CN106204502A - Based on mixing rank L0regularization fuzzy core method of estimation - Google Patents

Abstract

The present invention proposes a kind of mixing rankL ₀Regularization fuzzy core method of estimation, feature is that fuzzy core being estimated, the middle picture rich in detail in model carries out mixing rankL ₀Regularization constraint, utilizes single order confining guard image border, the ringing effect that second-order constraint suppression single order constraint produces, restores intermediate image clearly；Then in fuzzy core estimates model, increase the self-adaptative adjustment factor of improvement, from middle picture rich in detail, extract the more prominent edge information being conducive to fuzzy core to estimate.The fuzzy core that then can solve proposition according to half Secondary variable splitting technique estimates model.The experiment that the present invention is carried out at artificial broad image and realistic blur image proves: the fuzzy core method of estimation of proposition is effective, restores the image compared with the most great representational method, and subjective vision effect and objective evaluation index are all significantly improved.

Description

Based on mixing rank L0Regularization fuzzy core method of estimation

Technical field

The present invention relates to image processing method, particularly to based on mixing rank L₀Regularization fuzzy core method of estimation.

Background technology

Image acquisition, transmit and during storage etc., due to the physical imperfection of imaging device self, external environment Change, the impact of the factor such as misoperation of operator, inevitably lead to image and degeneration fall in various degree occur Matter, this not only has a strong impact on the visual effect of image, is also substantially reduced actual application value.Then image restoration technology is just met the tendency And give birth to, and it is widely applied to the fields such as astronomical observation, medical imaging, video multimedia, criminal investigation.The most numerous figures The shortcomings such as restored method is owing to requiring that prior information is more, or it is poor to there is effect, and algorithm complex is high.To this end, effectively, soon The image recovery method of speed is still the most challenging difficult problem in image processing field.

Research shows, when the fuzzy core of broad image is known or is known in advance by some technological means, and image restoration Translate into problem of simply deconvoluting, have such issues that many methods can well solve at present, such as liftering, wiener filter Ripple, R-L method etc..But in practice, fuzzy core (i.e. point spread function) the unknown often, here it is blindly restoring image is asked Topic.Being divided into fuzzy core to estimate and picture rich in detail recovery blindly restoring image due to prior blur identification in blindly restoring image, advantage is meter Calculation amount is less, it is easy to apply in practice, obtains the extensive concern of research worker in recent years.

Fuzzy core estimation accurately is the key point of blindly restoring image, owing to significant edge beneficially fuzzy core is estimated Meter, and detail section destroys the estimation procedure of fuzzy core, the most current most fuzzy core method all can first explicit or Implicitly extract the prominent edge of image, then utilize the edge of extraction to estimate accurate fuzzy core.But when figure When picture contains the Blur scale of abundant details or bigger, the fuzzy core that current method estimates is the most undesirable, natural root Restore the image according to coarse fuzzy core and can produce ringing effect in various degree.

By analyzing, when image detail is abundant or Blur scale is bigger, existing treatment technology is: 1) apply image single The single order regularization constraint of one, causes the accurate estimation of fuzzy core；2) according to the amplitude of image border rather than yardstick carries out mould Stick with paste kernel estimates, easily the details of image is mistaken for the edge of image, causes inaccurate fuzzy core to be estimated.

Summary of the invention

For above the deficiencies in the prior art, the main object of the present invention is: contain abundant details or fuzzy chi at image When spending bigger, by mixing rank L₀Regularization constraint and the self-adaptative adjustment factor, it is possible to accurate estimation from blindly restoring image Go out fuzzy core.

Concrete technical scheme is as follows:

A kind of based on mixing rank L₀Regularization fuzzy core method of estimation, comprises the following steps:

The first step: establish fuzzy core and estimate model, input initial broad image, obtains the fuzzy core estimated.

Second step: according to the fuzzy core estimated, restore initial broad image, obtains middle picture rich in detail.

3rd step: adjust fuzzy core according to middle picture rich in detail and estimate the value of self-adaptative adjustment factor ω in model, Estimate that middle picture rich in detail is processed by model by fuzzy core again, again obtain the fuzzy core estimated；Wherein self-adaptative adjustment Factor ω need not initialization, all utilizes middle picture rich in detail and corresponding formula to automatically compute.

