CN105957025A - Inconsistent image blind restoration method based on sparse representation - Google Patents

Abstract

The invention discloses an inconsistent image blind restoration method based on sparse representation. The method comprises steps of: creating an inconsistent image fuzzy degeneration model depending on a camera three-dimensional shaking model in combination with over-complete dictionary representation of a natural image; inputting a fuzzy image to be restored and an over-complete dictionary to solve an initial sparse coefficient and initializing a parameter; using the over-complete dictionary representation of the natural image sparsity of the fuzzy core and sparse coefficient as the regular constraint of the model, and transforming the resolution of the inconsistent blind image restoration model into multiple simple subproblems by using an alternate iteration method so as to achieve blind restoration of the fuzzy image y. The method has better restoration effect on the fuzzy image acquired on natural condition, achieves restored images with clear details, no distortion, and low noise, has better visual effects and extendibility.

Description

Non-uniform method for blindly restoring image based on rarefaction representation

Technical field

The present invention relates to a kind of Computer Image Processing method, especially relate to a kind of image recovery method.

Background technology

Imaging device is when gathering image, artificial shake or the intrinsic mechanical shaking of equipment can make the image collected the problems such as overall fuzzy, indefinite, the detailed information forfeiture in target object border occur, bring the biggest problem to the application of the computer vision fields such as topographic(al) reconnaissance, target recognition, self-navigation.Therefore, blur image restoration becomes popular problem urgently to be resolved hurrily.The blind recovery of existing broad image is the most globally consistent according to fuzzy core, can be divided into the blind recovery of coherent image and non-uniform blindly restoring image.It practice, the shake that camera is in three dimensions, that can cause in imaging plane is non-uniform fuzzy, therefore, and non-uniform blindly restoring image more practicality.

By studying the model space geometric of camera shake, Whyte O et al.^[1]Non-uniform broad image degradation model in constructing plane.Due to the complexity of natural image, the fuzzy core estimated from single image according to this model is likely to exist bigger error in subregion.By natural image gradient heavytailed distribution feature^[2]Standardization sparse with fuzzy core^[3]Regularization method as priori is the typical method solving the problems referred to above, but the method is inadequate to the punishment dynamics of flat site, and norm constraint is difficult to approach completely the heavytailed distribution of gradient, is easily generated ring, and recovery effect is undesirable.

[list of references]

[1]Whyte O,Sivic J,Zisserman A,et al.Non-uniform Deblurring for Shaken Images.International Journal of Computer Vision,2012,98(2):168-186.

[2]Fergus R,Singh B,Hertzmann A,et al.Removing camera shake from a single photograph.Acm Transactions on Graphics,2006,25(3):787-794.

[3]Krishnan D,Fergus R.Fast Image Deconvolution using Hyper-Laplacian.Proceedings of Neural Information Processing Systems,2009:1033-1041.

[4] Yang Aiping, clock soars, He Yuqing. the super-resolution rebuilding of dictionary learning is coupled based on non local similarity and classification half. and University Of Tianjin's journal: natural science and engineering version, 2015,1 (01): 87-94.

[5] Cheng Guangtao, Song Zhanjie, old snow. rarefaction representation sorting technique based on two dimensional image matrix. University Of Tianjin's journal: natural science and engineering version, 2014,47 (06): 541-545.

[6]Levin A,Weiss Y,Durand F,et al.Efficient Marginal Likelihood Optimization in Blind Deconvolution.In:Colorado Springs.Proceeding of Computer Vision and Pattern Recognition,2011:2657-2664.

[7]Babacan S D,Molina R,Do M N,et al.Bayesian Blind Deconvolution with General Sparse Image Priors.Computer Vision,Springer Berlin Heidelberg,2012:341-355.

[8]Hu Z,Huang J B,Yang M H.Single image deblurring with adaptive dictionary learning. In:Hongkong.Proceeding of IEEE International Conference on Image Processing,2010:1169-1172.

[9]Yangyang X,Wotao Y.A fast patch-dictionary method for whole image recovery.CAM-report-13-38[R].Los Angeles,CA:UCLA,Applied Mathematics,2013.

