CN103337058A - Image blind restoration method based on blurred noise image pair joint optimization - Google Patents

Abstract

The invention discloses an image blind restoration method based on blurred noise image pair joint optimization, which is used for solving the technical problem that the available image blind restoration method is poor in image restoration effect. The method adopts the technical scheme that a noise image is introduced; effective edge information which is not blurred and contained in the noise image is utilized; a blurred kernel and a clear image are solved by joint objective function optimization of a joint blurred image and the noise image; the problems that the blurred kernel is misestimated and a restoration result is poor due to the fact that a non-blurred image edge is inaccurately estimated from the blurred image are solved; and the image with better effects and more details is obtained. The method improves the image restoration effect.

Description

Based on the method for blindly restoring image of fuzzy noise image to combined optimization

Technical field

The present invention relates to a kind of method for blindly restoring image, particularly relate to a kind of based on the method for blindly restoring image of fuzzy noise image to combined optimization.

Background technology

Document " based on the blind recovery of robust of the motion blur image of marginal information, photoelectron laser, 2011, Vol22 (10), p1982-1989 " discloses a kind ofly sane asks for fuzzy core and to the method for blindly restoring image of image deblurring from the single width blurred picture.This method is at first estimated the non-fuzzy image edge information by two-sided filter and shock wave wave filter, then, ask fuzzy core according to the relation of the edge between blurred picture and the non-fuzzy figure, at last, under multiple dimensioned framework, set auto-adaptive parameter at each subalgorithm, make up a sane method for blindly restoring image.The method has good recovery effect to fuzzy degraded image, has not only removed motion blur and noise effectively, and preserving edge details to a certain extent.The described method fuzzy core of document is found the solution the non-fuzzy image edge information that is based on estimation, because diversity and the complicacy of blurred picture, can cause the marginal information of blurred picture to be difficult to estimate, cause the fuzzy core misjudgment, simultaneously, because the pathosis of deconvolution problem, the fuzzy core of mistake can cause net result to produce ringing effect at strong edge, have a strong impact on final recovery result.

Summary of the invention

In order to overcome the deficiency of conventional images blind restoration method restored image weak effect, the invention provides a kind of based on the method for blindly restoring image of fuzzy noise image to combined optimization.This method comprises not fuzzy efficient frontier information by introducing noise image, utilizing in the noise image, find the solution fuzzy core and picture rich in detail by the joint objective function optimization of associating blurred picture and noise image.Avoided from blurred picture estimating the inaccurate of non-fuzzy image border and causing the fuzzy core misjudgment, caused the problem of difference as a result of restoring, obtained better effects if, have more the image of details.Can improve the effect of restored image.

The technical solution adopted for the present invention to solve the technical problems is: a kind of based on the method for blindly restoring image of fuzzy noise image to combined optimization, be characterized in may further comprise the steps:

Given blurred picture B and noise image N two width of cloth images, unite by target energy function shown in (1) formula and to find the solution picture rich in detail L and fuzzy core K:

$\{K,L\}=\underset{K,L}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\β}\left|\right|N-L\left|\right|}_2^2+{\mathrm{\λ}\left|\right|K\left|\right|}_2^2+{\mathrm{\η}\left|\right|G\⊗L\left|\right|}^{\mathrm{\α}}\}---\left(1\right)$

In the formula, G is gradient extraction filter group,

Be the two-dimensional convolution operation, γ, β, λ, η are the regularization coefficient, and α is that norm is selected parameter,

For calculating The α norm.For finding the solution of (1) formula, at first, L is carried out initialization, make L=N, then, circulation is carried out following steps 1,2 up to the iterations T that iterates to setting.

1. fixed L is found the solution image blurring nuclear K.

The objective function of (1) formula is reduced to following formula at this moment:

$K=\underset{K}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\λ}\left|\right|K\left|\right|}_2^2\}---\left(2\right)$

(2) formula is found the solution to accelerate to find the solution speed by conjugate gradient, and solution formula is converted into:

In the formula, F () and F ^-1() is respectively two dimension direct transform and the inverse transformation of Fu Li leaf transformation fast,

Be the conjugation of F ().Be the dot product operation of matrix, I is unit matrix.Find the solution (3) formula, obtain current images fuzzy core K.