4th step: according to the fuzzy core estimated, middle picture rich in detail iteration obtained in the previous step is entered obscuring after adjusting Kernel estimates model restores again, and then obtains the middle picture rich in detail become apparent from.

5th step: judge whether to meet iteration termination condition；If it is not, repeat the 3rd step and the 4th step；If so, obscured Core；Described iteration termination condition by | | uⁱ⁺¹-uⁱ||₂/||uⁱ||₂>=tol and β≤β_maxJointly limit, it is necessary to simultaneously full Foot the two condition could iteration terminate, and wherein i is iterations, uⁱ⁺¹It is the restored image after i+1 time iteration, uⁱIt is i-th Restored image after secondary iteration, as i=0, is assigned to u using initial broad image as initial value⁰；Tol is threshold value；β be one just Punishment parameter, optimize during be continually changing.

6th step: fuzzy core is used for non-blind and restores in framework, restore picture rich in detail.

Described fuzzy core estimates that model is the calculating process that an iteration updates, and carries out image mixing rank L₀Regularization Constraint；Utilize single order confining guard image border, the ringing effect that second-order constraint suppression single order constraint produces.

Described middle picture rich in detail is the image the most clearly obtained in iterative process, comes with this middle picture rich in detail Acquisition saliency structure the most accurately, thus the final restored map that the accuracy improving fuzzy core estimation not obtains Picture.

Specifically, fuzzy core estimates that model is:

$(\▿u^{*},k^{*})=\underset{\▿u,k}{\arg min}\left\{\right||\▿f-\▿u\⊗k|{|}_2^2+\mathrm{\γ}\left|\right|k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}(\mathrm{\σ}\left|\right|\▿u|{|}_0+|\left|{\▿}^{2}u\right|{|}_0\left)\right\}$

Wherein, k is fuzzy core to be estimated, and u is middle picture rich in detail to be estimated,For centre gradient clearly,u_xAnd u_yIn the middle of being respectively, picture rich in detail u first difference on x direction and y direction divides.It is fuzzy The gradient of image,f_xAnd f_yIt is respectively broad image f first difference on x direction and y direction to divide.u_xxFor u_xFirst difference in x direction divides, u_xyFor u_xIn y direction one Rank finite difference, u_yxFor u_yFirst difference in x direction divides, u_yyFor u_yFirst difference in y direction divides.σ is used for controllingWithThe relative weighting of both sparse prior regular terms, ω is a self-adaptative adjustment factor, γ be fuzzy core just Then item parameter, λ is image regular terms parameter, and parameter γ, λ, σ optimal setting respectively is 0.001,0.04,1.

Specifically, described fuzzy core estimates that self-adaptative adjustment factor ω in model is as follows:

$\mathrm{\ω}=\exp (-|r\left(p\right){|}^{\frac{2}{3}})$

In formula, the definition of r (p) is:

$r\left(p\right)=\frac{\left|\right|\underset{q\∈N_h\left(p\right)}{\Σ}\∂B\left(q\right)|{|}_2}{\underset{q\∈N_h\left(p\right)}{\Σ}\left|\right|\∂B\left(q\right)|{|}_2+0.5}$

Wherein, N_h(p) be one centered by pixel p size as h × window area of h, B is broad image, and q is h A pixel in × h window.When the window area of pixel p smooths, ω becomes big, and the smoothing weights i.e. applied is big.When There is significant image border in the window area of pixel p, ω diminishes, and the smoothing weights i.e. applied is little.Thus select adaptively Select the large scale prominent edge in image, and do not destroy the bulk properties of image itself.

Specifically, the solving of middle picture rich in detail:

$x^{*}=\underset{x}{\arg \min }\left\{\right||y-x\⊗k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\left(\mathrm{\σ}\right|\left|x\right|{|}_0+\left|\right|\▿x\left|{|}_0\right)\}$

Due to containing L in above formula₀Norm | | x | |₀WithTherefore it is a discrete optimization problem；Wherein x and y divides Yong Lai not representWithIt is used for representing

Specifically, fuzzy core estimates that solving of model is that concrete solution procedure is as follows based on half secondary punishment technology:

$a^{*}=\underset{a}{\arg \min }\left\{\right||y-x*k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\mathrm{\σ}\left|\right|a\left|{|}_0\right\}$

