Blind image deconvolution method based on adaptive weighted TV regularization

Abstract

The present invention discloses a blind image deconvolution working method based on adaptive weighted TV regularization, comprising the following steps: S1, forming a novel blind deconvolution model by combining an adaptive weighted matrix with a gradient operator; S2, solving the formed novel blind deconvolution model using an alternating direction multiplier method (ADMM), and performing blind image deconvolution according to set conditions; S3, numerically evaluating the restored image through an evaluation index, and evaluating the quality of the restored image from the perspective of visual effect.

Description

Technical Field

[0001] The present invention relates to the field of image processing, and in particular to a blind image deconvolution method based on adaptive weighted TV regularization. Background Art

[0002] Image deconvolution is a fundamental problem in image processing that has attracted increasing attention in recent years. Its goal is to reconstruct a noisy, blurred image into a sharp one; a blurred image is typically modeled as a linear convolution of the image and a blur kernel (also known as a point spread function (PSF)). Mathematically, the image degradation process is described as follows:

[0003] f=k*u+η,

[0004] Where u and f represent the clear image and degraded image respectively, k is the blur kernel, * represents the convolution operator, and η is additive Gaussian white noise. Image deconvolution includes two types: non-blind deconvolution and blind deconvolution. When the blur kernel k is known, the problem of obtaining the clear image u through f and k is called non-blind deconvolution. However, in many practical applications, the blur kernel is usually unknown. In this case, u and k need to be estimated from f. This problem is called blind deconvolution. Blind deconvolution is a research hotspot in the fields of image processing and computer vision. Unlike non-blind deconvolution, blind deconvolution is not only sensitive to noise but also may produce many solutions. For these reasons, blind image deconvolution is more challenging than non-blind image deconvolution.

[0005] In order to solve the blind deconvolution problem, the prior art proposes a blind deconvolution method using H 1 norm minimizes the image u and blur kernel k. H of u and k 1 The norm minimization problem can be expressed as

[0006]

[0007] The first term is the data fitting term, and the other two terms are the H of u and k respectively. 1 norm. α and β are two regularization parameters. However, H 1 The norm has a very strong isotropic smoothing property, which makes this method unsatisfactory in preserving image edges. The prior art has a total variation (TV) regularization model for Gaussian image denoising. This model can better preserve image edges while removing noise. Since then, TV regularization has been used instead of H. 1 A new blind deconvolution method proposed by Norm:

[0008]

[0009] TV regularization can remove noise and blur while preserving edges, particularly for piecewise constant images. However, due to the nonlinearity and non-differentiability of the TV model, it is computationally difficult to solve. Existing methods preprocess the degraded image using a shock filter and then use the preprocessed image as the initial condition for TV minimization blind deconvolution. This method can save computational time compared to existing methods. While TV regularization performs well at preserving edges, it performs poorly at preserving image texture. Therefore, existing methods have proposed an adaptive non-local TV regularization method for blind image restoration. This method fully utilizes spatial information distributed across different image regions through a non-local TV operator, thereby preserving more image details. Because cartoon and texture components have different representations in an image, existing methods use cartoon-texture decomposition techniques to preserve texture in blind image deconvolution. Furthermore, the TV norm tends to convert smooth signals into piecewise constants, resulting in staircase artifacts. To eliminate staircase artifacts, existing methods have proposed a non-convex high-order TV model for blind image deconvolution. However, high-order TV regularization is not ideal for preserving image edges.

[0010] Conventional blind deconvolution algorithms based on TV regularization are not ideal for processing local image structures. Total variation (TV) regularization can preserve image edges, but lacks adaptability and performs poorly when restoring images with complex structures. This urgently requires technical personnel to address these issues. Summary of the Invention

[0011] The present invention aims to at least solve the technical problems existing in the prior art, and in particular innovatively proposes a blind image deconvolution method based on adaptive weighted TV regularization.

[0012] In order to achieve the above-mentioned object of the present invention, the present invention provides a blind image deconvolution method based on adaptive weighted TV regularization, comprising the following steps:

[0013] S1, a novel blind deconvolution model is formed by combining the adaptive weighting matrix with the gradient operator;

[0014] S2, using the alternating direction multiplier method (ADMM) to solve the formed new blind deconvolution model, and perform blind image deconvolution according to the set conditions;

[0015] S3, numerically evaluates the restored image through evaluation indicators, and evaluates the quality of the restored image from a visual perspective.

