CN106204502B - Based on mixing rank L0Regularization fuzzy core estimation method - Google Patents
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Abstract
The present invention proposes a kind of mixing rankL 0Regularization fuzzy core estimation method, feature are to carry out mixing rank to the intermediate clear image in fuzzy kernel estimates modelL 0Regularization constraint, using single order confining guard image border, the ringing effect that second-order constraint inhibits single order constraint to generate restores out clearly intermediate image；Then increase improved adaptive Dynamic gene in fuzzy kernel estimates model, the prominent edge information for being more conducive to fuzzy kernel estimates is extracted from intermediate clear image.The fuzzy kernel estimates model of proposition can be then solved according to half Secondary variable splitting technique.The present invention artificial blurred picture and realistic blur image carry out experiments have shown that: the fuzzy core estimation method of proposition be it is effective, restore image out compared with representative method great in recent years, subjective vision effect and objectively evaluate index and be all significantly improved.
Description
Technical field
The present invention relates to image processing methods, in particular to based on mixing rank L0Regularization fuzzy core estimation method.
Background technique
Durings the acquisition of image, transimission and storage etc., due to the physical imperfection of imaging device itself, external environment
Variation, operator the factors such as misoperation influence, inevitably lead to image and different degrees of degeneration drop occur
Matter, this not only seriously affects the visual effect of image, also substantially reduces practical application value.Then image restoration technology is just met the tendency of
And it gives birth to, and be widely applied to the fields such as astronomical observation, medical imaging, video multimedia, criminal investigation.Figures numerous at present
The disadvantages of as restored method is due to requiring prior information more, or that there are effects is poor, and algorithm complexity is high.For this purpose, effectively, fastly
The image recovery method of speed is still most challenging problem in field of image processing.
Studies have shown that when knowing in advance known to the fuzzy core of blurred picture or by some technological means, image restoration
Problem of simply deconvoluting is translated into, there are many methods can be very good such issues that solve at present, as liftering, wiener are filtered
Wave, R-L method etc..However in practice, fuzzy core (i.e. point spread function) is often unknown, and here it is blindly restoring images
Problem.Since blindly restoring image is divided into fuzzy kernel estimates by prior blur identification and clear image is restored in blindly restoring image, advantage is
Calculation amount is less, is easy to apply in practice, obtains the extensive concern of researcher in recent years.
Accurately fuzzy kernel estimates are the key points of blindly restoring image, are estimated since significant edge is conducive to fuzzy core
Meter, and detail section destroys the estimation procedure of fuzzy core, thus at present most fuzzy kernel method all can it is explicit first or
The prominent edge for implicitly extracting image, then estimates accurate fuzzy core using the edge of extraction.But when figure
When as details rich in or biggish Blur scale, the fuzzy core that current method estimates is generally undesirable, natural root
Different degrees of ringing effect can be generated by restoring image out according to inaccurate fuzzy core.
Pass through analysis, when image detail is abundant or Blur scale is larger, existing processing technique are as follows: 1) apply to image single
One single order regularization constraint leads to the accurate estimation of fuzzy core；2) mould is carried out according to the amplitude of image border rather than scale
Kernel estimates are pasted, are easy to be mistaken for the details of image the edge of image, to lead to the fuzzy kernel estimates of inaccuracy.
Summary of the invention
For the above the deficiencies in the prior art, the main object of the present invention is: containing abundant details or fuzzy ruler in image
When spending larger, by mixing rank L0Regularization constraint and adaptive Dynamic gene can accurately be estimated from blindly restoring image
Fuzzy core out.
Specific technical solution is as follows:
One kind is based on mixing rank L0Regularization fuzzy core estimation method, comprising the following steps:
Step 1: establishing fuzzy kernel estimates model, initial blurred picture is inputted, the fuzzy core estimated.
Step 2: restoring according to the fuzzy core of estimation to initial blurred picture, intermediate clear image is obtained.
Step 3: the value of the adaptive Dynamic gene ω in fuzzy kernel estimates model is adjusted according to intermediate clear image,
Intermediate clear image is handled with fuzzy kernel estimates model again, the fuzzy core estimated again；Wherein adaptive adjustment
Factor ω does not need initialization, is automatically computed using intermediate clear image and corresponding formula.
Step 4: intermediate clear image iteration obtained in the previous step is obscured into adjusted according to the fuzzy core of estimation
The intermediate clear image restored, and then be more clear again in kernel estimates model.
