CN102354395B - Sparse representation-based blind restoration method of broad image - Google Patents

Abstract

The invention relates to a sparse representation-based blind restoration method of a broad image, aiming at solving the technical problem that an image restored by the existing broad image blind restoration method is bad in effect. The method has the technical scheme that the broad image is sparsely represented by a fuzzy dictionary and a brilliant image is rebuilt by a brilliant dictionary to restore the image due to the characteristic that the sparse coefficient of the broad image under the fuzzy redundancy dictionary is coincident with that of the brilliant image under the brilliant redundancy dictionary. The illcondition during deconvolution can be avoided, the ringing effect at a high edge during image restoration can be reduced, and the image which is more brilliant can be obtained.

Description

Blurred picture blind restoration method based on rarefaction representation

Technical field

The present invention relates to a kind of blurred picture blind restoration method, specifically is a kind of blurred picture blind restoration method based on rarefaction representation.

Background technology

Document " based on the regularization Blind image restoration algorithm of wavelet transformation; optical precision engineering; 2007; Vol15 (4); p582-586 " discloses a kind of regularization Blind image restoration algorithm based on wavelet transformation, this method combines wavelet transformation and adaptive regularization method, earlier the image after degenerating is carried out wavelet decomposition, obtains image in the information of different frequency sub-band; At frequency and the directivity characteristics of image in each frequency sub-band, use different adaptive regularization restored methods then, carry out deblurring at the low frequency frequency sub-band of image; The high frequency frequency sub-band then suppresses noise and protects edge feature; Image after obtaining restoring by wavelet inverse transformation at last.Wavelet decomposition makes the view data that participates in iterative computation diminish, and has reduced calculated amount to a certain extent, has improved algorithm performance; In addition, increase small echo in the experimentation except making an uproar process, overcome former algorithm to the shortcoming of noise-sensitive.But the described method of document is based on the deconvolution principle and goes to carry out image restoration, because the pathosis of deconvolution problem causes net result to produce ringing effect at strong edge easily, has a strong impact on the final recovery effect of image.

Summary of the invention

In order to solve the technical matters of existing blurred picture blind restoration method restored image weak effect, the invention provides a kind of blurred picture blind restoration method based on rarefaction representation.This method utilizes blurred picture in the characteristic consistent with the sparse coefficient of picture rich in detail under clear redundant dictionary of the sparse coefficient under the Fuzzy Redundancy dictionary, with blurred picture rarefaction representation under fuzzy dictionary, reconstructing restored image under the picture rich in detail under the clear dictionary then, can avoid the pathosis in the deconvolution process, restored image can be reduced in the ringing effect at strong edge, distinct image more can be obtained.

Technical scheme of the present invention is: a kind of blurred picture blind restoration method based on rarefaction representation is characterized in comprising the steps:

(a) from the picture rich in detail similar to the parked picture material, stochastic sampling is selected a large amount of image blocks, passes through from image block

$\underset{D,\mathrm{\α}}{\min }{\left|\right|X-D*\mathrm{\α}\left|\right|}_2^{2}s.t.{\left|\right|{\mathrm{\α}}_i\left|\right|}_0\≤T---\left(1\right)$

Train clear redundant dictionary.By bringing in constant renewal in dictionary, make the expression of all images piece under redundant dictionary of sampling satisfy the constraint of certain degree of rarefication.

In the formula, the image block of X for selecting at random, D is dictionary to be trained, α is the sparse coefficient vector of image block, α _iBe the sparse coefficient of i image block correspondence, wherein,

T is that image block is in the constraint that trains the sparse coefficient under the dictionary.

(b) objective function optimization is found the solution:

$\underset{x_h,h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+\frac{{\left|\right|x_h\left|\right|}_1}{{\left|\right|x_h\left|\right|}_2}+v{\left|\right|h\left|\right|}_1---\left(2\right)$

$\mathrm{Fy}=\left[\begin{array}{c}{F}_1*y\\ F_2*y\end{array}\right]---\left(3\right)$

In the formula, λ, ν are regularization parameter, and y is blurred picture, x _hBe the high fdrequency component of waiting to estimate picture rich in detail, h is point spread function to be estimated, F is the high fdrequency component that bank of filters is used to extract image, F ₁Be [1 ,-1], F ₂Be [1 ,-1] ^T, * is convolution operation.Formula has x in (2) _hWith two unknown quantitys of h, by the alternately method calculating of iteration.