[0016] Preferably, according to the above technical solution, S1 includes:

[0017] The following adaptive weighted TV model for blind image deconvolution is proposed:

[0018]

[0019] Where α and β are two regularization parameters used to balance the data fitting term and the regularization term, T is the adaptive weighting matrix, is the gradient operator. After experimental research, the present invention found that The performance is better than using ||k||1, so the L1 norm is used for the constraint

[0020] According to the preferred embodiment of the above technical solution, T is defined as follows:

[0021]

[0022] Among them G δ (·) represents a two-dimensional Gaussian convolution kernel, δ and ι are two parameters, and represents the difference of f in the horizontal and vertical directions, i and j represent the horizontal and vertical coordinates of the image pixel respectively.

[0023] Preferably, according to the above technical solution, S2 includes:

[0024] Introduce three auxiliary variables p, q, w, and The model is rewritten as a constrained optimization problem:

[0025]

[0026] To solve the above equation, three Lagrangian multipliers λ1, λ2, and λ3 are introduced to transform it into a saddle point problem. The augmented Lagrangian functional is:

[0027]

[0028] Where K represents the unknown blur matrix, which is a block circulant matrix formed by the point spread function k; r1, r2 and r3 are three penalty parameters.

[0029] According to the preferred technical solution above, when applying ADMM, it is necessary to minimize the five sub-problems k, u, p, q, and w. In each iteration, other variables are fixed and the three Lagrange multipliers λ1, λ2, and λ3 are updated. The following formula is obtained:

[0030]

[0031] The superscript n is the increasing symbol of the number of iterations, n≥0.

[0032] According to the preferred embodiment of the above technical solution, the k subproblem is expressed as

[0033]

[0034] Where U is a block circulant matrix formed by the image u. According to the optimality condition, the above Euler-Lagrange equation is obtained. The present invention assumes periodic boundary conditions, so the equation can be solved by fast Fourier transform (FFT) to obtain

[0035]

[0036] Where F represents FFT, F -1 represents its inverse transform, Represents the gradient operator The conjugate transpose of .

[0037] According to the preferred embodiment of the above technical solution, the u sub-problem is expressed as

[0038]

[0039] According to its optimality condition, and then using FFT, we get the formula:

[0040]

[0041] According to the preferred embodiment of the above technical solution, for the p-subproblem, it can be expressed as

[0042]

[0043] According to the optimality condition of the above formula, where p = [p1, p2], q = [q1, q2], λ m =[λ m1 ,λ m2 ](m=1,2); then the corresponding linear equations are expressed as

[0044]

[0045] By simple calculation, we can get p from the above linear equations. n+1 Explicit solution of :

[0046]

[0047] According to the preferred embodiment of the above technical solution, the q sub-problem is expressed as

[0048]

[0049] It has a closed-form solution given by the fast contraction formula

[0050]

[0051] The w subproblem is expressed as

[0052]

[0053] Similar to the q-subproblem, the solution to the w-subproblem can also be given by the fast contraction formula

[0054]

[0055] Preferably, according to the above technical solution, S3 includes:

[0056] definition:

[0057]

[0058]

[0059]

[0060] Where f, I, and u represent the degraded image, original image, and restored image, respectively; M and N are the length and width of the image; μ and σ represent the local mean and standard deviation of the image, respectively; σ Iu is the covariance value between I and u; c1 and c2 are two constants used to prevent the denominator from approaching zero; the higher the values of PSNR, ISNR and SSIM, the better the quality of image restoration; u n The relative error is defined as:

[0061]

[0062] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0063] This paper proposes a new blind image deconvolution model using adaptive weighted TV regularization. This model is able to better handle local image structure. Numerically, an efficient alternating direction method of multipliers (ADMM) is designed to solve the non-smooth model. Experimental results demonstrate that this method is superior to other related blind deconvolution methods.