[10]Aharon M,Elad M,Bruckstein A.K-SVD:An algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Transactions on Signal Processing,2006,54(11):4311–4322.

[11]Daubechies I,Defrise M,Mol C.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.Communications on Pure and Applied Mathematics,1988,57(11):1413–1457.

[12]Zhang Y,Yang J,Wotao Y.YALL1:Your algorithms for l1,MATLAB software,http://yall1.blogs.rice.edu/,2010.

Summary of the invention

For the problems referred to above, the present invention proposes a kind of non-uniform method for blindly restoring image based on rarefaction representation.According to non-uniform image blurring degradation model, set up total variation regularization model, and complete for the mistake of natural image dictionary is represented^[4,5], natural image cross complete dictionary represent under sparse characteristic and fuzzy core sparse characteristic as canonical bound term.The non-uniform smear restoration model built, can more accurately ambiguous estimation core, improve image restoration quality；The complete dictionary of mistake of unified with nature image represents and openness prior information, makes restored image more meet the feature of natural image, reduces distortion.

In order to solve above-mentioned technical problem, a kind of based on rarefaction representation the non-uniform method for blindly restoring image that the present invention proposes, comprise the following steps:

Step one, structure blindly restoring image model, including:

1-1) shake model according to camera three-dimensional, the non-uniform image blurring degradation model shown in structure formula (1):

$y=\underset{k}{\mathrm{\Σ}}{w}_k\left(\underset{j}{\mathrm{\Σ}}{C}_{ijk}{x}_j\right)+\mathrm{\ϵ}---\left(1\right)$

In formula (1), y is broad image, and x is original picture rich in detail, and ε is additive noise,Represent that picture rich in detail is θ at deviation angle_kTime migrated image；Deviation angle is θ_kTime, the pixel value x at picture rich in detail pixel j_jAt C_ijkEffect under correspond at the pixel i of broad image；w_kBe deviation angle be θ_kTime weights, referred to as fuzzy core；

When fuzzy core or picture rich in detail are known, model representation shown in formula (1) is following two linear models:

Y=∑_kC_ijkw_kx+ε

(2)

Y=∑_jC_ijkx_jw+ε

(3)

Cross complete dictionary shown to the rarefaction representation such as formula (4) of image:

$x=\underset{i}{\mathrm{\Σ}}{R}_i^T\left({\mathrm{D\α}}_i\right)---\left(4\right)$

In formula (4), R_iBeing the matrix manipulation symbol extracting image i-th image block, D was complete dictionary, α_iIt is that i-th image block is at the rarefaction representation coefficient crossed under complete dictionary represents；

1-2) according to the non-uniform blur degradation model of above-mentioned structure, and the complete dictionary of mistake of unified with nature image represents, the image restoration model shown in structure formula (5):

$\begin{array}{c}\{\hat{x},\hat{k}\}=\arg \min \left|\right|{\mathrm{\Σ}}_k{C}_{ijk}{w}_{k}x-y|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i||R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\λ}}_i\left|\right|{\mathrm{\α}}_i|{|}_1\\ \begin{array}{cccc}+{\mathrm{\γ}}_i\left|\right|w|{|}_1& s.t.& \left|\right|w|{|}_2=1,& w\≥0\end{array}\end{array}---\left(5\right)$

In formula (5), Section 1 is the data fidelity item constructed by non-uniform fuzzy model；Section 2 and Section 3 were that complete dictionary represents and sparse coefficient α respectively_iRegularization constraint item；Section 4 is fuzzy core constraint；Wherein, fuzzy core w has sparse characteristic, meets normalization and nonnegativity, uses l₁This fuzzy core w is retrained by norm；η(η_i)、λ(λ_i) and γ (γ_i) it is balance parameters, η (η_i)=0.05, λ (λ_i)=0.1, γ (γ_i) span be 4.0～5.5；Original picture rich in detail x and broad image y was the vector form of complete dictionary D arrangement；

Step 2, the broad image y of input parked and complete dictionary D excessively, wherein, crossing complete dictionary D is to use block neighborhood gradient dictionary learning method that 200 width images in Berkeley segmentation dataset data base extract 20000 8 × 8 pixel image blocks at random to carry out adaptive learning and obtain；

