Image Semi-Blind Deblurring Method Based on Convolutional Total Least Squares with Deviation Correction

Abstract

The present invention discloses an image semi-blind deblurring method based on deconvolution total least squares with deviation correction, which includes selecting a regularization term based on an image blurring imaging model; constructing an image semi-blind deblurring model based on deconvolution total least squares; solving for the parameter of the potentially clear image in the image semi-blind deblurring model; performing deviation correction; if the parameters do not converge or the maximum number of iterations is not reached, then solving for the parameter of the potentially clear image in the image semi-blind deblurring model, otherwise outputting the finally restored clear image. The beneficial effect of the present invention is to restore a blurred optical image to a clear one, improve the interpretability of the image, save the observation cost, and realize the reuse of blurred image resources.

Claims

1. Image semi-blind deblurring method based on deconvolution total least squares with bias correction, Characterized in that: Including, Based on the image blur imaging model, select the regularization term; Construct an image semi-blind deblurring model based on deconvolution total least squares; Solve for the parameter of the image semi-blind deblurring model, the potential clear image; Perform bias correction; If the parameter does not converge or the maximum number of iterations is not reached, solve for the parameter of the image semi-blind deblurring model, the potential clear image, otherwise output the finally restored clear image; The construction of the image semi-blind deblurring model based on deconvolution total least squares is specifically: minΦ(I,E k ,h) = ρ(n,E k ,h) + f(I,E k ) + g(h) (3) Among them, represents the fidelity term, g(h) = λ 4 ||h|| 0 and represents the regularization term, λ 1 , λ 2 , λ 3 and λ 4 are the balance parameters of the regularization term, l [0,1] (I) represents restricting the pixel value range of the potential clear image I to be between 0 and 1.

2. The image semi-blind deblurring method based on deconvolution total least squares with bias correction according to claim 1, Characterized in that: The image blur imaging model includes, Among them, B, I, and n are respectively the blurred image, the potential clear image, and the random noise, each of m rows and s columns, and k is the blur kernel, denotes the convolution operation.

3. The image semi-blind deblurring method based on deconvolution total least squares with bias correction according to claim 2, Characterized in that: In order to deblur the image, the regularization term needs to be introduced in the image blur imaging model. The regularization term adopts a sparse prior regularization term, which includes, Regularization term 1: Gradient sparse prior of the potential clear image I; Regularization term 2: Sparse prior of the blur kernel k; Regularization term 3: Sparse prior of the DCT of the ringing effect, i.e., the Discrete Cosine Transform coefficients; Regular term 4: Joint sparse prior based on the fuzzy kernel error E k and the potential clear image I.

4. The image semi-blind deblurring method based on deconvolution total least squares with bias correction according to claim 3, Characterized in that: The regularization term 1: the gradient sparsity prior of the potential clear image I, specifically: The regularization term 2: The sparse prior of the blur kernel k is specifically that the refined blur kernel needs to satisfy two constraints: Non-negativity: All elements in the blur kernel k are non-negative, i.e., k i,j ≥ 0, Normalization: The sum of all elements in the blur kernel k is 1, that is: Σ i Σ j k i,j = 1, The constraint conditions are usually implicitly reflected through the process of kernel normalization, that is, the negative elements in the blur kernel are forced to be set to 0 and normalized to 1; The regular term 3: the DCT of the ringing effect, that is, the sparse prior of the Discrete Cosine Transform coefficients, specifically: ||h|| 0 ; The regularization term 4: based on the fuzzy kernel error E k and the joint sparse prior of the potential clear image I, specifically:

5. The image semi-blind deblurring method based on deconvolution total least squares with bias correction according to claim 4, Characterized in that: The image blur imaging model can be refined through the sparse prior of the regularization term 3 as: Among them, C and h respectively represent the DCT matrix and coefficients of the ringing effect, k represents the blur kernel estimated by the existing blind deconvolution method, and E k represents the blur kernel error.