$b^{*}=\underset{b}{\arg \min }\left\{\right||y-x*k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\left|\right|b\left|{|}_0\right\}$

The solution obtained by approximation timates is respectively as follows:

$a=\left\{\begin{array}{cc}x& |x{|}^2\≥\frac{\mathrm{\ω}\mathrm{\λ}\mathrm{\σ}}{\mathrm{\β}}\\ 0& otherwise\end{array}\right.$

$b=\left\{\begin{array}{cc}\∂x& |\∂x{|}^2\≥\frac{\mathrm{\ω}\mathrm{\λ}}{\mathrm{\η}}\\ 0& otherwise\end{array}\right.$

Wherein, β and η is two positive punishment parameters, and they are continually changing during whole Optimization Solution；Auxiliary variable A and b=(b_h,b_v)^TIt is respectively intended to represent x and x.

Specifically, described tol threshold value optimal setting is constant 0.001；β_maxOptimal setting is 2³。

The present invention is firstly introduced into the L of image gradient₀Sparse prior, enters middle picture rich in detail in fuzzy core estimates model Row mixing rank L₀Regularization constraint, utilizes single order regularization constraint to protect the edge of image, second order regularization constraint to have well The ringing effect that suppression single order constraint in effect ground produces, thus obtain intermediate image clearly.Be conducive to fuzzy according to prominent edge Kernel estimates, detail portion branch destroys the feature that fuzzy core is estimated, draws in the image regular terms weight in fuzzy core estimates model Enter self-adaptative adjustment factor ω, be used for controlling image regulation parameter λ value, make λ value become big at the smooth region of image, The adjacent edges of image diminishes, it is possible to the large scale prominent edge being adaptive selected in image, and does not destroy image itself Bulk properties.Therefore, the present invention is when image contains abundant details or Blur scale is bigger, it is possible to obtain accurate fuzzy core, This fuzzy core is used for non-blind restore under framework, can restore relatively sharp image fast and effectively.

Accompanying drawing explanation

Fig. 1, the basic framework figure of the inventive method；

The picture rich in detail of 4 width standards used by the experiment of Fig. 2, the inventive method compliance test result and 8 realistic blur cores；

Fig. 3, utilize the inventive method for the 32 width broad images become by 4 width pictures rich in detail and 8 realistic blur karyomorphisms, 32 fuzzy core estimated, wherein bottom line is 8 real fuzzy core, above 4 behavior the inventive method estimate 32 fuzzy core；

Fig. 4, utilize the inventive method for the wherein width blur size in 32 width broad images be 27 × 27 fuzzy The actual restoration result of image.

Fig. 5, utilizing the result that realistic blur image restores by the inventive method, wherein, (a) figure enriches due to details (the Architectural fringes structure as complicated in figure), (c) figure is relatively big due to Blur scale, and major part method so can be caused to select knot The performance of structure aspect performance is the best, thus estimates inaccurate fuzzy core；B () figure and (d) figure are to utilize the inventive method to estimate The fuzzy core counted out restores the picture rich in detail.

Detailed description of the invention

The present invention implements the estimation of accurate fuzzy core on multiple dimensioned framework.Multiple dimensioned framework is by resolution from low to high Multi-layer image pyramid model composition, pyramid model can effectively avoid locally optimal solution, it is ensured that finally gives Solution converges on globally optimal solution, especially in the case of fog-level is more serious.

For each layer in image pyramid model, the present invention is the mould implementing to propose on the radio-frequency component of image Stick with paste kernel estimates method.

As it is shown in figure 1, one is based on mixing rank L₀Regularization fuzzy core method of estimation, comprises the following steps:

The first step: establish fuzzy core and estimate model, input initial broad image, obtains the fuzzy core estimated.

Second step: according to the fuzzy core estimated, restore initial broad image, obtains middle picture rich in detail.

3rd step: adjust fuzzy core according to middle picture rich in detail and estimate the value of self-adaptative adjustment factor ω in model, Estimate that middle picture rich in detail is processed by model by fuzzy core again, again obtain the fuzzy core estimated；Wherein self-adaptative adjustment Factor ω need not initialization, all utilizes middle picture rich in detail and corresponding formula to automatically compute.