Step 3, employing alternating iteration method carry out blind recovery to the broad image y of parked, including:

3-1) first iteration time, sparse coefficient α byObtain, and set the original picture rich in detail x broad image y as input；

3-2) according to sparse coefficient α and original picture rich in detail x ambiguous estimation core w, above-mentioned formula (5) is reduced to:

$\begin{array}{c}\hat{w}=\underset{w}{\mathrm{argmin}}\left|\right|{\mathrm{\Σ}}_k{C}_{ijk}{w}_{k}x-y|{|}_2^2+{\mathrm{\γ}}_i|\left|w\right|{|}_1\\ \begin{array}{ccc}s.t.& \left|\right|w|{|}_2=1,& w\≥0\end{array}\end{array}---\left(6\right)$

And use iterative shrinkage soft-threshold algorithm ambiguous estimation core w；

3-3) estimate original picture rich in detail x according to fuzzy core w and sparse coefficient α, broad image y be decomposed into multiple different overlapping block, each overlapping block is estimated, and the operation of original picture rich in detail x, above-mentioned formula (5) are reduced to:

$\hat{x}=\left|\right|Ax-y|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i||R_{i}x-{\mathrm{D\α}}_i|{|}_2^2---\left(7\right)$

In formula (7), A=∑_kC_ijkw_k, utilize fast fourier transform algorithm to estimate original picture rich in detail x；

3-4) estimating sparse coefficient α according to original picture rich in detail x and fuzzy core w, above-mentioned formula (5) is reduced to:

${\widehat{\mathrm{\α}}}_i=\underset{\mathrm{\α}}{\mathrm{argmin}}\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i\left|\right|R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\λ}}_i||{\mathrm{\ω}}_i*{\mathrm{\α}}_i|{|}_1---\left(8\right)$

In formula (8), Part II is l₁The weighted optimization form of norm, weights ω_iUse sparse coefficient inverse function form；It is separate owing to crossing in complete dictionary method between each image block, therefore, formula (8) is reduced to formula (9), thus the Solve problems of original picture rich in detail x sparse coefficient is converted into the Solve problems of the sparse coefficient of each image block

${\widehat{\mathrm{\α}}}_i=\underset{\mathrm{\α}}{\mathrm{argmin}}{\mathrm{\η}}_i\left|\right|R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+{\mathrm{\λ}}_i||{\mathrm{\ω}}_i*{\mathrm{\α}}_i|{|}_1---\left(9\right)$

YALL1 algorithm is used to estimate sparse coefficient α；

3-5) when iterations is less than 2, return step 3-2)；Otherwise, step 3-6 is performed)；

3-6) calculate the squared difference between fuzzy core w that adjacent twice iteration is tried to achieve poor, if the value of this squared difference difference is less than 10^-4, then stop iteration, the image of output is original picture rich in detail x, otherwise returns step 3-2).

Compared with prior art, the invention has the beneficial effects as follows:

The present invention complete dictionary of mistake based on image non-uniform blur degradation model and image represents, set up non-uniform fuzzy restoration model, complete for the mistake of natural image dictionary is represented, and the openness canonical as model of fuzzy core and sparse coefficient retrains, and alternating iteration is used to ask the method for unknown quantity to solve.The algorithm that the present invention proposes has more preferable recovery effect to the broad image obtained under natural conditions, and restored image details is obvious, undistorted, noise is low, has more preferable visual effect, and method for solving has extensibility.

Accompanying drawing explanation

Fig. 1 is the present invention non-uniform method for blindly restoring image flow chart based on rarefaction representation；

Fig. 2 (a) is a width " figure of buddha " real scene shooting broad image；

Fig. 2 (b) is the result utilizing Levin algorithm to real scene shooting blur image restoration shown in Fig. 2 (a)；

Fig. 2 (c) is the result utilizing Babacan algorithm to real scene shooting blur image restoration shown in Fig. 2 (a)；

Fig. 2 (d) is the result utilizing Hu algorithm to real scene shooting blur image restoration shown in Fig. 2 (a)；

Fig. 2 (e) is the inventive method result to real scene shooting blur image restoration shown in Fig. 2 (a)；

Fig. 3 (a) is a width " fish " real scene shooting broad image；

Fig. 3 (b) is the result utilizing Levin algorithm to real scene shooting blur image restoration shown in Fig. 3 (a)；

Fig. 3 (c) is the result utilizing Babacan algorithm to real scene shooting blur image restoration shown in Fig. 3 (a)；

Fig. 3 (d) is the result utilizing Hu algorithm to real scene shooting blur image restoration shown in Fig. 3 (a)；

Fig. 3 (e) is the inventive method result to real scene shooting blur image restoration shown in Fig. 3 (a).