(1) initialization h.

(2) fixing h by the formula of minimizing (4), estimates x _h

$\underset{x_h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+\frac{{\left|\right|x_h\left|\right|}_1}{{\left|\right|x_h\left|\right|}_2}---\left(4\right)$

(3) fixing x _h, by the formula of minimizing (5), estimate h

$\underset{h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+v{\left|\right|h\left|\right|}_1---\left(5\right)$

Repeating step (2), (3), the point spread function h that obtains estimating.

(c) for each the atom image block in the clear dictionary, the atom image block is extended to the new image block of three times of sizes of atom image block by the mode of symmetry expansion, the point spread function estimated of convolution then, the blurred picture piece of three times of sizes of atom image block; In the middle of taking out from the blurred picture piece and the image block corresponding size of clear dictionary deduct its average with each image block in the clear dictionary, the clear dictionary D of acquisition high frequency as atom image block corresponding in the fuzzy dictionary _h

(d) blurred picture is resolved into stacked image block mutually, identical according to picture rich in detail blurred picture sparse coefficient under fuzzy dictionary under the sparse coefficient under the clear dictionary, carry out rarefaction representation for each blurred picture piece under fuzzy dictionary, concrete steps are as follows:

(1) based on the orthogonal matching pursuit algorithm, according to formula

min||α _i|| ₀s.t.||y _i-D _blurα _i|| ₂≤ε (6)

Calculate i blurred picture piece y _iAt fuzzy dictionary D _BlurUnder sparse factor alpha _iIn the formula, ε is the error behind the rarefaction representation.

(2) use sparse factor alpha _iReconstruct picture rich in detail piece x on the clear dictionary of high frequency _iHFS x ' _i,

x′ _i＝D _hα _i (7)

(3) adopt following formula

$x_i^{\′}=x_i^{\′}\frac{\mathrm{Var}\left(x_i^{\′}\right)}{{\left|\right|x_i^{\′}\left|\right|}_2}---\left(8\right)$

To x ' _iCarry out variance correction, in the formula, || x ' _i|| ₂Be x ' _iTwo norms, x ' _iBe by a series of Var (x ' _i) be the variance yields after to be corrected, provided by formula (9), Var (x ' _i) be blurred picture piece y _iVariance during divided by the image block rarefaction representation dictionary corresponding variance promote and compare r _jAverage, r _jProvided by formula (10):

$\mathrm{Var}\left(x_i^{\′}\right)=\frac{\mathrm{Var}\left(y_i\right)}{\mathrm{mean}\left(\underset{{\mathrm{\α}}_{\mathrm{ij}}\≠0}{\mathrm{\Σ}}{r}_j\right)}---\left(9\right)$

$r_j=\frac{\mathrm{Var}\left(D_{{\mathrm{blur}}_j}\right)}{\mathrm{Var}\left(D_{h_j}\right)}---\left(10\right)$

In the formula,

With

Be respectively D _BlurAnd D _hJ atom image block.

(4) will proofread and correct x ' later _iAdd blurred picture piece y _iAverage, just obtained blurred picture piece y _iCorresponding picture rich in detail piece x _i

x _i＝x′ _i+mean(y _i) (11)

At x _sOn and y _iCorrespondence position adds picture rich in detail piece x _i, simultaneously, at x _wGo up and y _iCorrespondence position adds 1.At last, with x _sDivided by x _wObtain whole distinct image:

$x=\frac{x_s}{x_w}---\left(12\right).$

The invention has the beneficial effects as follows: owing to utilize blurred picture in the characteristic consistent with the sparse coefficient of picture rich in detail under clear redundant dictionary of the sparse coefficient under the Fuzzy Redundancy dictionary, with blurred picture rarefaction representation under fuzzy dictionary, reconstructing restored image under the picture rich in detail under the clear dictionary then, avoided the pathosis in the deconvolution process, reduce the ringing effect of restored image at strong edge, obtained distinct image more.