4th step: according to the fuzzy core estimated, middle picture rich in detail iteration obtained in the previous step is entered obscuring after adjusting Kernel estimates model restores again, and then obtains the middle picture rich in detail become apparent from.

5th step: judge whether to meet iteration termination condition；If it is not, repeat the 3rd step and the 4th step；If so, obscured Core；Described iteration termination condition by | | uⁱ⁺¹-uⁱ||₂/||uⁱ||₂>=tol and β≤β_maxJointly limit, it is necessary to simultaneously full Foot the two condition could iteration terminate, and wherein i is iterations, uⁱ⁺¹It is the restored image after i+1 time iteration, uⁱIt is i-th Restored image after secondary iteration, as i=0, is assigned to u using initial broad image as initial value⁰；Tol is threshold value；β be one just Punishment parameter, optimize during be continually changing.

6th step: fuzzy core is used for non-blind and restores in framework, restore picture rich in detail.

The final restored image that described middle picture rich in detail not obtains.

The fuzzy core estimation that this patent is carried is the process that an iteration updates, and this middle picture rich in detail is iterative process The image the most clearly of middle acquisition, obtains saliency structure the most accurately with this middle picture rich in detail, thus carries The accuracy that high fuzzy core is estimated.

The complete fuzzy core that the present invention proposes estimates that model is that the fuzzy core adding the self-adaptative adjustment factor estimates mould Type, as follows:

$(\▿u^{*},k^{*})=\underset{\▿u,k}{\arg min}\left\{\right||\▿f-\▿u\⊗k|{|}_2^2+\mathrm{\γ}\left|\right|k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}(\mathrm{\σ}\left|\right|\▿u|{|}_0+|\left|{\▿}^{2}u\right|{|}_0\left)\right\}$

Wherein, k is fuzzy core to be estimated, and u is middle picture rich in detail to be estimated.Ladder for middle picture rich in detail Degree,u_xAnd u_yIn the middle of being respectively, picture rich in detail u first difference on x direction and y direction divides.For mould Stick with paste the gradient of image,f_xAnd f_yIt is respectively broad image f first difference on x direction and y direction Point.u_xxFor u_xFirst difference in x direction divides, u_xyFor u_xIn y direction First difference divide, u_yxFor u_yFirst difference in x direction divides, u_yyFor u_yFirst difference in y direction divides.To image Single order and second-order constraint all use L₀Norm | | | |₀.σ is used for controllingWithBoth sparse prior regular terms Relative weighting, ω is a self-adaptative adjustment factor, and γ is fuzzy core regular terms parameter, and λ is image regular terms parameter, parameter γ, λ, σ optimal setting respectively is 0.001,0.04,1.

$\mathrm{\ω}=\exp (-|r\left(p\right){|}^{\frac{2}{3}})$

In formula, the definition of r (p) is:

$r\left(p\right)=\frac{\left|\right|\underset{q\∈N_h\left(p\right)}{\Σ}\∂B\left(q\right)|{|}_2}{\underset{q\∈N_h\left(p\right)}{\Σ}\left|\right|\∂B\left(q\right)|{|}_2+0.5}$

Wherein, N_h(p) be one centered by pixel p size as h × window area of h, B is broad image, B (q) For a pixel in h × h window.When the window area of pixel p is smoother, need to apply bigger smooth power Weight, i.e. ω becomes big；When the window area of pixel p exists significant image border, need to apply less smoothing weights, i.e. ω Diminish.

Expand a kind of iterative algorithm by alternating minimization based on half secondary punishment technology and solve the fuzzy of proposition Kernel estimates model.

For the convenience on describing, introduce auxiliary variable x and y is respectively intended to representWithThenIt is expressed as The fuzzy core of proposition is estimated that model is rewritten as:

$(x^{*},k^{*})=\underset{x,k}{\arg \min }\left\{\right||y-x\⊗k|{|}_2^2+\mathrm{\γ}\left|\right|k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}(\mathrm{\σ}\left|\right|x|{|}_0+||\▿x|{|}_0\left)\right\}$

Above formula is a height non-convex problem, solves to be optimized it, it usually needs from initial x and k Start alternating iteration and update them.

