CN103337057B - Based on the motion blur image blind restoration method of multiple dimensioned self similarity - Google Patents
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Abstract
The invention discloses a kind of motion blur image blind restoration method based on multiple dimensioned self similarity, for solving the technical matters of conventional images blind restoration method restored image weak effect.Technical scheme is incorporated in image restoration problem using Image Multiscale self-similarity nature as prior imformation, using prior-constrained as next yardstick of the picture rich in detail of a upper size estimation, carry out image restoration, decrease the ringing effect of restored image at strong edge, image more clearly can be obtained.Improve the effect of restored image.
Description
Technical Field
The invention relates to an image blind restoration method, in particular to a motion blurred image blind restoration method based on multi-scale self-similarity.
Background
The document "robust blind restoration of motion blurred images based on edge information, photoelectronic laser 2011, Vol22(10), p 1982-1989" proposes a robust image blind restoration method for solving a blur kernel from a single blurred image and deblurring the image. The method comprises the steps of firstly estimating edge information of a non-fuzzy image through a bilateral filter and a shock wave filter, then solving a fuzzy core according to an edge relation between the fuzzy image and the non-fuzzy image, and finally setting self-adaptive parameters for each sub-algorithm under a multi-scale framework to construct a steady image blind restoration method. The method has good restoration effect on the blurred and degraded image, effectively removes motion blur and noise, and can keep edge details to a certain extent. The method disclosed by the literature is characterized in that fuzzy kernel solution is based on estimated non-fuzzy image edge information, the edge information of a fuzzy image is difficult to estimate due to diversity and complexity of the fuzzy image, so that fuzzy kernel estimation is wrong, and meanwhile, due to the ill-posed characteristic of a deconvolution problem, a final result generates a ringing effect at a strong edge due to a wrong fuzzy kernel, so that a final recovery result is seriously influenced.
Disclosure of Invention
In order to overcome the defect that the conventional image blind restoration method is poor in image restoration effect, the invention provides a motion blurred image blind restoration method based on multi-scale self-similarity. According to the method, the multi-scale self-similarity characteristic of the image is introduced into the image restoration problem as prior information, the clear image estimated in the previous scale is used as prior constraint of the next scale for image restoration, the ringing effect of the restored image at a strong edge is reduced, and a clearer image can be obtained. The effect of restoring the image can be improved.
The technical scheme adopted by the invention for solving the technical problems is as follows: a blind restoration method of a motion blurred image based on multi-scale self-similarity is characterized by comprising the following steps:
step one, carrying out multi-scale down-sampling on a blurred image B, wherein B is respectivelyo，B1，…Bs，…，BSWhere S is the number of downsamplings, B0＝B，Bs＝DBs-1And D is a down-sampling operator. The smaller s is, the larger the image scale is, and when s is 0, the original blurred image is obtained.
And step two, carrying out optimization solution on the blurred image with the scale S from S to 0 according to the following optimization functions in sequence:
in the formula, Ks,LsThe scale of each is estimated as the blur kernel and sharp image under s, G is the gradient extraction filter bank,for the two-dimensional convolution operation, α, λ, τ, β are regularization coefficients, η is a norm selection parameter,to calculateEta norm of, Ls′＝D-1Ls+1，D-1The inverse operation of the down-sampling operator D is the corresponding up-sampling. It should be noted that when S ═ S, S +1 does not exist, and in this case, the optimization function is:
for the solution of the expressions (1) and (2), first, L is calculatedsInitialization is carried out, and then the following steps 1 and 2 are executed in a circulating mode until the iteration is carried out to the set iteration number T.
1. Fixed LsSolving the fuzzy kernel Ks。
In this case, the objective functions of both the equations (1) and (2) are simplified as follows:
(3) the formula is solved through conjugate gradient to accelerate solving speed, and the solving formula is converted into:
（4）
wherein F (. cndot.) and F-1(. cndot.) is respectively the forward transform and inverse transform of two-dimensional fast Fourier transform,is the conjugate of F (·), o is the dot product operation of the matrix, and I is the identity matrix. Solving the formula (4) to obtain the current image fuzzy kernel Ks。
2. Fixed KsSolving for sharp image Ls。
When S ═ S, the optimization function (2) is simplified to the following equation:
when S ≠ S, the optimization function (1) is simplified to:
suppose that the gradient filter bank G consists of C gradient filters G1,G2,...,GC]The components of the formula (5) and the formula (6) comprise eta norm, and the approximation solution is carried out by an iterative weighted minimum mean square error method, and the steps are as follows:
and (3) iteratively solving the following steps 1) and 2) until the iteration is carried out to the set iteration number M.