[0064] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0066] Figure 1 It is the overall flow chart of the present invention;

[0067] Figure 2 It is a clear picture of the data experiment of the present invention;

[0068] Figure 3 (a) to 3(d) are the effects of linear motion blur, Gaussian blur, defocus blur and custom blur set by the present invention;

[0069] Figure 4 (a) to 4(d) are four effect diagrams of the Satellite linear motion blur state of the present invention;

[0070] Figure 5 (a) to 5(d) are four effect diagrams of the Satellite Gaussian blur state of the present invention;

[0071] Figure 6 (a) to 6(d) are four effect diagrams of the Satellite defocused blur state of the present invention;

[0072] Figure 7 (a) to 7(d) are four renderings of the Satellite custom fuzzy state of the present invention;

[0073] Figure 8 (a) to 8(d) are four effect diagrams of the Lena linear motion blur state of the present invention;

[0074] Figure 9 (a) to 9 (d) are four effect diagrams of Lena Gaussian blur state of the present invention;

[0075] Figure 10 (a) to 10 (d) are four effect diagrams of Lena in the defocused blur state of the present invention;

[0076] Figure 11 (a) to 11(d) are four effect diagrams of Lena in the custom blur state of the present invention;

[0077] Figure 12 (a) to 12 (d) are four effect diagrams of the Peppers linear motion blur state of the present invention;

[0078] Figure 13 (a) to 13 (d) are four effect diagrams of the Peppers Gaussian blur state of the present invention;

[0079] Figure 14 (a) to 14 (d) are four effect diagrams of the Peppers defocused blur state of the present invention;

[0080] Figure 15 (a) to 15 (d) are four effect diagrams of Peppers in the custom fuzzy state of the present invention;

[0081] Figure 16 (a) to 16 (d) are four effect diagrams of the House linear motion blur state of the present invention;

[0082] Figure 17 (a) to 17 (d) are four effect diagrams of the House Gaussian blur state of the present invention;

[0083] Figure 18 (a) to 18 (d) are four effect diagrams of the House defocused blur state of the present invention;

[0084] Figure 19 (a) to 19(d) are four renderings of the House custom fuzzy state of the present invention;

[0085] Figure 20 It is the Peppers restoration diagram of the present invention;

[0086] Figure 21 This is the restoration diagram of Lena according to the present invention. DETAILED DESCRIPTION

[0087] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0088] like Figure 1 As shown, the present invention discloses a blind image deconvolution method based on adaptive weighted TV regularization, comprising the following steps:

[0089] S1, a novel blind deconvolution model is formed by combining the adaptive weighting matrix with the gradient operator;

[0090] S2, using the alternating direction multiplier method (ADMM) to solve the formed new blind deconvolution model, and perform blind image deconvolution according to the set conditions;

[0091] S3, numerically evaluates the restored image through evaluation indicators, and evaluates the quality of the restored image from a visual perspective.

[0092] Since different regions of the image have different structures. For the proposed model, maintaining the local structure is crucial. Since the finite difference method of the gradient only depends on the horizontal and vertical directions, the traditional TV-based model cannot effectively couple with the local structure of the image. To overcome this shortcoming, the prior art proposes an anisotropic TV (ATV) model for Gaussian image denoising, which can better diffuse along the tangent direction of local features. In order to couple with the local structure more effectively, different weights are constructed by adding an adaptive weighting matrix T. The definition of T is as follows:

[0093]

[0094] Among them G δ (·) represents a two-dimensional Gaussian convolution kernel, δ and ι are two parameters, and represents the difference of f in the horizontal and vertical directions, i and j represent the horizontal and vertical coordinates of the image pixel respectively.

[0095] For blind image deconvolution, the adaptive weight matrix T is combined with the gradient operator In addition, the L1 norm is used to constrain Therefore, the following adaptive weighted TV model for blind image deconvolution is proposed:

[0096]

[0097] Where α and β are two regularization parameters used to balance the data fitting term and the regularization term. The performance is better than using ||k||1.

[0098] The present invention uses ADMM to solve The model transforms the solution of the initial problem into several simple sub-problems that are calculated alternately. ADMM is widely used in convex and non-convex optimization and has many applications in the field of blind image deconvolution.