Step 5: judging whether to meet iteration termination condition；If it is not, repeating third step and the 4th step；If so, being obscured
Core；The iteration termination condition by | | ui+1-ui||2/||ui||2>=tol and β≤βmaxIt is limited jointly, it is necessary to full simultaneously
Foot the two conditions ability iteration terminates, and wherein i is the number of iterations, ui+1It is the restored image after i+1 time iteration, uiIt is i-th
Restored image after secondary iteration is assigned to u using initial blurred picture as initial value as i=00；Tol is threshold value；β be one just
Punishment parameter, be continually changing in optimization process.
Step 6: fuzzy core is used in non-blind recovery frame, clear image out is restored.
The fuzzy kernel estimates model is the calculating process that an iteration updates, and carries out mixing rank L to image0Regularization
Constraint；Using single order confining guard image border, second-order constraint inhibits the ringing effect of single order constraint generation.
The intermediate clear image is the relatively clear image that obtains in iterative process, with the intermediate clear image come
More accurate saliency structure is obtained, so that the accuracy for improving fuzzy kernel estimates is not obtained final restored map
Picture.
Specifically, kernel estimates model is obscured are as follows:
Wherein, k is fuzzy core to be estimated, and u is intermediate clear image to be estimated,For intermediate clearly gradient,uxAnd uyFirst difference point of the respectively intermediate clear image u on the direction x and the direction y.It is fuzzy
The gradient of image,fxAnd fyRespectively first difference of the blurred picture f on the direction x and the direction y point.uxxFor uxFirst difference point in the direction x, uxyFor uxIn the direction y
First difference point, uyxFor uyFirst difference point in the direction x, uyyFor uyFirst difference point in the direction y.σ is used to control
SystemWithThe relative weighting of both sparse prior regular terms, ω are an adaptive Dynamic genes, and γ is fuzzy
Core regular terms parameter, λ are image regular terms parameters, and it is 0.001,0.04,1 that parameter γ, λ, σ, which distinguish optimal setting,.
Specifically, the adaptive Dynamic gene ω in the fuzzy kernel estimates model is as follows:
In formula, r's (p) is defined as:
Wherein, NhIt (p) is a window area using pixel p as center size for h × h, B is blurred picture, q h
A pixel in × h window.When the window area of pixel p is smooth, ω becomes larger, that is, the smoothing weights applied are big.When
There are significant image border, ω to become smaller for the window area of pixel p, that is, the smoothing weights applied are small.To adaptively select
The large scale prominent edge in image is selected, and does not destroy the bulk properties of image itself.
Specifically, the solution of intermediate clear image:
Due to containing L in above formula0Norm | | x | |0WithIt therefore is a discrete optimization problem；Wherein x and y points
It Yong Lai not indicateWithFor indicating
Specifically, the solution for obscuring kernel estimates model is based on half secondary punishment technology, and specific solution procedure is as follows:
It is respectively as follows: by the solution that approximation timates obtain
Wherein, β and η is two positive punishment parameters, they constantly change during entire Optimization Solution；Auxiliary variable
A and b=(bh,bv)TIt is respectively intended to indicate x and ▽ x.
Specifically, the tol threshold value optimal setting is constant 0.001；βmaxOptimal setting is 23。
The present invention is firstly introduced into the L of image gradient0Sparse prior, in fuzzy kernel estimates model to intermediate clear image into
Row mixing rank L0Regularization constraint, the edge of image is protected using single order regularization constraint well, and second order regularization constraint has
The ringing effect that effect ground inhibits single order constraint to generate, to obtain clearly intermediate image.Be conducive to obscure according to prominent edge
The characteristics of kernel estimates, detail section can destroy fuzzy kernel estimates, draws in the image regular terms weight in fuzzy kernel estimates model
Enter an adaptive Dynamic gene ω makes λ value become larger in the smooth region of image for controlling image regularization parameter λ value,
The adjacent edges of image become smaller, and the large scale prominent edge in image can be adaptive selected, without destroying image itself
Bulk properties.Therefore, the present invention can obtain accurate fuzzy core when image contains abundant details or larger Blur scale,
The fuzzy core is used under non-blind recovery frame, image relatively sharp out can be quickly and effectively restored.
Detailed description of the invention
The basic framework figure of Fig. 1, the method for the present invention；
The clear image of 4 width standards used in Fig. 2, the experiment of the method for the present invention compliance test result and 8 realistic blur cores；
Fig. 3, using the method for the present invention be directed to by 4 width clear images and 8 realistic blur karyomorphisms at 32 width blurred pictures,
32 fuzzy cores estimated, wherein bottom line be 8 true fuzzy cores, above 4 behavior the method for the present invention estimate
32 fuzzy cores；
Fig. 4, using the method for the present invention for the wherein width blur size in 32 width blurred pictures be 27 × 27 it is fuzzy
The practical restoration result of image.