Detailed description of the invention

For verifying the effectiveness of method for blindly restoring image of the present invention, choose " figure of buddha " and " fish " two width real scene shooting broad image below as specific embodiment, carrying out blind recovery under Matlab platform to test, simultaneously more ripe with the prior art blind restoration algorithm of single image (includes the spatial domain restored method of Levin and Babacan^[6,7], and the sparse territory restored method of Hu^[8]) compare.The present invention is only explained, not in order to limit the present invention by described specific embodiment.

Embodiment 1:

As a example by Fig. 2 (a) " figure of buddha ", a kind of based on rarefaction representation the non-uniform method for blindly restoring image using the present invention to propose restores, thus obtains the original picture rich in detail after recovery, as shown in Fig. 2 (e).As it is shown in figure 1, its processing procedure comprises the following steps:

Step one, structure blindly restoring image model, including:

Model is shaken, the non-uniform image blurring degradation model shown in structure formula (1) according to camera three-dimensional:

$y=\underset{k}{\mathrm{\Σ}}{w}_k\left(\underset{j}{\mathrm{\Σ}}{C}_{ijk}{x}_j\right)+\mathrm{\ϵ}---\left(1\right)$

In formula (1), y is broad image, and x is original picture rich in detail, and ε is additive noise,Represent that picture rich in detail is θ at deviation angle_kTime migrated image；Deviation angle is θ_kTime, the pixel value x at picture rich in detail pixel j_jAt C_ijkEffect under correspond at the pixel i of broad image；w_kBe deviation angle be θ_kTime weights, referred to as fuzzy core；I.e. this model representation broad image be under different angles the weighting of migrated image tired and.

When fuzzy core or picture rich in detail are known, model representation shown in formula (1) is following two linear models:

Y=∑_kC_ijkw_kx+ε

(2)

Y=∑_jC_ijkx_jw+ε

(3)

Cross complete dictionary shown to the rarefaction representation such as formula (4) of image:

$x=\underset{i}{\mathrm{\Σ}}{R}_i^T\left({\mathrm{D\α}}_i\right)---\left(4\right)$

In formula (4), R_iBeing the matrix manipulation symbol extracting image i-th image block, D was complete dictionary, α_iIt is that i-th image block is at the rarefaction representation coefficient crossed under complete dictionary represents；

1-2) according to the non-uniform blur degradation model of above-mentioned structure, and the complete dictionary of mistake of unified with nature image represents, the image restoration model shown in structure formula (5):

$\begin{array}{c}\{\hat{x},\hat{k}\}=\arg \min \left|\right|{\mathrm{\Σ}}_k{C}_{ijk}{w}_{k}x-y|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i||R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\λ}}_i\left|\right|{\mathrm{\α}}_i|{|}_1\\ \begin{array}{cccc}+{\mathrm{\γ}}_i\left|\right|w|{|}_1& s.t.& \left|\right|w|{|}_2=1,& w\≥0\end{array}\end{array}---\left(5\right)$

In formula (5), Section 1 is the data fidelity item constructed by non-uniform fuzzy model；Section 2 and Section 3 were that complete dictionary represents and sparse coefficient vector α respectively_iRegularization constraint item；Section 4 is fuzzy core constraint；Wherein, fuzzy core w has sparse characteristic, uses l₁This fuzzy core w is retrained by norm, and meanwhile, fuzzy core w meets normalization and nonnegativity；η(η_i)、λ(λ_i) and γ (γ_i) it is balance parameters, η (η_i)=0.05, λ (λ_i)=0.1, γ (γ_i) span be 4.0～5.5, γ (γ in the present embodiment_i)=4.6；Original picture rich in detail x and broad image y was the vector form of complete dictionary D arrangement；