Below in conjunction with embodiment the present invention is elaborated.

Embodiment

1. clear redundant dictionary training.

Stochastic sampling goes out 50000 9 * 9 image block from 100 width of cloth pictures rich in detail identical with the parked image definition, trains clear redundant dictionary from the image block of sampling.By bringing in constant renewal in dictionary, make the expression of all images piece under redundant dictionary of sampling satisfy the requirement of certain degree of rarefication, train by optimizing following formula:

$\underset{D,\mathrm{\α}}{\min }{\left|\right|X-D*\mathrm{\α}\left|\right|}_2^{2}s.t.{\left|\right|{\mathrm{\α}}_i\left|\right|}_0\≤T---\left(13\right)$

In the formula, 50000 image blocks of X for selecting at random, D is dictionary to be trained, and D comprises 1024 9 * 9 image block in the present embodiment, and α is the sparse coefficient vector of image block, α _iBe the sparse coefficient of i image block correspondence, wherein,

T be image block in the constraint that trains the sparse coefficient under the dictionary, value is 20 in the present embodiment.

2. the point spread function of ambiguous estimation image.

Estimate to cause image blurring point spread function.The estimation of point spread function is found the solution based on following objective function optimization:

$\underset{x_h,h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+\frac{{\left|\right|x_h\left|\right|}_1}{{\left|\right|x_h\left|\right|}_2}+v{\left|\right|h\left|\right|}_1---\left(14\right)$

$\mathrm{Fy}=\left[\begin{array}{c}{F}_1*y\\ F_2*y\end{array}\right]---\left(15\right)$

In the formula, λ, ν are regularization parameter, and y is blurred picture, x _hBe the high fdrequency component of waiting to estimate picture rich in detail, h is point spread function to be estimated, F is the high fdrequency component that bank of filters is used to extract image, F ₁Be [1 ,-1], F ₂Be [1 ,-1] ^T, * is convolution operation.Formula has x in (14) _hWith two unknown quantitys of h, by the alternately method calculating of iteration.In the present embodiment, the λ value is that 200, ν value is 1.

(4) initialization h, random initializtion h in the present embodiment.

(5) fixing h by the formula of minimizing (4), estimates x _h

$\underset{x_h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+\frac{{\left|\right|x_h\left|\right|}_1}{{\left|\right|x_h\left|\right|}_2}---\left(16\right)$

(6) fixing x _h, by the formula of minimizing (5), estimate h

$\underset{h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+v{\left|\right|h\left|\right|}_1---\left(17\right)$

(7) behind the repeating step (2), (3) 200 times, the h of gained is the point spread function of estimation.

3. it is right to generate clear dictionary and fuzzy dictionary.

Comprise two contents, one is to generate fuzzy dictionary according to the clear dictionary of training and the point spread function of estimation, and another is the high fdrequency component of extracting clear dictionary.

1) fuzzy dictionary D _BlurGeneration.For each the atom image block in the clear dictionary, generate the atom image block in the corresponding fuzzy dictionary according to the following steps.

(1) the atom image block of clear dictionary is placed in the middle of, to around symmetry be extended to the new image block of 3 times of sizes;

(2) with the point spread function that estimates in the newly-generated image block convolution step 2, generate the blurred picture piece of 3 times of sizes;

(3) in the middle of taking out from the blurred picture piece and the image block corresponding size of clear dictionary are as atom image block corresponding in the fuzzy dictionary.

2) after fuzzy dictionary generates, extract the high fdrequency component of clear dictionary atom image block, in the present embodiment, each image block in the clear dictionary is deducted its average, obtain the clear dictionary D of high frequency _h

4. the sparse reconstruct of blurred picture rarefaction representation and picture rich in detail.