[0099] In order to apply ADMM, three auxiliary variables p, q, and w are introduced. The model is rewritten as a constrained optimization problem:

[0100]

[0101] To solve the above equation, we introduce three Lagrangian multipliers λ1, λ2, and λ3, and transform it into a saddle point problem. Its augmented Lagrangian functional is:

[0102]

[0103] Where K represents the unknown blur matrix, which is a block circulant matrix formed by the point spread function k. r1, r2, and r3 are three penalty parameters.

[0104] When applying ADMM, we need to minimize five subproblems, fix other variables at each iteration, and update three Lagrange multipliers. That is, we have

[0105]

[0106] The explicit solution to the above subproblem is given below. Where superscript n is the increasing symbol of the number of iterations, n≥0;

[0107] The k-subproblem is expressed as

[0108]

[0109] Where U is a block circulant matrix formed by the image u. According to the optimality condition, the above Euler-Lagrange equation is obtained. The present invention assumes periodic boundary conditions, so the equation can be effectively solved by fast Fourier transform (FFT) to obtain

[0110]

[0111] Where F represents FFT, F -1 represents its inverse transformation. Represents the gradient operator The conjugate transpose of .

[0112] The u subproblem is expressed as

[0113]

[0114] According to its optimality condition, and then using FFT, we get the formula:

[0115]

[0116] For the p-subproblem, it is expressed as

[0117]

[0118] According to the optimality condition of the above formula, where p = [p1, p2], q = [q1, q2], λ m =[λ m1 ,λ m2 ](m=1,2). Then the corresponding linear equations are expressed as

[0119]

[0120] Obviously, the p subproblem is a smooth optimization problem. Therefore, we can obtain p from the above linear equations by simple calculation. n +1 Explicit solution of :

[0121]

[0122] The q subproblem is expressed as

[0123]

[0124] It has a closed-form solution given by the fast contraction formula

[0125]

[0126] The w subproblem is expressed as

[0127]

[0128] Similar to the q-subproblem, the solution to the w-subproblem can also be given by the fast contraction formula

[0129]

[0130] because The solution (k, u) of the model is not unique. Therefore, some constraints need to be imposed on k and u to obtain a unique reasonable solution. The present invention normalizes the estimated PSF and considers the non-negativity of the image intensity during the iteration process. Therefore, the calculation of ∫k n (x,y)dxdy=1 and

[0131]

[0132] In order to reduce the influence of noise in the estimated point spread function PSF, a dynamic threshold constraint is used to further optimize the PSF; the following formula is used:

[0133]

[0134] Where max(k n ) represents the maximum value of the n-th estimated PSF, and ξ is a small positive constant. In the experiment, ξ = 0.05 is set.

[0135] In order to demonstrate the effectiveness and superiority of the blind image deconvolution method in this invention over other blind deconvolution methods: TV-BDSB and EP-LOGG. For simplicity of representation, the proposed method is denoted as AWTV-BD. All numerical experiments are performed in the MATLAB environment using peak signal-to-noise ratio (PSNR), improved signal-to-noise ratio (ISNR) and structural similarity (SSIM) as quantitative indicators to evaluate the quality of the restoration results, which are defined as follows:

[0136]

[0137]

[0138]

[0139] Where f, I, and u represent the degraded image, original image, and restored image, respectively. M and N are the length and width of the image. μ and σ represent the local mean and standard deviation of the image, respectively. Iu is the covariance value between I and u. c1 and c2 are two constants used to prevent the denominator from approaching zero. The higher the values of PSNR, ISNR and SSIM, the better the quality of image restoration. un The relative error is defined as:

[0140]

[0141] In all experiments, when R(u n )<10 -4 Or when the number of iterations reaches 500 steps, the iteration will terminate.

[0142] exist Figure 2 In the figure, there are four test images, including a: Satellite (256×256), b: Peppers (256×256), c: Lena (256×256), and d: House (256×256). The intensities of these images are scaled to between 0 and 1. In order to obtain degraded images, the Matlab command “fspecial” is used to generate three different blur kernels, such as Figure 3 As shown, it includes a: linear motion blur (length 8 pixels, direction 45 degrees), b: Gaussian blur (size 7×7 pixels, variance 25) and c: defocus blur (radius 3 pixels). The last custom blur Figure 3 (d) is the simulated irregular motion blur, which is manually set to ([0 1 1 1 1 0 0; 1 1 0 0 0 1 0; 0 0 0 0 1 1 0; 0 0 1 1 0 0 0; 0 1 1 0 0 1 1; 0 10 0 1 1 0; 0 1 1 1 1 0 0] / 22). The blur kernel used is as follows: Figure 3 shown.