Step 2, the broad image y of input parked, as shown in Fig. 2 (a), and cross complete dictionary D, and wherein, crossing complete dictionary D is to use block neighborhood gradient dictionary learning method^[9]To Berkeley segmentation dataset^[10]200 width images in data base extract 20000 8 × 8 pixel image blocks at random and carry out what adaptive learning obtained；

Step 3, due in the non-uniform blind restoration model formula (5) that builds in the present invention, containing fuzzy core w, original picture rich in detail x and sparse coefficient α_iThree unknown quantitys, directly it being solved existence convergence and slowly and be easily trapped into the problems such as local optimum, therefore, the present invention uses alternating iteration method that solving of non-uniform blind restoration model is converted into multiple simple subproblem, thus realize the blind recovery to broad image y, detailed process includes:

3-1) first iteration time, sparse coefficient α byObtaining, original picture rich in detail x is set to the broad image y of input；

3-2) according to sparse coefficient α and original picture rich in detail x ambiguous estimation core w, above-mentioned formula (5) is reduced to:

$\begin{array}{c}\hat{w}=\underset{w}{\mathrm{argmin}}\left|\right|{\mathrm{\Σ}}_k{C}_{ijk}{w}_{k}x-y|{|}_2^2+{\mathrm{\γ}}_i|\left|w\right|{|}_1\\ \begin{array}{ccc}s.t.& \left|\right|w|{|}_2=1,& w\≥0\end{array}\end{array}---\left(6\right)$

This is that typical least square problem combines non-negative l₁The problem of norm, can use iterative shrinkage soft-threshold (Iterative Shrinkage-Thresholding Algorithm, ISTA)^[11]Algorithm solves, thus ambiguous estimation core w；

3-3) estimate original picture rich in detail x according to fuzzy core w and sparse coefficient α, broad image y be decomposed into multiple different overlapping block, each overlapping block is estimated, and the operation of original picture rich in detail x, above-mentioned formula (5) are reduced to:

$\hat{x}=\left|\right|Ax-y|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i||R_{i}x-{\mathrm{D\α}}_i|{|}_2^2---\left(7\right)$

In formula (7), A=∑_kC_ijkw_k, formula (7) is typical least square problem, utilizes fast fourier transform algorithm to estimate original picture rich in detail x；

3-4) estimating sparse coefficient α according to original picture rich in detail x and fuzzy core w, above-mentioned formula (5) is reduced to:

${\widehat{\mathrm{\α}}}_i=\underset{\mathrm{\α}}{\mathrm{argmin}}\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i\left|\right|R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\λ}}_i||{\mathrm{\ω}}_i*{\mathrm{\α}}_i|{|}_1---\left(8\right)$

In formula (8), Part II is l₁The weighted optimization form of norm, weights ω_iUse sparse coefficient inverse function form；It is separate owing to crossing in complete dictionary method between each image block, therefore, formula (8) is reduced to formula (9), thus the Solve problems of original picture rich in detail x sparse coefficient is converted into the Solve problems of the sparse coefficient of each image block

${\widehat{\mathrm{\α}}}_i=\underset{\mathrm{\α}}{\mathrm{argmin}}{\mathrm{\η}}_i\left|\right|R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+{\mathrm{\λ}}_i||{\mathrm{\ω}}_i*{\mathrm{\α}}_i|{|}_1---\left(9\right)$

Use YALL1^[12]Algorithm estimates sparse coefficient α；

3-5) when iterations is less than 2, return step 3-2)；Otherwise, step 3-6 is performed)；

3-6) calculate the squared difference between fuzzy core w that adjacent twice iteration is tried to achieve poor, if the value of this squared difference difference is less than 10^-4, then stop iteration, the image of output is original picture rich in detail x, otherwise returns step 3-2).