Blurred picture is carried out rarefaction representation under fuzzy dictionary, simultaneously, sparse coefficient is carried out sparse reconstruct restored image under clear dictionary.Generate complete 0 image of the same two big width of cloth with blurred picture of size, a width of cloth is used for adding up and x of picture rich in detail piece _s, another width of cloth is used for the weighting coefficient x of each pixel of storage picture rich in detail _wFrom left to right, from top to bottom adjacent 1 pixel is taken out 9 * 9 mutual stacked image blocks successively, and each blurred picture piece is carried out following operation, calculates the image block of its picture rich in detail correspondence position from blurred picture:

(5) according to formula (6), based on orthogonal matching pursuit (OMP) algorithm, calculate i blurred picture piece y _iAt fuzzy dictionary D _BlurUnder sparse factor alpha _i:

min||α _i|| ₀s.t.||y _i-D _blurα _i|| ₂≤ε (18)

Wherein, ε is the error behind the rarefaction representation, and value is ε=10 in the present embodiment ^-5

(6) use sparse factor alpha _iReconstruct picture rich in detail piece x on the clear dictionary of high frequency _iHFS x ' _i,

x′ _i＝D _hα _i (19)

(7) through type (8) carries out x ' _iCarry out variance correction,

$x_i^{\′}=x_i^{\′}\frac{\mathrm{Var}\left(x_i^{\′}\right)}{{\left|\right|x_i^{\′}\left|\right|}_2}---\left(20\right)$

In the formula, || x ' _i|| ₂Be x ' _iTwo norms because x ' _iBe by a series of Var (x ' _i) be the variance yields after to be corrected, to be calculated by formula (9), it is blurred picture piece y _iVariance during divided by the image block rarefaction representation dictionary corresponding variance promote and compare r _jAverage, r _jCalculating provided by formula (10):

$\mathrm{Var}\left(x_i^{\′}\right)=\frac{\mathrm{Var}\left(y_i\right)}{\mathrm{mean}\left(\underset{{\mathrm{\α}}_{\mathrm{ij}}\≠0}{\mathrm{\Σ}}{r}_j\right)}---\left(21\right)$

$r_j=\frac{\mathrm{Var}\left(D_{{\mathrm{blur}}_j}\right)}{\mathrm{Var}\left(D_{h_j}\right)}---\left(22\right)$

In the formula,

With

Be respectively D _BlurAnd D _hJ atom image block.

(8) will proofread and correct x ' later _iAdd blurred picture piece y _iAverage, just obtained blurred picture piece y _iCorresponding picture rich in detail piece x _i

x _i＝x′ _i+mean(y _i) (23)

At x _sOn and y _iCorrespondence position adds picture rich in detail piece x _i, simultaneously, at x _wGo up and y _iCorrespondence position adds 1.At last, with x _sDivided by x _wObtain whole distinct image:

$x=\frac{x_s}{x_w}---\left(24\right).$

Claims (1)

1. the blurred picture blind restoration method based on rarefaction representation is characterized in that comprising the steps:

(a) from the picture rich in detail similar to the parked picture material, stochastic sampling is selected a large amount of image blocks, passes through from image block

$\underset{D,\mathrm{\α}}{\min }{\left|\right|X-D*\mathrm{\α}\left|\right|}_2^{2}s.t.{\left|\right|{\mathrm{\α}}_i\left|\right|}_0\≤T---\left(1\right)$

Train clear redundant dictionary; By bringing in constant renewal in dictionary, make the expression of all images piece under redundant dictionary of sampling satisfy the constraint of certain degree of rarefication;

In the formula, the image block of X for selecting at random, D is dictionary to be trained, α is the sparse coefficient vector of image block, α _iBe the sparse coefficient vector of i image block correspondence, T is that image block is in the constraint that trains the sparse coefficient under the dictionary;

(b) objective function optimization is found the solution:

$\underset{x_h,h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+\frac{{\left|\right|x_h\left|\right|}_1}{{\left|\right|x_h\left|\right|}_2}+{v\left|\right|h\left|\right|}_1---\left(2\right)$

$\mathrm{Fy}=\left[\begin{array}{c}{F}_1*y\\ F_2*y\end{array}\right]---\left(3\right)$