Fig. 5, the result that realistic blur image is restored using the method for the present invention, wherein (a) figure is abundant due to details
(complicated Architectural fringes structure in such as figure), (c) figure due to Blur scale it is larger, will lead to so most of method selection tie
The performance showed in terms of structure is bad, to estimate the fuzzy core of inaccuracy；(b) figure and (d) figure are estimated using the method for the present invention
The fuzzy core counted out restores clear image out.
Specific embodiment
The present invention implements the estimation of accurate fuzzy core on multiple dimensioned frame.Multiple dimensioned frame be by resolution ratio from low to high
Multi-layer image pyramid model composition, pyramid model can effectively avoid locally optimal solution, guarantee finally obtained
Solution converges on globally optimal solution, especially in the case where fog-level is more serious.
For each layer in image pyramid model, the present invention is the mould for implementing to propose on the radio-frequency component of image
Paste kernel estimates method.
As shown in Figure 1, a kind of based on mixing rank L0Regularization fuzzy core estimation method, comprising the following steps:
Step 1: establishing fuzzy kernel estimates model, initial blurred picture is inputted, the fuzzy core estimated.
Step 2: restoring according to the fuzzy core of estimation to initial blurred picture, intermediate clear image is obtained.
Step 3: the value of the adaptive Dynamic gene ω in fuzzy kernel estimates model is adjusted according to intermediate clear image,
Intermediate clear image is handled with fuzzy kernel estimates model again, the fuzzy core estimated again；Wherein adaptive adjustment
Factor ω does not need initialization, is automatically computed using intermediate clear image and corresponding formula.
Step 4: intermediate clear image iteration obtained in the previous step is obscured into adjusted according to the fuzzy core of estimation
The intermediate clear image restored, and then be more clear again in kernel estimates model.
Step 5: judging whether to meet iteration termination condition；If it is not, repeating third step and the 4th step；If so, being obscured
Core；The iteration termination condition by | | ui+1-ui||2/||ui||2>=tol and β≤βmaxIt is limited jointly, it is necessary to full simultaneously
Foot the two conditions ability iteration terminates, and wherein i is the number of iterations, ui+1It is the restored image after i+1 time iteration, uiIt is i-th
Restored image after secondary iteration is assigned to u using initial blurred picture as initial value as i=00；Tol is threshold value；β be one just
Punishment parameter, be continually changing in optimization process.
Step 6: fuzzy core is used in non-blind recovery frame, clear image out is restored.
The intermediate clear image is not obtained final restored image.
The fuzzy kernel estimates that this patent is mentioned are the processes that an iteration updates, which is iterative process
The relatively clear image of middle acquisition obtains more accurate saliency structure with the intermediate clear image, to mention
The accuracy of the fuzzy kernel estimates of height.
Completely fuzzy kernel estimates model proposed by the present invention is the fuzzy kernel estimates mould for increasing adaptive Dynamic gene
Type, as follows:
Wherein, k is fuzzy core to be estimated, and u is intermediate clear image to be estimated.For the ladder of intermediate clear image
Degree,uxAnd uyFirst difference point of the respectively intermediate clear image u on the direction x and the direction y.For
The gradient of blurred picture,fxAnd fyRespectively single order of the blurred picture f on the direction x and the direction y is limited
Difference.uxxFor uxFirst difference point in the direction x, uxyFor uxIn y
The first difference in direction point, uyxFor uyFirst difference point in the direction x, uyyFor uyFirst difference point in the direction y.It is right
The single order and second-order constraint of image are all made of L0Norm | | | |0.σ is used to controlWithBoth sparse priors are just
The then relative weighting of item, ω are an adaptive Dynamic genes, and γ is fuzzy core regular terms parameter, and λ is image regular terms parameter,
It is 0.001,0.04,1 that parameter γ, λ, σ, which distinguish optimal setting,.
In formula, r's (p) is defined as:
Wherein, NhIt (p) is a window area using pixel p as center size for h × h, B is blurred picture, B (q)
For a pixel in h × h window.When the window area of pixel p is smoother, need to apply biggish smooth power
Weight, i.e., ω becomes larger；When the window area of pixel p is there are significant image border, need to apply lesser smoothing weights, i.e. ω
Become smaller.