The concrete solution procedure of each iteration x and k be presented herein below:

1. x subproblem

In the more new stage of middle picture rich in detail gradient x, the k that last iterative estimate obtains is immobilized, then x Problem is converted into following minimization problem:

$x^{*}=\underset{x}{\arg \min }\left\{\right||y-x\⊗k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\left(\mathrm{\σ}\right|\left|x\right|{|}_0+\left|\right|\▿x\left|{|}_0\right)\}$

Due to containing L in above formula₀Norm | | x | |₀WithTherefore it is a discrete optimization problem, it is impossible to by tradition Gradient descent method it is solved, and brute-force searching algorithm is the most time-consuming.

Present invention introduces two auxiliary variables a and b=(b_h,b_v)^TBe respectively intended to represent x andb_hAnd b_vFor auxiliary variable B divides at first difference both horizontally and vertically.Above formula can be rewritten as:

$(x^{*},a^{*},b^{*})=\underset{x,a,b}{\arg \min }\left\{\begin{array}{c}\left|\right|y-x\⊗k|{|}_2^2+\mathrm{\β}||x-a|{|}_2^2+\\ \mathrm{\η}\left|\right|\▿x-b|{|}_2^2+\mathrm{\ω}\mathrm{\λ}(\mathrm{\σ}\left|\right|a|{|}_0+|\left|b\right|{|}_0\end{array}\right\}$

Wherein, β and η is two positive punishment parameters, and they are continually changing during whole Optimization Solution.Below by way of Fixing other two variable the most alternately to solve x, a and b, i.e. fixes x and a and solves b, and fixing x and b solves a, and fixing a and b asks Solve x.

Above formula splits into two separate cost functions solve:

$a^{*}=\underset{a}{\arg \min }\left\{\right||y-x*k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\mathrm{\σ}\left|\right|a\left|{|}_0\right\}$

$b^{*}=\underset{b}{\arg \min }\left\{\right||y-x*k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\left|\right|b\left|{|}_0\right\}$

Obtain solution by approximation timates to be respectively as follows:

$a=\left\{\begin{array}{cc}x& |x{|}^2\≥\frac{\mathrm{\ω}\mathrm{\λ}\mathrm{\σ}}{\mathrm{\β}}\\ 0& otherwise\end{array}\right.$

$b=\left\{\begin{array}{cc}\∂x& |\∂x{|}^2\≥\frac{\mathrm{\ω}\mathrm{\λ}}{\mathrm{\η}}\\ 0& otherwise\end{array}\right.$

Being immobilized by a and b that last iterative estimate obtains, x subproblem can be reduced to:

$x^{*}=\underset{x}{\arg \min }\left\{\right||y-x\⊗k|{|}_2^2+\mathrm{\β}\left|\right|x-a|{|}_2^2+\mathrm{\η}||\▿x-b|{|}_2^2\}$

Obviously, above formula is a least square problem, and the solution of the closing form quickly being obtained it by Fourier transformation is:

$x=F^{-1}\left(\frac{\stackrel{\‾}{F\left(k\right)}F\left(y\right)+\mathrm{\β}F\left(a\right)+{\mathrm{\ηF}}_B}{\stackrel{\‾}{F\left(k\right)}F\left(k\right)+\mathrm{\η}\stackrel{\‾}{F(\▿)}F(\▿)+\mathrm{\β}}\right)$

Wherein, F () and F^-1() represents fast Fourier transform and inverse fast Fourier transform respectively,Represent multiple Adjoint operator,HereWithIt is respectively intended to represent that horizontal and vertical single order has Limit difference operator.

2. k subproblem

In the more new stage of fuzzy core k, being immobilized by the x that last iterative estimate obtains, k subproblem is converted into as follows Minimization problem:

$k^{*}=\underset{k}{\arg \min }\left|\right|y-x\⊗k|{|}_2^2+\mathrm{\γ}|\left|k\right|{|}_2^2$

Equally, above formula is a least square problem, and the solution of its closing form quickly can be asked by Fourier transformation :

$k=F^{-1}\left(\frac{\stackrel{\‾}{F\left(x\right)}F\left(y\right)}{\stackrel{\‾}{F\left(x\right)}F\left(x\right)+\mathrm{\γ}}\right)$

After estimating fuzzy core k, it is applied normalization constraint and dynamic threshold constraint, in order in suppression noise jamming While protect fuzzy core intrinsic characteristic be not destroyed.

