A method for restoring degraded and blurred images based on regularized constrained Poisson noise.

Abstract

This invention discloses a method for restoring blurred images degraded by Poisson noise based on an improved regularization constraint. First, within a Bayesian probabilistic framework, a clear image is modeled, and an improved total variational regularization coefficient is introduced to construct an optimal estimation problem model. Second, the problem model is decomposed into two optimal estimation sub-problems, and the two sub-problems are iteratively solved using a quadratic penalty function method. The penalty coefficient is updated based on the iteration results to achieve denoising of the noisy image. Compared with traditional image restoration methods, this invention can significantly suppress Poisson noise and enhance image detail information, thereby producing a high-quality restored image.

Description

Technical Field

[0001] This invention relates to the field of computer digital image processing technology, specifically to a method for restoring degraded and blurred images based on improved regularized constrained Poisson noise. Background Technology

[0002] In fields such as everyday photography, optical remote sensing, and medical imaging, background light, atmospheric turbulence, and instrument noise often introduce noise signals during image formation, affecting image quality and hindering subsequent image processing. Therefore, image denoising is fundamental and a prerequisite for image processing, and represents a crucial research direction in the field.

[0003] Traditional image denoising algorithms perform linear operations on local regions, such as mean filtering and median filtering. While simple, easy to use, and fast, these algorithms can destroy image details and reduce information.

[0004] In mathematics, image degradation can be described by the convolution operation of a sharp image and a point spread function; the inverse process, the degraded image restoration process, is called deconvolution. By finding similar regions between the blurred image and the convolved image on a global scale, the loss of detail information can be effectively reduced. However, deconvolution is a typical ill-conditioned process, meaning that even a small amount of noise in the blurred image is amplified and propagates back into the restored image, causing the restored result to deviate significantly from the true sharp image. Therefore, a total variational regularization term is usually added during deconvolution to constrain noise, but a simple total variational regularization term is generally not very effective at constraining noise. Summary of the Invention

[0005] To address the problems raised in the background art, the present invention provides a method for restoring blurred images with degraded noise based on improved regularization-constrained Poisson noise, which can effectively suppress noise and thus produce high-quality restored images.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for restoring degraded and blurred images based on improved regularization-constrained Poisson noise, comprising the following steps:

[0007] S1. Within the Bayesian probability framework, the noise is modeled using the Poisson probability model, and the clear image is modeled using the improved total variation.

[0008] S2. Introduce a penalty factor and auxiliary variables, and sum the two models in S1 with weights to construct a clear image estimation problem model.

[0009] S3. Decompose the model in S2 into two optimal estimation problems concerning the sharp image and auxiliary variables;

[0010] S4. Initialize the estimated values ​​of the clear image using the noisy image;

[0011] S5. With the estimated value of the fixed clear image, the conjugate gradient iteration method is used to solve the optimal estimation problem of the auxiliary variable to obtain the estimated value of the auxiliary variable;

[0012] S6. With the auxiliary variables fixed, the optimal estimation problem for the sharp image is solved using the quadratic penalty function method to obtain the estimated value of the sharp image.

[0013] S7. Update the penalty factor in S2;

[0014] S8. Repeat steps S5, S6, and S7 until the penalty coefficient reaches its maximum value, obtaining an estimated value of the clear image, i.e., the restored image.

[0015] Preferably, the expression for modeling noise using the Poisson probability model in S1 is: The expression for modeling sharp images using the improved total variation is:

[0016] Where g represents the blurred image, o represents the sharp image, and h represents the point spread function; P(g|o) is the probability distribution of random noise, and P(o) is the probability distribution of the sharp image. and Let represent the gradient operators in the horizontal and vertical directions, respectively; let i represent the pixel index in the sharp image; and let μ represent the weights of the horizontal and vertical gradients in the sharp image.

[0017] Preferably, the penalty factor β and the auxiliary variable u in S2 are weighted by λ, and the model for the noisy image restoration problem is as follows:

[0018]

[0019] Preferably, the two optimal estimation problems in S3 concerning the sharp image and auxiliary variables are as follows:

[0020]

[0021]

[0022] Preferably, in step S4, the estimated value of the clear image from the noisy image is initialized to o = g, and the initial value of the penalty coefficient is set to β = β. initial The maximum value is β max , iteration coefficient r.

[0023] Preferably, in step S5, the steps of fixing the estimated value of the clear image, solving the optimal estimation problem of the auxiliary variable, obtaining the estimated value of the auxiliary variable, and updating the value of the auxiliary variable are as follows:

[0024] 1) Fix o = g, and decompose the subproblem into independent problem solutions.

[0025]

[0026] The result is:

[0027]

[0028] 2) Update u.