Fig. 2 (b) to Fig. 2 (e) is the result utilizing art methods and the inventive method to restore " figure of buddha " real scene shooting broad image Fig. 2 (a) Suo Shi respectively, can be seen that, what Fig. 2 (b) illustrated utilizes the restoration result of Levin algorithm to have obvious distortion, figure of buddha body contour is the most sharp-pointed, the restoration result of what Fig. 2 (c) illustrated utilize Babacan algorithm is the fuzzyyest, the recovery effect of what Fig. 2 (d) illustrated utilize Hu algorithm is the most undesirable, there are serious distortion and noise, and the result of the inventive method recovery as shown in Fig. 2 (e) is preferable, details is clear, whole structure natural reality.

Embodiment 2:

In like manner, as a example by Fig. 3 (a) " fish ", a kind of based on rarefaction representation the non-uniform method for blindly restoring image using the present invention to propose restores, thus obtains the original picture rich in detail after recovery, as shown in Fig. 3 (e).Fig. 3 (b) to Fig. 3 (d) is the restoration result utilizing art methods.Can be seen that, the restoration result distortion of what Fig. 3 (b) illustrated utilize Levin algorithm is obvious, back fin deformity, the restoration result of what Fig. 3 (c) illustrated utilize Babacan algorithm is preferable, what Fig. 3 (d) illustrated utilizes the restoration result noise of Hu algorithm substantially, and detailed information is lost, and inventive algorithm restoration result as shown in Fig. 3 (e) is preferable, it can be seen that fin and the texture of rope cloth, whole structure is natural.In a word, the recovery of natural broad image is had a clear superiority in by inventive algorithm.

To sum up, the algorithm that the present invention proposes has more preferable recovery effect to the broad image obtained under natural conditions, and restored image details is obvious, undistorted, noise is low, has more preferable visual effect, and method for solving has extensibility.

Although above in conjunction with accompanying drawing, invention has been described; but the invention is not limited in above-mentioned detailed description of the invention; above-mentioned detailed description of the invention is only schematically; rather than it is restrictive; those of ordinary skill in the art is under the enlightenment of the present invention; without deviating from the spirit of the invention, it is also possible to make many variations, within these belong to the protection of the present invention.

Claims (1)

1. a non-uniform method for blindly restoring image based on rarefaction representation, comprises the following steps:

Step one, structure blindly restoring image model, including:

1-1) shake model according to camera three-dimensional, the non-uniform image blurring degradation model shown in structure formula (1):

$y=\underset{k}{\mathrm{\Σ}}{w}_k\left(\underset{j}{\mathrm{\Σ}}{C}_{ijk}{x}_j\right)+\mathrm{\ϵ}---\left(1\right)$

In formula (1), y is broad image, and x is original picture rich in detail, and ε is additive noise,Represent picture rich in detail It is θ at deviation angle_kTime migrated image；Deviation angle is θ_kTime, the pixel value x at picture rich in detail pixel j_jAt C_ijk's Correspond under effect at the pixel i of broad image；w_kBe deviation angle be θ_kTime weights, referred to as fuzzy core；

When fuzzy core or picture rich in detail are known, model representation shown in formula (1) is following two linear models:

Y=∑_kC_ijkw_kx+ε (2)

Y=∑_jC_ijkx_jw+ε (3)

Cross complete dictionary shown to the rarefaction representation such as formula (4) of image:

$x=\underset{i}{\mathrm{\Σ}}{R}_i^T\left({\mathrm{D\α}}_i\right)---\left(4\right)$

In formula (4), R_iBeing the matrix manipulation symbol extracting image i-th image block, D was complete dictionary, α_iIt it is i-th figure As block is at the rarefaction representation coefficient crossed under complete dictionary represents；

1-2) according to the non-uniform blur degradation model of above-mentioned structure, and the complete dictionary of mistake of unified with nature image represents, builds Image restoration model shown in formula (5):

$\begin{array}{c}\{\hat{x},\hat{k}\}=\arg \min \left|\right|{\mathrm{\Σ}}_k{C}_{ijk}{w}_{k}x-y|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i||R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\λ}}_i\left|\right|{\mathrm{\α}}_i|{|}_1\\ \begin{array}{cccc}+{\mathrm{\γ}}_i\left|\right|w|{|}_1& s.t.& \left|\right|w|{|}_2=1,& w\≥0\end{array}\end{array}---\left(5\right)$