[0143] Before executing the proposed algorithm, seven parameters need to be set: α, β, ι, δ, r1, r2, and r3. α controls the weight of the image regularization term. If α is too large, the restored image will be too smooth and some image details will be lost. Conversely, if α is too small, the noise cannot be removed well. In summary, the choice of α is generally related to the degree of noise contamination of the image. When the original clear image is contaminated by high noise, a larger α should be selected. In the experiment, α ∈ [0.000001, 0.01] is set. β is the regularization term parameter of the blur kernel k and affects the spread of the PSF. If β is too large, the estimated PSF will be more diffuse. Conversely, if β is too small, the support domain of the estimated PSF will not be fully expanded. In the experiment, β ∈ [0.0001, 10] is set. Choosing appropriate values for these two parameters is crucial to obtain satisfactory blind deconvolution results.

[0144] ι is a parameter used to control local adaptivity, and δ is the standard deviation. During parameter adjustment, the choice of ι is affected by the test image and blur type. Therefore, adjustments need to be made based on specific experiments. Furthermore, δ has little effect on the PSNR of the restored image.

[0145] The three penalty parameters r1, r2, and r3 control the update of p, q, and w. Set r1∈[0.00001,10] and r2∈[0.000001,1]. To obtain the highest PSNR value, set the value of r3 to a multiple of 5.

[0146] The present invention focuses on blind deconvolution and first tests the blind deconvolution performance of AWTV-BD under low noise level. Figure 3 The four different blur kernels in are added to the test image to generate blurred images, and the blurred images are all contaminated by additive Gaussian white noise with a standard deviation of 0.001. For blind image deconvolution, it is necessary to set the support domain of the PSF. Since the true support domain size of the PSF is unknown, the size of the initial support domain of the PSF is set to be larger than the size of the true support domain but smaller than the size of the image. In the experiment, the size of the PSF support domain is set to 101×101 pixels. It can be seen from the results in Tables 1 and 2 that in most cases, the AWTV-BD proposed in the present invention can obtain the highest PSNR, ISNR and SSIM values compared with other methods. In particular, for linear motion blur, Gaussian blur and defocus blur, the PSNR and ISNR values of AWTV-BD are always the highest.

[0147] In order to intuitively evaluate the results of different methods, Figures 4 to 7 and Figures 8 to 11 The restoration results of the Satellite image and the Lena image are shown respectively, and the selected local magnified image is placed in the lower left corner. In addition, the restored blur kernel is placed in the lower right corner of the image.

[0148] from Figures 4 to 7 The restoration results of the satellite image show that the image restored by EP-L0RG loses many details and cannot achieve a satisfactory visual effect. The restored blur kernel is also very different from the original blur kernel. Fortunately, the restored blur kernel of AWTV-BD proposed in this paper is closest to the original blur kernel compared with the other two methods.

[0149] Figure 4 a is the original image under the linear motion blur test state, Figure 4 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 4 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restored image, Figure 4d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0150] Figure 5 a is the original image under Gaussian blur test state, Figure 5 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 5 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restored image, Figure 5 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0151] Figure 6 a is the original image under the defocus blur test state, Figure 6 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 6 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restored image, Figure 6 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0152] Figure 7 a is the original image in the custom fuzzy test state, Figure 7 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 7 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restored image, Figure 7 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0153] from Figures 8 to 11 As can be seen, the image restored by EP-LORG is also overly smooth, resulting in the loss of some details in the original image. Furthermore, some images obtained by TV-BDSB exhibit a noticeable stair-step effect in flat areas. The AWTV-BD proposed in the present invention, due to its use of an adaptive weighting matrix, can better preserve the local structure of the image, particularly the face and mouth corners. The restored blur kernel shows that the blur kernel restored by the AWTV-BD proposed in the present invention is closest to the original blur kernel.