1) Calculating C weighting matrices, each being ω1,ω2,...,ωCAnd the dimension of each weighting matrix is equal to LsSame for the c-th weighting matrix omegacThe method comprises the following steps:
wherein,to representThe element in the ith row and the jth column of the matrix after convolution.
2) The solution of equation (5) is approximated as
（8）
(6) The solution of equation is approximated as
（9）
(8) The equations (9) and (2) are 2 norm constraint solving problems
（10）
（11）
Only need to make E1、E2To LsIs 0, is solved by a conjugate gradient descent method to obtain the L solved by the current iterations。
Step three, making L equal to L0And L is the solved sharp image.
The invention has the beneficial effects that: according to the method, the multi-scale self-similarity characteristic of the image is introduced into the image restoration problem as prior information, and the clear image estimated in the previous scale is used as the prior constraint of the next scale for image restoration, so that the ringing effect of the restored image at a strong edge is reduced, and a clearer image can be obtained. The effect of restoring the image is improved.
The present invention will be described in detail with reference to the following embodiments.
Detailed Description
The blind restoration method of the motion blurred image based on the multi-scale self-similarity comprises the following specific steps:
1. carrying out multi-scale down-sampling on the blurred image B, wherein B is respectivelyo，B1，…Bs，…，BSWhere S is the number of downsamplings, B0＝B，Bs＝DBs-1And D is a down-sampling operator. The smaller s is, the larger the image scale is, and when s is 0, the original blurred image is obtained. In this example, S is 3 and D is 0.5 times down-sampled, e.g., Bs-1Has an image size of 256 × 256, then passes through Bs＝DBs-1Then, BsHas an image size of Bs-1Is 0.5 times of the total weight of the powder, namely 128 multiplied by 128.
2. And (3) carrying out optimization solution on the blurred image with the scale s from 3 to 0 according to the following optimization functions in sequence:
in the above formula, Ks,LsThe scales of the image blur kernel and the clear image are estimated under s, G is a gradient extraction filter bank, alpha, lambda, tau and beta are regularization coefficients, eta is a norm selection parameter,to calculateEta norm of, Ls′＝D-1Ls+1，D-1The inverse operation of the down-sampling operator D is the corresponding up-sampling. In this embodiment, α is 0.1, λ is 0.006, τ is 2000, β is 0.1, and η is 0.8. It should be noted that when s is 3, the optimization function is:
the solution of equations (1) and (2) is mainly performed by a method according to which alternating iterations are employed. First, for LsInitialization is carried out, and then the following steps 1 and 2 are executed in a circulating mode until the iteration is carried out to the set iteration number T.
2.1 fixation of LsSolving the fuzzy kernel Ks
In this case, the objective functions of both the equations (1) and (2) can be simplified as follows:
the formula can be solved through conjugate gradient to accelerate the solving speed, and the solving formula can be converted into:
（4）
in the above formula, F (-) and F-1(. cndot.) is respectively the forward transform and inverse transform of two-dimensional fast Fourier transform,is the conjugate of F (·), o is the dot product operation of the matrix, and I is the identity matrix. Solving the formula (4) to obtain the current image blur kernel Ks。
2.2 fixed KsSolving for sharp image Ls
When S ═ S, the optimization function (2) can be simplified to the following equation:
when S ≠ S, the optimization function (1) can be simplified as:
suppose that the gradient filter bank G consists of 5 gradient filters G1,G2,G3,G4,G5](G1＝[1,-1],G2＝[1,-1]T,G3＝[1,-2,1],G4＝[1,-2,1]T,G5＝[1,-1;-1,1]) Composition, in this case, C ═ 5. (5) The formula (6) and the formula (eta norm) can be approximately solved by an iterative weighted least mean square error method, and the method comprises the following steps:
and (3) iteratively solving the following steps 1) and 2) until the iteration is carried out until the set iteration number M is 20.
1) Calculate 5 weighting matrices, each ω1,ω2,...,ω5And the dimension of each weighting matrix is equal to LsSame for the c-th weighting matrix omegacThe method comprises the following steps:
wherein,to representThe element in the ith row and the jth column of the matrix after convolution.