2. fixing K finds the solution restored image L.

The objective function of (1) formula is reduced to (4) formula at this moment:

$L=\underset{L}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\β}\left|\right|N-L\left|\right|}_2^2+{\mathrm{\η}\left|\right|G\⊗L\left|\right|}^{\mathrm{\α}}\}---\left(4\right)$

In the formula, gradient filter group G is by C gradient filter [G ₁, G ₂..., G _C] form, comprise the α norm in (4) formula, carry out approximate solution by the iteration weighted least mean square theory of error, its step is as follows:

Below the iterative 1), 2) two steps, up to the iterations M that iterates to setting.

1) calculates C weighting matrix, be respectively ω ¹, ω ²..., ω ^c..., ω ^C, and the dimension of each weighting matrix is all identical with L, for c weighting matrix ω ^cIt asks method as follows:

${\mathrm{\ω}}_{i,j}^c={\left|{(G_c\⊗L)}_{i,j}\right|}^{a-2}---\left(5\right)$

In the formula,

Expression

The i of matrix is capable after the convolution, the element of j row.

2) formula (4) is found the solution be approximately

(6) formula is that 2 norm constraint are found the solution problem, utilizes the conjugate gradient descending method to find the solution, and obtains the L that current iteration is asked.

The invention has the beneficial effects as follows: because this method comprises not fuzzy efficient frontier information by introducing noise image, utilizing in the noise image, find the solution fuzzy core and picture rich in detail by the joint objective function optimization of associating blurred picture and noise image.Avoided from blurred picture estimating the inaccurate of non-fuzzy image border and causing the fuzzy core misjudgment, caused the problem of difference as a result of restoring, obtained better effects if, have more the image of details.Improved the effect of restored image.

Below in conjunction with embodiment the present invention is elaborated.

Embodiment

It is as follows to the method for blindly restoring image concrete steps of combined optimization to the present invention is based on the fuzzy noise image:

Given blurred picture B and noise image N two width of cloth images, unite by target energy function shown in (1) formula and to find the solution picture rich in detail L and fuzzy core K:

$\{K,L\}=\underset{K,L}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\β}\left|\right|N-L\left|\right|}_2^2+{\mathrm{\λ}\left|\right|K\left|\right|}_2^2+{\mathrm{\η}\left|\right|G\⊗L\left|\right|}^{\mathrm{\α}}\}---\left(1\right)$

In the formula, G is gradient extraction filter group, γ, and β, λ, η are the regularization coefficient, in the present embodiment, γ=0.1, β=1, λ=0.01, η=2000, α=0.5.α is that norm is selected parameter,

For calculating

The α norm.Mainly be by according to adopting alternately the method for iteration to find the solution for finding the solution of (1) formula.At first, L is carried out initialization, make L=N, then, circulation is carried out following steps 1,2 up to the iterations T=10 that iterates to setting.

1. fixed L is found the solution image blurring nuclear K.

The objective function of (1) formula can be reduced to following formula at this moment:

$K=\underset{K}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\λ}\left|\right|K\left|\right|}_2^2\}---\left(2\right)$

(2) formula can find the solution to accelerate to find the solution speed by conjugate gradient, and solution formula can be converted into:

In the following formula, F () and F ^-1() is respectively two dimension direct transform and the inverse transformation of Fu Li leaf transformation fast, Be the conjugation of F (), be the dot product operation of matrix, I is unit matrix.Find the solution (3) formula, just can obtain current images fuzzy core K.

2. fixing K finds the solution restored image L.