∫ k (p) dxdy=1

$k\left(p\right)=\left\{\begin{array}{cc}k\left(p\right)& k\left(p\right)\≥\mathrm{\δ}max\left(k\right)\\ 0& otherwise\end{array}\right.$

Wherein, k (p) is the intensity in fuzzy core k at pixel p, and max (k) represents the ash of all pixels in fuzzy core k Degree maximum, δ is a smaller positive number, and rule of thumb the present invention is set to 0.05 in all experiments, and it is permissible It is used for the noise suppressed in fuzzy core.

Fig. 2 is the picture rich in detail of 4 width standards used in the experiment of the inventive method compliance test result and 8 realistic blur cores.

Fig. 3 is to utilize the inventive method for the 32 width fuzzy graphs become by 4 width pictures rich in detail and 8 realistic blur karyomorphisms Picture, 32 fuzzy core estimated, wherein bottom line is 8 real fuzzy core, above 4 behavior the inventive method estimate 32 fuzzy core gone out, the fuzzy core that therefrom can be estimated by the inventive method is in close proximity to real fuzzy core.

Fig. 4 be utilize the inventive method for the wherein width blur size in 32 width broad images be 27 × 27 fuzzy The actual restoration result of image, it can be seen that the fuzzy core estimated by the inventive method to restore the image edge details non- The most clear.

Fig. 5 is the result utilizing the inventive method to restore realistic blur image, and wherein, (a) figure is rich due to details Rich (the Architectural fringes structure as complicated in figure), (c) figure is relatively big due to Blur scale, and major part method so can be caused to select The performance of configuration aspects performance is the best, thus estimates inaccurate fuzzy core；B () figure and (d) figure are to utilize the inventive method The fuzzy core estimated restores the picture rich in detail.There it can be seen that when image contains abundant details or Blur scale ratio Time big, the inventive method is still it is estimated that accurate fuzzy core, thus restores image clearly.

Experiment shows that the present invention is directed to broad image can estimate accurate fuzzy core, especially contains when image When abundant details or Blur scale are bigger, the inventive method the fuzzy core that estimates resilient go out more clear than traditional method Clear image.

Claims (6)

1. one kind based on mixing rank L₀Regularization fuzzy core method of estimation, it is characterised in that method comprises the following steps:

The first step: establish fuzzy core and estimate model, input initial broad image, obtains the fuzzy core estimated；

Second step: according to the fuzzy core estimated, restore initial broad image, obtains middle picture rich in detail；

3rd step: adjust fuzzy core according to middle picture rich in detail and estimate the value of self-adaptative adjustment factor ω in model, then use Fuzzy core estimates that middle picture rich in detail is processed by model, again obtains the fuzzy core estimated；The wherein self-adaptative adjustment factor ω need not initialization, all utilizes middle picture rich in detail and corresponding formula to automatically compute；

4th step: according to the fuzzy core estimated, the fuzzy core that middle picture rich in detail iteration obtained in the previous step is entered after adjusting is estimated Meter model restores again, and then obtains the middle picture rich in detail become apparent from；

5th step: judge whether to meet iteration termination condition；If it is not, repeat the 3rd step and the 4th step；If so, fuzzy core is obtained； Described iteration termination condition by | | uⁱ⁺¹-uⁱ||₂/||uⁱ||₂>=tol and β≤β_maxJointly limit, it is necessary to meet simultaneously The two condition could iteration terminate, and wherein i is iterations, uⁱ⁺¹It is the restored image after i+1 time iteration, uⁱIt it is i & lt Restored image after iteration, as i=0, is assigned to u using initial broad image as initial value⁰；Tol is threshold value；β be one positive Punishment parameter, is continually changing during optimizing；

6th step: fuzzy core is used for non-blind and restores in framework, restore picture rich in detail；

Described fuzzy core estimates that model is the calculating process that an iteration updates, and carries out image mixing rank L₀Regularization constraint； Utilize single order confining guard image border, the ringing effect that second-order constraint suppression single order constraint produces；

Described middle picture rich in detail is the image the most clearly obtained in iterative process, obtains with this middle picture rich in detail Saliency structure the most accurately, thus the final restored image that the accuracy improving fuzzy core estimation not obtains.