2) The solution of equation (5) can be approximated as
（8）
(6) The solution of the formula can be approximated as
（9）
(8) The equations (9) and (2) are 2 norm constraint solving problems
（10）
（11）
Only need to make E1、E2To LsThe derivative is 0, and the solution is carried out by using a conjugate gradient descent method, so that the L solved by the current iteration can be obtaineds。
3. Finally, let L equal to L0At this time, L is a clear image for solution.
Claims (1)
1. A blind restoration method of a motion blurred image based on multi-scale self-similarity is characterized by comprising the following steps:
step one, carrying out multi-scale down-sampling on a blurred image B, wherein B is respectivelyo，B1，…Bs，…，BSWhere S is the number of downsamplings, B0＝B，Bs＝DBs-1D is a down-sampling operator; the smaller s is, the larger the image scale is, and when s is 0, the original blurred image is obtained;
and step two, carrying out optimization solution on the blurred image with the scale S from S to 0 according to the following optimization functions in sequence:
（1）
in the formula, Ks,LsThe scale of each is estimated as the blur kernel and sharp image under s, G is the gradient extraction filter bank,for the two-dimensional convolution operation, α, λ, τ, β are regularization coefficients, η is a norm selection parameter,to calculateEta norm of, Ls′＝D-1Ls+1，D-1Performing inverse operation of the down-sampling operator D, namely corresponding up-sampling; it should be noted that when S ═ S, S +1 does not exist, and in this case, the optimization function is:
（2）
for the solution of the expressions (1) and (2), first, L is calculatedsInitializing, and then circularly executing the following steps 1 and 2 until the iteration is carried out to a set iteration time T;
1. fixed LsSolving the fuzzy kernel Ks；
In this case, the objective functions of both the equations (1) and (2) are simplified as follows:
（3）
(3) the formula is solved through conjugate gradient to accelerate solving speed, and the solving formula is converted into:
（4）
wherein F (. cndot.) and F-1(. cndot.) is respectively the forward transform and inverse transform of two-dimensional fast Fourier transform,is the conjugate of F (·), is the dot product operation of the matrix, and I is the identity matrix; solving the formula (4) to obtain the current image fuzzy kernel Ks；
2. Fixed KsSolving for sharp image Ls；
When S ═ S, the optimization function (2) is simplified to the following equation:
（5）
when S ≠ S, the optimization function (1) is simplified to:
（6）
suppose that the gradient filter bank G consists of C gradient filters G1,G2,...,GC]The components of the formula (5) and the formula (6) comprise eta norm, and the approximation solution is carried out by an iterative weighted minimum mean square error method, and the steps are as follows:
iteratively solving the following steps 1) and 2) until iteration reaches a set iteration number M;
1) calculating C weighting matrices, each being ω1,ω2,...,ωCAnd the dimension of each weighting matrix is equal to LsSame for the c-th weighting matrix omegacThe method comprises the following steps:
（7）
wherein,to representThe element of the ith row and the jth column of the matrix after convolution;
2) the solution of equation (5) is approximated as
（8）
(6) The solution of equation is approximated as
（9）
(8) The equations (9) and (2) are 2 norm constraint solving problems
（10）
（11）
Only need to make E1、E2To LsIs 0, is solved by a conjugate gradient descent method to obtain the L solved by the current iterations；
Step three, making L equal to L0And L is the solved sharp image.
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| CN104021529B (en) * | 2014-06-17 | 2017-01-11 | 中国电子科技集团公司第二十八研究所 | Blurred image non-blind restoration method |
| CN104134196B (en) * | 2014-08-08 | 2017-02-15 | 重庆大学 | Split Bregman weight iteration image blind restoration method based on non-convex higher-order total variation model |
| CN104851079B (en) * | 2015-05-06 | 2016-07-06 | 中国人民解放军国防科学技术大学 | Low-light (level) license plate image restoration methods based on noise/broad image pair |
| CN105160687B (en) * | 2015-10-21 | 2018-01-02 | 华中科技大学 | A kind of Pneumatic optical heat radiated noise bearing calibration and system |
| CN105976332B (en) * | 2016-05-03 | 2019-03-01 | 北京大学深圳研究生院 | Image deblurring method based on bright fringes information in image |
| CN105957043B (en) * | 2016-06-22 | 2018-12-14 | 西北工业大学 | The blurred picture blind restoration method activated automatically based on gradient |
| CN107742278B (en) * | 2017-10-25 | 2021-07-13 | 重庆邮电大学 | Binding of L0Motion blurred image blind restoration method based on norm and spatial scale information |
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