A kind of iterative algorithm by alternating minimization is expanded based on half secondary punishment technology to solve the fuzzy of proposition
Kernel estimates model.
For the convenience described, introduces auxiliary variable x and y and be respectively intended to indicateWithThenIt is expressed asThe fuzzy kernel estimates model of proposition is rewritten are as follows:
Above formula is the non-convex problem of height, in order to optimize to it, it usually needs the x and k initial from one
Start alternating iteration and updates them.
Here is the specific solution procedure of each iteration x and k:
1. x subproblem
In the more new stage of intermediate clear image gradient x, the k that last iterative estimate obtains is immobilized, then x
Problem is converted into following minimization problem:
Due to containing L in above formula0Norm | | x | |0WithTherefore it is a discrete optimization problem, tradition can not be used
Gradient descent method it is solved, and brute-force searching algorithm is too time-consuming.
Present invention introduces two auxiliary variable a and b=(bh,bv)TBe respectively intended to indicate x andbhAnd bvFor auxiliary variable
B is in first difference both horizontally and vertically point.Above formula can be rewritten are as follows:
Wherein, β and η is two positive punishment parameters, they constantly change during entire Optimization Solution.Below by way of
Fixed other two variable alternately to solve x, a and b respectively, i.e., fixed x and a solves b, and fixed x and b solves a, fixed a and b
Solve x.
Above formula is split into two mutually independent cost functions to solve:
Solution is obtained by approximation timates to be respectively as follows:
A and b that last iterative estimate obtains are immobilized, x subproblem can simplify are as follows:
Obviously, above formula is a least square problem, and the solution of its closing form is quickly obtained by Fourier transformation are as follows:
Wherein, F () and F-1() respectively indicates Fast Fourier Transform (FFT) and inverse fast Fourier transform,Indicate multiple
Adjoint operator,HereWithIt is respectively intended to indicate that horizontal and vertical single order has
Limit difference operator.
2. k subproblem
In the more new stage of fuzzy core k, the x that last iterative estimate obtains is immobilized, k subproblem is converted into as follows
Minimization problem:
Equally, above formula is a least square problem, and the solution of closing form can quickly be asked by Fourier transformation
:
After estimating fuzzy core k, apply normalization constraint and dynamic threshold constraint to it, to inhibit noise jamming
While protect fuzzy core intrinsic characteristic not to be destroyed.
∫ k (p) dxdy=1
Wherein, k (p) is the intensity in fuzzy core k at pixel p, and max (k) indicates the ash of all pixels point in fuzzy core k
Maximum value is spent, δ is a smaller positive number, and rule of thumb the present invention is set to 0.05 in all experiments, it can be with
For inhibiting the noise in fuzzy core.
Clear image and 8 realistic blur cores of the Fig. 2 for 4 width standards used in the experiment of the method for the present invention compliance test result.
Fig. 3 be directed to using the method for the present invention by 4 width clear images and 8 realistic blur karyomorphisms at 32 width fuzzy graphs
Picture, 32 fuzzy cores estimated, wherein bottom line be 8 true fuzzy cores, above 4 behavior the method for the present invention estimation
32 fuzzy cores out, the fuzzy core that can be therefrom estimated by the method for the present invention are in close proximity to true fuzzy core.
Fig. 4 be using the method for the present invention for the wherein width blur size in 32 width blurred pictures be 27 × 27 it is fuzzy
The practical restoration result of image, it can be seen that it is non-to restore image edge detailss out by the fuzzy core that the method for the present invention estimates
It is often clear.
Fig. 5 is the result restored using the method for the present invention to realistic blur image, wherein (a) figure is rich due to details
Rich (complicated Architectural fringes structure in such as figure), (c) figure due to Blur scale it is larger, will lead to most of method in this way and selecting
The performance for selecting configuration aspects performance is bad, to estimate the fuzzy core of inaccuracy；(b) figure and (d) figure are to utilize present invention side
The fuzzy core that method estimates restores clear image out.There it can be seen that working as image details rich in or Blur scale
Than it is big when, the method for the present invention is still estimated that accurate fuzzy core, to restore clearly image out.
Experiment shows that the present invention can estimate accurate fuzzy core for blurred picture, especially when image contains
When details abundant or larger Blur scale, the fuzzy core estimated by the method for the present invention is resilient more more clear than conventional method out
Clear image.