In formula (5), Section 1 is the data fidelity item constructed by non-uniform fuzzy model；Section 2 and Section 3 were respectively Complete dictionary represents and sparse coefficient α_iRegularization constraint item；Section 4 is fuzzy core constraint；Wherein, fuzzy core w has Sparse characteristic, meets normalization and nonnegativity, uses l₁This fuzzy core w is retrained by norm；η(η_i)、λ(λ_i) and γ (γ_i) For balance parameters, η (η_i)=0.05, λ (λ_i)=0.1, γ (γ_i) span be 4.0～5.5；Original picture rich in detail x and mould Stick with paste image y and be the vector form of complete dictionary D arrangement；

Step 2, the broad image y of input parked and complete dictionary D excessively, wherein, crossing complete dictionary D is to use block neighborhood 200 width images in Berkeley segmentation dataset data base are extracted 20000 by gradient dictionary learning method at random 8 × 8 pixel image blocks carry out what adaptive learning obtained；

Step 3, employing alternating iteration method carry out blind recovery to the broad image y of parked, including:

3-1) first iteration time, sparse coefficient α is by min | | α | |₀ s.t.Obtain, and set original picture rich in detail x Broad image y for input；

3-2) according to sparse coefficient α and original picture rich in detail x ambiguous estimation core w, above-mentioned formula (5) is reduced to:

$\begin{array}{c}\hat{w}=\underset{w}{\mathrm{argmin}}\left|\right|{\mathrm{\Σ}}_k{C}_{ijk}{w}_{k}x-y|{|}_2^2+{\mathrm{\γ}}_i|\left|w\right|{|}_1\\ \begin{array}{ccc}s.t.& \left|\right|w|{|}_2=1,& w\≥0\end{array}\end{array}---\left(6\right)$

And use iterative shrinkage soft-threshold algorithm ambiguous estimation core w；

3-3) estimate original picture rich in detail x according to fuzzy core w and sparse coefficient α, broad image y is decomposed into multiple difference Overlapping block, each overlapping block is estimated, and the operation of original picture rich in detail x, above-mentioned formula (5) are reduced to:

$\hat{x}=\left|\right|Ax-y|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i||R_{i}x-{\mathrm{D\α}}_i|{|}_2^2---\left(7\right)$

In formula (7), A=∑_kC_ijkw_k, utilize fast fourier transform algorithm to estimate original picture rich in detail x；

3-4) estimating sparse coefficient α according to original picture rich in detail x and fuzzy core w, above-mentioned formula (5) is reduced to:

${\widehat{\mathrm{\α}}}_i=\underset{\mathrm{\α}}{\mathrm{argmin}}\underset{i=1}{\mathrm{\Σ}}{\mathrm{\η}}_i\left|\right|R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+\underset{i=1}{\mathrm{\Σ}}{\mathrm{\λ}}_i||{\mathrm{\ω}}_i*{\mathrm{\α}}_i|{|}_1---\left(8\right)$

In formula (8), Part II is l₁The weighted optimization form of norm, weights ω_iUse sparse coefficient inverse function form；By It is separate in crossing in complete dictionary method between each image block, therefore, formula (8) is reduced to formula (9), thus The Solve problems of original picture rich in detail x sparse coefficient is converted into the Solve problems of the sparse coefficient of each image block,

${\widehat{\mathrm{\α}}}_i=\underset{\mathrm{\α}}{\mathrm{argmin}}{\mathrm{\η}}_i\left|\right|R_{i}x-{\mathrm{D\α}}_i|{|}_2^2+{\mathrm{\λ}}_i||{\mathrm{\ω}}_i*{\mathrm{\α}}_i|{|}_1---\left(9\right)$

YALL1 algorithm is used to estimate sparse coefficient α；

3-5) when iterations is less than 2, return step 3-2)；Otherwise, step 3-6 is performed)；

3-6) calculate the squared difference between fuzzy core w that adjacent twice iteration is tried to achieve poor, if the value of this squared difference difference is less than 10^-4, then stop iteration, the image of output is original picture rich in detail x, otherwise returns step 3-2).