The objective function of (1) formula can be reduced to (4) formula at this moment:

$L=\underset{L}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\β}\left|\right|N-L\left|\right|}_2^2+{\mathrm{\η}\left|\right|G\⊗L\left|\right|}^{\mathrm{\α}}\}---\left(4\right)$

Gradient filter group G in the following formula is by five gradient filter [G ₁, G ₂, G ₃, G ₄, ₅G (] G ₁=[1 ,-1], G ₂=[1 ,-1] ^T, G ₃=[1 ,-2,1], G ₄=[1 ,-2,1] ^T, G ₅=[1 ,-1;-1,1]) form, at this moment, C=5.(4) comprise the α norm in the formula, can carry out approximate solution by the iteration weighted least mean square theory of error, its step is as follows:

Below the iterative 1), 2) two steps, up to the iterations M=20 that iterates to setting.

1) calculates five weighting matrixs, be respectively ω ¹, ω ²..., ω ^c..., ω ⁵, and the dimension of each weighting matrix is all identical with L, for c weighting matrix ω ^cIt asks method as follows:

${\mathrm{\ω}}_{i,j}^c={\left|{(G_c\⊗L)}_{i,j}\right|}^{a-2}---\left(5\right)$

Wherein,

Expression

The i of matrix is capable after the convolution, the element of j row.

2) formula (4) is found the solution be approximately

Following formula is that 2 norm constraint are found the solution problem, can utilize the conjugate gradient descending method to find the solution, and just can obtain the L that current iteration is asked.

Claims (1)

1. one kind based on the method for blindly restoring image of fuzzy noise image to combined optimization, it is characterized in that may further comprise the steps:

Given blurred picture B and noise image N two width of cloth images, unite by target energy function shown in (1) formula and to find the solution picture rich in detail L and fuzzy core K:

$\{K,L\}=\underset{K,L}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\β}\left|\right|N-L\left|\right|}_2^2+{\mathrm{\λ}\left|\right|K\left|\right|}_2^2+{\mathrm{\η}\left|\right|G\⊗L\left|\right|}^{\mathrm{\α}}\}---\left(1\right)$

In the formula, G is gradient extraction filter group,

Be the two-dimensional convolution operation, γ, β, λ, η are the regularization coefficient, and α is that norm is selected parameter,

For calculating

The α norm; For finding the solution of (1) formula, at first, L is carried out initialization, make L=N, then, circulation is carried out following steps 1,2 up to the iterations T that iterates to setting;

1. fixed L is found the solution image blurring nuclear K;

The objective function of (1) formula is reduced to following formula at this moment:

$K=\underset{K}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\λ}\left|\right|K\left|\right|}_2^2\}---\left(2\right)$

(2) formula is found the solution to accelerate to find the solution speed by conjugate gradient, and solution formula is converted into:

In the formula, F () and F ^-1() is respectively two dimension direct transform and the inverse transformation of Fu Li leaf transformation fast,

Be the conjugation of F (), be the dot product operation of matrix, I is unit matrix; Find the solution (3) formula, obtain current images fuzzy core K;

2. fixing K finds the solution restored image L;

The objective function of (1) formula is reduced to (4) formula at this moment:

$L=\underset{L}{\arg \min }\{\mathrm{\γ}{\left|\right|B-K\⊗L\left|\right|}_2^2+{\mathrm{\β}\left|\right|N-L\left|\right|}_2^2+{\mathrm{\η}\left|\right|G\⊗L\left|\right|}^{\mathrm{\α}}\}---\left(4\right)$

In the formula, gradient filter group G is by C gradient filter [G ₁, G ₂..., G _C] form, comprise the α norm in (4) formula, carry out approximate solution by the iteration weighted least mean square theory of error, its step is as follows:

Below the iterative 1), 2) two steps, up to the iterations M that iterates to setting;

1) calculates C weighting matrix, be respectively ω ¹, ω ²..., ω ^c..., ω ^C, and the dimension of each weighting matrix is all identical with L, for c weighting matrix ω ^cIt asks method as follows:

${\mathrm{\ω}}_{i,j}^c={\left|{(G_c\⊗L)}_{i,j}\right|}^{a-2}---\left(5\right)$

In the formula,

Expression

The i of matrix is capable after the convolution, the element of j row;

2) formula (4) is found the solution be approximately

(6) formula is that 2 norm constraint are found the solution problem, utilizes the conjugate gradient descending method to find the solution, and obtains the L that current iteration is asked.