[0154] Figure 8 a is the original image under the linear motion blur test state, Figure 8 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 8 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restored image, Figure 8 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0155] Figure 9 a is the original image under Gaussian blur test state, Figure 9 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 9 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restored image, Figure 9 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0156] Figure 10 a is the original image under the defocus blur test state, Figure 10 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 10 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restored image, Figure 10 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0157] Figure 11 a is the original image in the custom fuzzy test state, Figure 11 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 11 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restored image, Figure 11 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0158]

[0159] Table 1 Numerical results of blind deconvolution under Gaussian noise with a standard deviation of 0.001.

[0160]

[0161] Table 2 Numerical results of blind deconvolution under Gaussian noise with a standard deviation of 0.001.

[0162] In addition, in the case of higher noise levels, such as the Peppers image and the House image, additive Gaussian white noise with a standard deviation of 0.01 is added. The blur kernel used for image blurring is the same as in the previous experiments. As can be seen in Table 3, in most cases, the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD) still achieves the highest PSNR, ISNR, and SSIM values. In order to visually evaluate the restored image, Figures 12 to 15 The restored Peppers image is shown, where the restored blur kernel is placed in the lower right corner of the image. Figures 12 to 15It can be seen that under high noise levels, the restored image obtained by edge-preserving L0 regularized gradient prior (EP-L0RG) is also too smooth, although for Figure 15 The custom blur in , its restored blur kernel is closer to the original blur kernel.

[0163] in, Figure 12 a is the original image under the linear motion blur test state, Figure 12 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 12 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restoration image, Figure 12 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0164] Figure 13 a is the original image under Gaussian blur test state, Figure 13 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 13 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restoration image, Figure 13 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0165] Figure 14 a is the original image under the defocus blur test state, Figure 14 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 14 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restoration image, Figure 14 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0166] Figure 15 a is the original image in the custom fuzzy test state, Figure 15 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 15 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restoration image, Figure 15 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0167] from Figures 16 to 19 The restored House image shows that the over-smoothing effect produced by EP-LORG is very obvious, while the AWTV-BD proposed in this invention overcomes this problem. In addition, as can be seen from these groups of figures, the image restored by AWTV-BD is more natural compared to the other two methods.

[0168] in, Figure 16a is the original image under the linear motion blur test state, Figure 16 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 16 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restoration image, Figure 16 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0169] Figure 17 a is the original image under Gaussian blur test state, Figure 17 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 17 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restoration image, Figure 17 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0170] Figure 18 a is the original image under the defocus blur test state, Figure 18 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 18 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restoration image, Figure 18 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0171] Figure 19 a is the original image in the custom fuzzy test state, Figure 19 b is the restored image of TV regularized blind deconvolution method (TV-BDSB), Figure 19 c is the edge-preserving L0 regularized gradient prior (EP-L0RG) restoration image, Figure 19 d is the restored image using the adaptive weighted TV regularized blind image deconvolution method (AWTV-BD).

[0172]

[0173]

[0174] Table 3 Numerical results of blind deconvolution under Gaussian noise with a standard deviation of 0.01.

[0175] The present invention shows the results of non-blind image deconvolution for non-blind deconvolution, when the PSF is completely known. The non-blind deconvolution problem corresponding to the model is expressed as

[0176]

[0177] Similarly, the model of TV-BDSB non-blind deconvolution is as follows:

[0178]

[0179] Here, K is the unknown blur matrix. The two models are solved using the ADMM and split Bregman methods, respectively. These are denoted as the adaptive weighted TV regularized non-blind deconvolution model (AWTV-NBD) and the TV regularized non-blind deconvolution model (TV-NBD). In the experiment, a custom blur kernel is used to blur the original image. Additive Gaussian white noise with a standard deviation of 0.01 is added to the blurred image. Figure 20 and Figure 21 The restored Peppers image and Lena image are shown, and the locally enlarged image is also given. The first column shows the degraded image, the second column shows the restored image using the TV regularized non-blind deconvolution model (TV-NBD), and the third column shows the restored image using the adaptive weighted TV regularized non-blind deconvolution model (AWTV-NBD). As shown in Table 4, AWTV-NBD has higher PSNR and SSIM values than TV-NBD. Figure 20 and Figure 21 As can be seen from the figure, the image restored by AWTV-NBD is more natural due to the use of the adaptive weighting matrix.

[0180]

[0181] Table 4 Comparison of non-blind deconvolution methods under Gaussian noise with a standard deviation of 0.01.