6. The image semi-blind deblurring method based on deconvolution total least squares with bias correction according to claim 5, Characterized in that: The parameters in the image semi-blind deblurring model for solving the potential clear image are specifically: iteratively solving for I, E k and h, and the analytical expressions for the (i + 1)-th iteration process of I, E k and h, including i) I - sub - problem: Fix E k and h i and solve for I i+1 , ii) E k - Sub - problem: Fix I i+1 and h i and solve for iii) h-subproblem: Fix I i+1 and Solve for h i+1 , 7. The image semi-blind deblurring method based on deconvolution total least squares with bias correction according to claim 6, Characterized in that: The α in the I-subproblem 1 , α 2 and α 3 represent relatively large penalty parameters. and w = I, the initial values of u, v, and w are set to 0, α l = 10 -4 , κ l = 2, (l = 1, 2, 3); The j + 1-th iteration step of the I-subproblem is as follows: Step 1: I can be obtained according to Equation (7) i,j+1 , where F(g) and F -1 (g) represent the fast Fourier transform and the inverse fast Fourier transform respectively, and the symbol represents the conjugate transpose, and represent the horizontal and vertical difference operations respectively; Step 2: Obtain u according to Equation (8) j+1 , Step 3: Obtain v according to Equation (9) j+1 , Step 4: Obtain w according to Equation (10) j+1 , w j+1 = max(0, min(I i,j+1 , 1)) (10) Step 5: Update the penalty parameter α according to Equation (11) 1 , α 2 and α 3 , where κ 1 , κ 2 and κ 3 are scale factors, is the maximum threshold for α 1 , α 2 and α 3 ; The said E k－ In the sub-problem, γ 1 and γ 2 are penalty parameters, the initial value of r is set to 0, β l = 10 -4 , β max = 10 5 , δ = 2; Regarding E k－ The (j + 1)-th iteration step of the sub-problem is as follows: Step 1: It can be obtained according to Equation (12) Step 2: p can be obtained according to Equation (13) j+1 , Step 3: q can be obtained according to Equation (14) j+1 , Step 4: Update the penalty parameter γ according to Equation (15) 1 and γ 2 , Among them, τ 1 and τ 2 are scale factors to accelerate iterative convergence, is the maximum threshold for γ 1 and γ 2 ; In the h-subproblem, β is the penalty parameter, the initial values of p and q are set to 0, and γ l = 10 -4 , τ l = 2, (l = 1, 2); The j + 1-th iteration step of the h-subproblem is as follows: Step 1: h can be obtained according to Equation (16) i,j+1 , Step 2: r can be obtained according to Equation (17) j+1 , Step 3: Update the penalty parameter β according to Equation (18), β = min(δβ, β max ) (18) where δ is a scaling factor, β max is the maximum threshold of β.

8. The image semi-blind deblurring method based on deconvolution total least squares with bias correction according to claim 7, Characterized in that: The performance of bias correction is specifically: Step 1: Estimate the blur kernel error and the image using the iterative solution method, and calculate the bias term Step 2: Use TV, i.e., total variation prior or gradient sparsity prior based on L 0 norm to calculate a rough bias correction result Step 3: Use an image deblurring method based on Laplacian prior to calculate another rough deviation correction result Step 4: For the and difference of perform bilateral filtering, and subtract the result of the filtering from to obtain the final deviation correction term where and represent the deviation correction method and the corresponding deviation correction result.

9. The image semi-blind deblurring method based on deconvolution total least squares with bias correction according to any one of claims 1 to 8, Characterized in that: If the parameter does not converge or the maximum number of iterations is not reached, solve for the parameter of the image semi-blind deblurring model, the potential clear image, otherwise output the finally restored clear image, specifically: Calculate the relative error ρ; if ρ > tol or i < MaxIter, then solve for the parameter of the image semi-blind deblurring model, the potential clear image, otherwise output the final result I.

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