Fuzzy core method of estimation the most according to claim 1, it is characterised in that fuzzy core estimates that model is:

$(\▿u^{*},k^{*})=\underset{\▿u,k}{\arg \min }\left\{\right||\▿f-\▿u\⊗k|{|}_2^2+\mathrm{\γ}\left|\right|k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}(\mathrm{\σ}\left|\right|\▿u|{|}_0+|\left|{\▿}^{2}u\right|{|}_0\left)\right\}$

Wherein, k is fuzzy core to be estimated, and u is middle picture rich in detail to be estimated,For centre gradient clearly,u_xAnd u_yIn the middle of being respectively, picture rich in detail u first difference on x direction and y direction divides；It is fuzzy The gradient of image,f_xAnd f_yIt is respectively broad image f first difference on x direction and y direction to divide；u_xxFor u_xFirst difference in x direction divides, u_xyFor u_xIn y direction one Rank finite difference, u_yxFor u_yFirst difference in x direction divides, u_yyFor u_yFirst difference in y direction divides；σ is used for controllingWithThe relative weighting of both sparse prior regular terms, ω is a self-adaptative adjustment factor, γ be fuzzy core just Then item parameter, λ is image regular terms parameter, and parameter γ, λ, σ optimal setting respectively is 0.001,0.04,1.

Fuzzy core method of estimation the most according to claim 1 and 2, it is characterised in that described fuzzy core is estimated in model Self-adaptative adjustment factor ω as follows:

$\mathrm{\ω}=\exp (-|r\left(p\right){|}^{\frac{2}{3}})$

In formula, the definition of r (p) is:

$r\left(p\right)=\frac{\left|\right|\underset{q\∈N_h\left(p\right)}{\Σ}\∂B\left(q\right)|{|}_2}{\underset{q\∈N_h\left(p\right)}{\Σ}\left|\right|\∂B\left(q\right)|{|}_2+0.5}$

Wherein, N_h(p) be one centered by pixel p size as h × window area of h, B is broad image, and q is h × h window A pixel in Kou；When the window area of pixel p smooths, ω becomes big, and the smoothing weights i.e. applied is big；Work as pixel There is significant image border in the window area of p, ω diminishes, and the smoothing weights i.e. applied is little；Thus it is adaptive selected image In large scale prominent edge, and do not destroy the bulk properties of image itself.

Fuzzy core method of estimation the most according to claim 1 and 2, it is characterised in that solving of middle picture rich in detail:

$x^{*}=\underset{x}{\arg \min }\left\{\right||y-x\⊗k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\left(\mathrm{\σ}\right|\left|x\right|{|}_0+\left|\right|\▿x\left|{|}_0\right)\}$

Due to containing L in above formula₀Norm | | x | |₀WithTherefore it is a discrete optimization problem；Wherein x and y is respectively intended to RepresentWith It is used for representing

Fuzzy core method of estimation the most according to claim 1, it is characterised in that: fuzzy core estimate model solve be based on Half secondary punishment technology, concrete solution procedure is as follows:

$a^{*}=\underset{a}{\arg \min }\left\{\right||y-x*k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\mathrm{\σ}\left|\right|a\left|{|}_0\right\}$

$b^{*}=\underset{b}{\arg \min }\left\{\right||y-x*k|{|}_2^2+\mathrm{\ω}\mathrm{\λ}\left|\right|b\left|{|}_0\right\}$

The solution obtained by approximation timates is respectively as follows:

$a=\left\{\begin{array}{cc}x& |x{|}^2\≥\frac{\mathrm{\ω}\mathrm{\λ}\mathrm{\σ}}{\mathrm{\β}}\\ 0& otherwise\end{array}\right.$

$b=\left\{\begin{array}{cc}\∂x& |\∂x{|}^2\≥\frac{\mathrm{\ω}\mathrm{\λ}}{\mathrm{\η}}\\ 0& otherwise\end{array}\right.$

Wherein, β and η is two positive punishment parameters, and they are continually changing during whole Optimization Solution；Auxiliary variable a and b =(b_h,b_v)^TBe respectively intended to represent x and

Fuzzy core method of estimation the most according to claim 1, it is characterised in that: described tol threshold value optimal setting is normal Several 0.001；β_maxOptimal setting is 2³。