[0029] Preferably, in step S6, the estimated value of the fixed auxiliary variable is used to solve the optimal estimation problem of the sharp image using the quadratic penalty function method to obtain the estimated value of the sharp image. The steps for updating the sharp image value and the penalty coefficient are as follows:

[0030] 1) Introduce a penalty coefficient η Two auxiliary variables, w and d, transform the function into:

[0031]

[0032] 2) Decompose the function into two optimal estimation problems with respect to the sharp image and auxiliary variables:

[0033]

[0034]

[0035] 3) Calculate the estimated value of o using the conjugate gradient method, and decompose the subproblem into independent problems to solve w. , d, whose solution is a non-negative root of the following system of equations:

[0036] Solve for w , d;

[0037] 4) Update the penalty coefficient η = η * R, where R > 1.

[0038] Preferably, in step S7, the penalty factor in S2 is updated to β = β*r, where r > 1.

[0039] Compared with existing technologies, the advantages of this invention are as follows: This invention uses a method for restoring blurred images degraded by Poisson noise. Within a Bayesian probabilistic framework, it models a clear image and introduces an improved total variational regularization coefficient to construct an optimal estimation problem model. Then, an iterative optimization algorithm is designed, and the penalty coefficient is updated based on the iteration results to achieve denoising of the noisy image and obtain a high-quality restored image. Attached Figure Description

[0040] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0041] In the attached diagram:

[0042] Figure 1 This is a flowchart of the blurred image restoration method of the present invention;

[0043] Figure 2 This is the clear image corresponding to the blurred image in the embodiments of the present invention;

[0044] Figure 3 This is the blurred image in the embodiments of the present invention;

[0045] Figure 4 This is the restored image obtained in the embodiments of the present invention. Detailed Implementation

[0046] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0047] Example: Figure 1 As shown, the restoration method for degraded blurred images based on improved regularization-constrained Poisson noise includes the following steps:

[0048] S1. Within the Bayesian probability framework, the noise is modeled using the Poisson probability model, and the clear image is modeled using the improved total variation.

[0049] The expression for modeling noise using the Poisson probability model is as follows:

[0050]

[0051] The expression for modeling sharp images using the improved total variation is:

[0052]

[0053] Where g represents the blurred image, o represents the sharp image, and h represents the point spread function; P(g|o) is the probability distribution of random noise, and P(o) is the probability distribution of the sharp image. and Let i and μ represent the gradient operators in the horizontal and vertical directions, respectively; let i represent the pixel index in the sharp image; and let μ represent the weights of the horizontal and vertical gradients in the sharp image.

[0054] S2. Introduce a penalty factor and auxiliary variables, and sum the two models in S1 with weights to construct a clear image estimation problem model.

[0055] The penalty factor β and the auxiliary variable u are weighted by λ. The model for the noisy image restoration problem is as follows:

[0056]

[0057] S3. Decompose the model in S2 into two optimal estimation problems concerning the sharp image and auxiliary variables;

[0058] The two optimal estimation problems concerning the clear image and auxiliary variables are as follows:

[0059]

[0060]

[0061] S4. Initialize the estimated values ​​of the clear image using the noisy image;

[0062] The estimation of the sharp image from the noisy image is initialized as o = g, and the initial value of the penalty coefficient is set as β = β. initial The maximum value is β max The iteration coefficient r;

[0063] S5. With the estimated value of the fixed clear image, the conjugate gradient iteration method is used to solve the optimal estimation problem of the auxiliary variable to obtain the estimated value of the auxiliary variable;

[0064] The steps for obtaining the estimated values ​​of the fixed, clear image, solving the optimal estimation problem for the auxiliary variables, and updating the auxiliary variable values ​​are as follows:

[0065] 1) Fix o = g, and decompose the subproblem into independent problem solutions.

[0066]

[0067] The result is:

[0068]

[0069] 2) Update u;

[0070] S6. With the auxiliary variables fixed, the optimal estimation problem for the sharp image is solved using the quadratic penalty function method to obtain the estimated value of the sharp image.

[0071] The estimated values ​​of the fixed auxiliary variables are obtained by solving the optimal estimation problem of the sharp image using the quadratic penalty function method. The steps for updating the sharp image value and the penalty coefficient are as follows:

[0072] 1) Introduce a penalty coefficient η Two auxiliary variables, w and d, transform the function into:

[0073]

[0074] 2) Decompose the function into two optimal estimation problems with respect to the sharp image and auxiliary variables:

[0075]

[0076]

[0077] 3) Calculate the estimated value of o using the conjugate gradient method, decompose the subproblem into independent problems to solve w and d, the solution of which is a non-negative root of the following system of equations:

[0078] Solve for w , d;

[0079] 4) Update the penalty coefficient η = η * R, where R > 1;

[0080] S7. Update the penalty factor in S2; where the penalty factor in S2 is updated to β=β*r, where r>1;

[0081] S8. Repeat steps S5, S6, and S7 until the penalty coefficient reaches its maximum value, obtaining an estimated value of the clear image, i.e., the restored image.