[0182] This paper proposes an adaptive weighted total variation regularization method for blind image deconvolution. To better describe the local structure of the image, an adaptive weighting matrix is combined with a gradient operator. Furthermore, an efficient ADMM is used to solve the model. The proposed method can restore various types of blur. Experimental results demonstrate that this method exhibits good restoration performance for images degraded by linear motion blur, Gaussian blur, and out-of-focus blur.

[0183] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A blind image deconvolution method based on adaptive weighted TV regularization, characterized in that: The steps include: S1, a novel blind deconvolution model is formed by combining the adaptive weighting matrix with the gradient operator; Said S1 comprises: The following adaptive weighted TV model for blind image deconvolution is proposed: Where α and β are two regularization parameters used to balance the data fitting term and the regularization term, T is the adaptive weighting matrix, ▽ is the gradient operator, and the performance of ||▽k||1 is better than using ||k||1, so the L1 norm is used to constrain ▽k; S2, using the alternating direction multiplier method ADMM to solve the formed new blind deconvolution model, and perform blind image deconvolution according to the set conditions; The S2 includes: Introduce three auxiliary variables p, q, w, and The model is rewritten as a constrained optimization problem: To solve the above equation, three Lagrangian multipliers λ1, λ2, and λ3 are introduced to transform it into a saddle point problem. The augmented Lagrangian functional is: Where K represents the unknown fuzzy matrix, which is a block circulant matrix formed by the point spread function k; r1, r2 and r3 are three penalty parameters; S3, numerically evaluates the restored image through evaluation indicators, and evaluates the quality of the restored image from a visual perspective.

2. The blind image deconvolution method based on adaptive weighted TV regularization according to claim 1, characterized in that: The definition of T is as follows: Among them G δ (·) represents a two-dimensional Gaussian convolution kernel, δ and ι are two parameters, ▽ x f and ▽ y f represents the difference of f in the horizontal and vertical directions, i and j represent the horizontal and vertical coordinates of the image pixel, respectively.

3. The blind image deconvolution method based on adaptive weighted TV regularization according to claim 2, characterized in that: When applying ADMM, it is necessary to minimize the five sub-problems k, u, p, q, and w, and fix other variables at each iteration, update the three Lagrange multipliers λ1, λ2, and λ3, and obtain the following formula: The superscript n is the increasing symbol of the number of iterations, n≥0.

4. The blind image deconvolution method based on adaptive weighted TV regularization according to claim 3, characterized in that: The k-subproblem is expressed as Where U is a block circulant matrix formed by the image u. According to the optimality condition, the above Euler-Lagrange equation is obtained. The present invention assumes periodic boundary conditions, so the equation can be solved by fast Fourier transform FFT to obtain Where F represents FFT, F -1 represents its inverse transformation, ▽ T represents the conjugate transpose of the gradient operator ▽.

5. The blind image deconvolution method based on adaptive weighted TV regularization according to claim 4, characterized in that: The u subproblem is expressed as According to its optimality condition, and then using FFT, we get the formula:

6. The blind image deconvolution method based on adaptive weighted TV regularization according to claim 5, characterized in that: For the p-subproblem, it is expressed as According to the optimality condition of the above formula, where p = [p1, p2], q = [q1, q2], λ m =[λ m1 ,λ m2 ],m=1,2; then the corresponding linear equations are expressed as By simple calculation, we can get p from the above linear equations. n+1 Explicit solution of :

7. The blind image deconvolution method based on adaptive weighted TV regularization according to claim 6, characterized in that: The q subproblem is expressed as It has a closed-form solution given by the fast contraction formula The w subproblem is expressed as Similar to the q-subproblem, the solution to the w-subproblem can also be given by the fast contraction formula 8. The blind image deconvolution method based on adaptive weighted TV regularization according to claim 7, characterized in that: The S3 includes: definition: Where f, I, and u represent the degraded image, original image, and restored image, respectively; M and N are the length and width of the image; μ and σ represent the local mean and standard deviation of the image, respectively; σ Iu is the covariance value between I and u; c1 and c2 are two constants used to prevent the denominator from approaching zero; the higher the values of PSNR, ISNR and SSIM, the better the quality of image restoration; u n The relative error is defined as:

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