations is completed, and select the optimal solution that meets the conditions as the optimal solution u of this inner loop. 1* ;

[0092] (40) Alternately iterate to obtain the optimal solution u. *

[0093] (41) Repeat the loop iteration from steps (21)-(36) until the requirement for stopping the outer loop iteration is met, and output the optimal individual u. * .

[0094] The adaptive restoration method for Poisson noise images of the present application is based on the forward-backward solution framework, avoiding the operation of inverting the blurring matrix. At the same time, the deblurring problem is converted into a denoising problem, and various regularization terms can be embedded in the denoising model, improving the adaptation range of the model; and a genetic algorithm is embedded in the alternating iteration process. Utilizing the characteristics of the genetic algorithm with high search accuracy and not easily falling into local optimal points, the adaptive selection of regularization parameters is effectively realized, without the need for manual parameter adjustment, improving the practicality and intelligence level of the model.

[0095] Many specific details are set forth in the above description to facilitate a full understanding of the present invention. However, the above description is only a preferred embodiment of the present invention, and the present invention can be implemented in many other ways different from those described herein. Therefore, the present invention is not limited by the specific implementations disclosed above. At the same time, any person skilled in the art can make many possible changes and modifications to the technical solution of the present invention, or modify it into an equivalent embodiment with equivalent changes, without departing from the scope of the technical solution of the present invention. Any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. An adaptive restoration method for Poisson noise images, characterized in that: Based on the forward-backward algorithm, intermediate variables are introduced, and the Poisson noise image restoration optimization problem is decomposed into two alternately iterative sub-problems. A clear restored image is obtained through alternating iteration, including the following steps: (1) Define the Poisson noise restoration optimization model based on the maximum a posteriori estimation: ， (2)Based on the forward-backward algorithm, introduce intermediate variables , and transform the above optimization model into the following alternating iteration problem: ， wherein represents the iteration step size, is the Lipschitz constant of, and ， ； (3)Select initial parameters , , regular function ; (4) Substitute parameters and , solve the intermediate variable ; (5) Based on intermediate variables , relying on the genetic algorithm to complete the automatic optimization of the regularization parameter and in each iteration process; (6) Steps (4) and (5) are alternately iterated to complete the solution of the optimal solution. The solution of; Embed the inner loop of the genetic algorithm in the solution process of step (5), and use the regularization parameter as a variable to dynamically determine the optimal regularization parameter for each alternating iteration, and output the restoration result corresponding to the optimal regularization parameter; In the solution process of step (5), a quality evaluation function based on the local structure tensor is constructed as the fitness function of the genetic algorithm to evaluate the clarity and deblurring effect of the restored result of each iteration. The quality evaluation function based on the local structure tensor includes the following steps: (1) Divide the image into sub-regions; (2) Calculate the local gradient vector matrix of each sub-region; (3) Calculate the covariance matrix based on the local gradient vector matrix, and perform singular value decomposition on the covariance matrix to obtain eigenvalues. and ; (4) Through eigenvalues and , calculate the local quality metrics of each sub-region; (5) Sum the local quality metrics of each point in the image to obtain the quality evaluation result of the image; Among them, is the estimated value after alternating iteration, is the image to be restored or the original image, is the inner product operator, is a column or row vector with all element values being 1, is the blurring function, is the observed data or the blurred image, is the logarithmic function, is the regularization parameter, non - negative, is the data fidelity term, is the regularization function; is the number of alternating cyclic iterations; is the conjugate complex number, is the identity matrix, is the convolution operator.

2. The adaptive restoration method for Poisson noise images according to claim 1, characterized in that: In step (4) can be solved quickly based on the Fourier transform.

3. The adaptive restoration method for Poisson noise images according to claim 1, characterized in that: In step (5) According to the definition of the approximate mapping operator, the optimization solution model can be regarded as a denoising problem with a noise level of Based on the regularization term Select the corresponding solution strategy to generate the restored image after denoising.

4. The adaptive restoration method for Poisson noise images according to claim 1, characterized in that: In the solution process of step (5), set the value range of , and design the population size, binary coding length, crossover probability, and mutation probability.

5. The adaptive restoration method for Poisson noise images according to claim 1, characterized in that: The inner loop of the genetic algorithm includes: In the solution process of step (5), denote the optimal regularization parameter obtained by the -th alternating iteration calculation as and . Take as the initial parameter of the -th alternating iteration, and perform binary encoding on to form the initial population ; For each individual in the population perform binary decoding calculation ; According to Calculate the fitness function of each individual, obtain the fitness values of each individual, and determine the position of the individual with the optimal fitness value in the population; Sort all individuals in the population from largest to smallest according to the fitness value, and select the top 80% of the individuals as the optimal individuals; Perform crossover and mutation operations on the selected optimal individuals, calculate the new fitness values corresponding to each optimal individual respectively, determine the new positions of these optimal individuals, and form a new population ; Output the optimal individual of this inner loop iteration by performing the crossover and mutation operations multiple times and ; By repeating the above steps until the end of the inner loop of the -th alternating iteration, while outputting the optimal individual of the inner loop of the -th alternating iteration and .

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