[0082] In specific implementation, such as Figure 2 The image shown is clear. Figure 3 For noisy images, Figure 4 This is the restored image obtained from an embodiment of the present invention.

[0083] This invention proposes a method for restoring Poisson noise-degraded blurred images based on an improved total variational regularization constraint. This method effectively removes noise from images and restores blurred images with high quality, significantly improving image quality and enhancing the resolution of image details. Figure 4 and Figure 3The comparison shows that Poisson noise in the image is effectively removed and image details are effectively restored.

[0084] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for restoring blurred images degraded by Poisson noise based on improved regularization constraints, characterized in that, Includes the following steps: S1. Within the Bayesian probability framework, the noise is modeled using the Poisson probability model, and the clear image is modeled using the improved total variation. S2. Introduce a penalty factor and auxiliary variables, and sum the two models in S1 with weights to construct a clear image estimation problem model. S3. Decompose the model in S2 into two optimal estimation problems concerning the sharp image and auxiliary variables; S4. Initialize the estimated values ​​of the clear image using the noisy image; S5. With the estimated value of the fixed clear image, the conjugate gradient iteration method is used to solve the optimal estimation problem of the auxiliary variable to obtain the estimated value of the auxiliary variable; S6. With the auxiliary variables fixed, the optimal estimation problem for the sharp image is solved using the quadratic penalty function method to obtain the estimated value of the sharp image. S7. Update the penalty factor in S2; S8. Repeat steps S5, S6, and S7 until the penalty coefficient reaches its maximum value, and obtain an estimated value of the clear image, i.e., the restored image.

2. The method for restoring degraded and blurred images based on improved regularized constrained Poisson noise according to claim 1, characterized in that: The expression for modeling noise using the Poisson probability model in S1 is as follows: The expression for modeling sharp images using the improved total variation is: Where g represents the blurred image, o represents the sharp image, and h represents the point spread function; P(g|o) is the probability distribution of random noise, and P(o) is the probability distribution of the sharp image. and Let represent the gradient operators in the horizontal and vertical directions, respectively; let i represent the pixel index in the sharp image; and let μ represent the weights of the horizontal and vertical gradients in the sharp image.

3. The method for restoring degraded and blurred images based on improved regularized constrained Poisson noise according to claim 1, characterized in that: The penalty factor β and auxiliary variable u in S2 are weighted by λ. The model for the noisy image restoration problem is as follows:

4. The method for restoring degraded and blurred images based on improved regularized constrained Poisson noise according to claim 1, characterized in that: The two optimal estimation problems concerning the sharp image and auxiliary variables in S3 are as follows:

5. The method for restoring degraded and blurred images based on improved regularized constrained Poisson noise according to claim 1, characterized in that: In step S4, the estimated value of the clear image from the noisy image is initialized to o = g, and the initial value of the penalty coefficient is set to β = β. initial The maximum value is β max , iteration coefficient r.

6. The method for restoring degraded and blurred images based on improved regularized constrained Poisson noise according to claim 1, characterized in that: The steps in S5, which involve fixing the estimated value of the clear image, solving the optimal estimation problem for the auxiliary variables, obtaining the estimated values ​​of the auxiliary variables, and updating the values ​​of the auxiliary variables, are as follows: 1) Fix o = g, and decompose the subproblem into independent problem solutions. The result is: 2) Update u.

7. The method for restoring degraded and blurred images based on improved regularized constrained Poisson noise according to claim 1, characterized in that: The estimated values ​​of the fixed auxiliary variables in S6 are used to solve the optimal estimation problem of the sharp image using the quadratic penalty function method, resulting in the estimated value of the sharp image. The steps for updating the sharp image value and the penalty coefficient are as follows: 1) Introducing a penalty coefficient η, and two auxiliary variables w and d, the function is transformed into: 2) Decompose the function into two optimal estimation problems with respect to the sharp image and auxiliary variables: 3) Calculate the estimated value of o using the conjugate gradient method, and decompose the subproblem into independent problems to solve w and d. The solution is a non-negative root of the following system of equations: Solve for w and d; 4) Update the penalty coefficient η = η * R, where R > 1.

8. The method for restoring degraded and blurred images based on improved regularized constrained Poisson noise according to claim 1, characterized in that: In step S7, the penalty factor in S2 is updated to β = β*r, where r > 1.

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