In the formula, λ, v are regularization parameter, and y is blurred picture, x _hBe the high fdrequency component of waiting to estimate picture rich in detail, h is point spread function to be estimated, F is the high fdrequency component that bank of filters is used to extract image, F ₁Be [1 ,-1], F ₂Be [1 ,-1] ^T, * is convolution operation; Formula has x in (2) _hWith two unknown quantitys of h, by the alternately method calculating of iteration;

1) initialization h;

2) fixing h by the formula of minimizing (4), estimates x _h

$\underset{x_h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+\frac{{\left|\right|x_h\left|\right|}_1}{{\left|\right|x_h\left|\right|}_2}---\left(4\right)$

3) fixing x _h, by the formula of minimizing (5), estimate h

$\underset{h}{\min }\mathrm{\λ}{\left|\right|\mathrm{Fy}-h*\left(x_h\right)\left|\right|}_2+{v\left|\right|h\left|\right|}_1---\left(5\right)$

Repeating step 2), 3), the point spread function h that obtains estimating;

(c) for each the atom image block in the clear dictionary, the atom image block is extended to the new image block of three times of sizes of atom image block by the mode of symmetry expansion, the point spread function estimated of convolution then generates the blurred picture piece of three times of sizes of atom image block; In the middle of taking out from the blurred picture piece and the image block corresponding size of clear dictionary deduct its average with each image block in the clear dictionary, the clear dictionary D of acquisition high frequency as atom image block corresponding in the fuzzy dictionary _h

(d) blurred picture is resolved into stacked image block mutually, according to picture rich in detail at the sparse coefficient under the clear dictionary and blurred picture the sparse coefficient principle of identity under fuzzy dictionary, carry out rarefaction representation for each blurred picture piece under fuzzy dictionary, concrete steps are as follows:

1) based on the orthogonal matching pursuit algorithm, according to formula

min||α _i|| ₀s.t.||y _i-D _blurα _i|| ₂≤ε (6)

Calculate i blurred picture piece y _iAt fuzzy dictionary D _BlurUnder sparse factor alpha _iIn the formula, ε is the error behind the rarefaction representation;

2) use sparse factor alpha _iReconstruct picture rich in detail piece x on the clear dictionary of high frequency _iHFS x ' _i,

x′ _i＝D _hα _i (7)

3) adopt following formula

$x_i^{\′}=x_i^{\′}\frac{\mathrm{Var}\left(x_i^{\′}\right)}{{\left|\right|x_i^{\′}\left|\right|}_2}---\left(8\right)$

To x ' _iCarry out variance correction, in the formula, || x ' _i|| ₂Be x ' _iTwo norms, x ' _iBe by a series of Var (x ' _i) be the variance yields after to be corrected, provided by formula (9), Var (x ' _i) be blurred picture piece y _iVariance during divided by the image block rarefaction representation dictionary corresponding variance promote and compare r _jAverage, r _jProvided by formula (10):

$\mathrm{Var}\left(x_i^{\′}\right)=\frac{\mathrm{Var}\left(y_i\right)}{\mathrm{mean}\left(\underset{{\mathrm{\α}}_{\mathrm{ij}}\≠0}{\mathrm{\Σ}}{r}_j\right)}---\left(9\right)$

$r_j=\frac{\mathrm{Var}\left(D_{{\mathrm{blur}}_j}\right)}{\mathrm{Var}\left(D_{h_j}\right)}---\left(10\right)$

In the formula,

With

Be respectively D _BlurAnd D _hJ atom image block;

4) will proofread and correct x ' later _iAdd blurred picture piece y _iAverage, just obtained blurred picture piece y _iCorresponding picture rich in detail piece x _i

x _i＝x′ _i+mean(y _i) (11)

At x _sOn and y _iCorrespondence position adds picture rich in detail piece x _i, simultaneously, at x _wGo up and y _iCorrespondence position adds 1; At last, with x _sDivided by x _wObtain whole distinct image:

$x=\frac{x_s}{x_w}---\left(12\right)$

In the formula, x _sBe the picture rich in detail piece add up and, x _wIt is the weighting coefficient of each pixel of storage picture rich in detail.