Claims (3)
1. one kind is based on mixing rank L0Regularization fuzzy core estimation method, which is characterized in that method the following steps are included:
Step 1: establishing fuzzy kernel estimates model, initial blurred picture is inputted, the fuzzy core estimated；
Step 2: restoring according to the fuzzy core of estimation to initial blurred picture, intermediate clear image is obtained；
Step 3: adjusting the value of the adaptive Dynamic gene ω in fuzzy kernel estimates model according to intermediate clear image, then use
Fuzzy kernel estimates model handles intermediate clear image, the fuzzy core estimated again；Wherein adaptive Dynamic gene
ω does not need initialization, is automatically computed using intermediate clear image and corresponding formula；
Step 4: intermediate clear image iteration obtained in the previous step is estimated into fuzzy core adjusted according to the fuzzy core of estimation
The intermediate clear image restored in meter model, and then be more clear again；
Step 5: judging whether to meet iteration termination condition；If it is not, repeating third step and the 4th step；If so, obtaining fuzzy core；
The iteration termination condition by | | ui+1-ui||2/||ui||2>=tol and β≤βmaxIt is limited jointly, it is necessary to meet simultaneously
The two conditions ability iteration terminates, and wherein i is the number of iterations, ui+1It is the restored image after i+1 time iteration, uiIt is i-th
Restored image after iteration is assigned to u using initial blurred picture as initial value as i=00；Tol is threshold value；β is one positive
Punishment parameter is continually changing in optimization process；
Step 6: fuzzy core is used in non-blind recovery frame, clear image out is restored；
The fuzzy kernel estimates model is the calculating process that an iteration updates, and carries out mixing rank L to image0Regularization constraint；
Using single order confining guard image border, second-order constraint inhibits the ringing effect of single order constraint generation；Fuzzy kernel estimates model are as follows:
Wherein, k is fuzzy core to be estimated, and u is intermediate clear image to be estimated, and ▽ u is intermediate clearly gradient,uxAnd uyFirst difference point of the respectively intermediate clear image u on the direction x and the direction y；▽ f is fuzzy
The gradient of image,fxAnd fyRespectively first difference of the blurred picture f on the direction x and the direction y point；uxxFor uxFirst difference point in the direction x, uxyFor uxIn the direction y
First difference point, uyxFor uyFirst difference point in the direction x, uyyFor uyFirst difference point in the direction y；σ is used to control
SystemWithThe relative weighting of both sparse prior regular terms, ω are an adaptive Dynamic genes, and γ is fuzzy
Core regular terms parameter, λ are image regular terms parameters, and parameter γ, λ, σ are respectively set to 0.001,0.04,1；
The intermediate clear image is the relatively clear image obtained in iterative process, is obtained with the intermediate clear image
More accurate saliency structure, so that the accuracy for improving fuzzy kernel estimates is not obtained final restored image；
Adaptive Dynamic gene ω in the fuzzy kernel estimates model is as follows:
In formula, r's (p) is defined as:
Wherein, NhIt (p) is a window area using pixel p as center size for h × h, B is blurred picture, and q is h × h window
A pixel in mouthful；When the window area of pixel p is smooth, ω becomes larger, that is, the smoothing weights applied are big；Work as pixel
There are significant image border, ω to become smaller for the window area of p, that is, the smoothing weights applied are small；To which image be adaptive selected
In large scale prominent edge, and do not destroy the bulk properties of image itself；
The solution of the intermediate clear image:
Due to containing L in above formula0Norm | | x | |0With | | ▽ x | |0, therefore be a discrete optimization problem；Wherein x and y difference
For indicating that ▽ u and ▽ f, ▽ x are used to indicate ▽2u。
2. fuzzy core estimation method according to claim 1, it is characterised in that: the solution of fuzzy kernel estimates model is to be based on
Half secondary punishment technology, specific solution procedure are as follows:
It is respectively as follows: by the solution that approximation timates obtain
Wherein, β and η is two positive punishment parameters, they constantly change during entire Optimization Solution；Auxiliary variable a and b
=(bh,bv)TIt is respectively intended to indicate x and ▽ x.
3. fuzzy core estimation method according to claim 1, it is characterised in that: the tol threshold value is set as constant
0.001；βmaxIt is set as 23。
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| CN107146202B (en) * | 2017-03-17 | 2020-05-19 | 中山大学 | Image blind deblurring method based on L0 regularization and fuzzy kernel post-processing |
| 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 |
| CN108629741B (en) * | 2018-03-26 | 2020-06-16 | 中南大学 | Fuzzy kernel estimation method based on L0 and L1 regular terms |
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