CN104392415A - Image restoration method in combination with weight factor and gradient restriction - Google Patents

Abstract

The invention discloses an image restoration method in combination with a weight factor and gradient restriction. The image restoration method comprises the steps of (1) mathematically deducing and establishing an image restoration model by uniting a Bayes frame and image relevant characteristics, (2) designing a weight factor coefficient matrix, and (3) optimizing and obtaining the optimal restored image. The image restoration method in combination with the weight factor and the gradient restriction is characterized in that the requirements of signal fidelity and detail retention in image restoration are taken into account, an image restoration cost function on the basis of energy minimization is provided from the perspective of Bayes conditional probability according to the ideas of high fidelity and good detail retention, the image restoration model is established, and finally, the optimal solution of image restoration can be obtained by virtue of deduction optimization. According to the image restoration method, an observation blurred noise image is input and a corresponding degenerate function is provided, and then an excellent restoration result can be obtained quickly. The image restoration method in combination with the weight factor and the gradient restriction is applicable to processing, such as deblurring, denoising and the like, images of visible light, infrared and the like, and capable of realizing image restoration quickly.

Description

A kind of image recovery method restricted in conjunction with weight factor and gradient

Technical field

The present invention relates to computer image processing technology, particularly relate to a kind of image recovery method restricted in conjunction with weight factor and gradient.

Background technology

In daily imaging with photography, people often can run into the not enough situation of illumination, and this just needs to want prolonging exposure time.The negative effect of the prolongation of time shutter be handheld camera shake cause image blurring.For obtaining image clearly, the method that people commonly use includes and opens flashlamp, improves camera light sensitivity or Bian tripod, the object of certain first two method is to shorten the time shutter to reduce to shake the impact caused, but flashlamp causes scenery tonal variation, light sensitivity adjustment can introduce more noises, and tripod too heaviness seldom carry.In present slr camera, adopt eyeglass compensation way more, but cost is very large.And adopt algorithm software mode to carry out Recovery image to realize deblurring and restraint speckle, be then cost low, have the thing that can accomplish, therefore its research is also relatively very popular.

Postprocessing technique after analysis obtains degenrate function is called non-blind image deconvolution.Non-blind image deconvolution is the inverse process of a two-dimensional convolution computing, and it is an ill-conditioning problem.In Postprocessing technique, due to the existence of noise and Gibbs' effect, restoration result will be subject to the impact of noise and ring response, and this is inevitable.Conventional method is the character according to Fourier transform as direct liftering, the convolution relation in spatial domain is converted into the dot product relation in frequency domain; To the image that is restored, only the Fourier transform results of the Fourier transform results of blurred picture and degenrate function need be divided by and be done inverse fourier transform.Although the method is simple, seriously, thus its application is subject to great restriction for the noise comprised in normally result and ringing effect.In addition, although the recovery algorithms effect of a large amount of belt restrainings is fine, travelling speed is not good enough.Therefore, the travelling speed of recovery algorithms and efficiency are also problems needing to consider, usual way efficiency is not high, run slow, and are difficult to application.So, need the image recovery method that development efficiency is high, effect is good.

Summary of the invention

The present invention proposes a kind of image recovery method restricted in conjunction with weight factor and gradient, is a kind of non-blind image recovery method.

The image recovery method main thought that exploitation right repeated factor of the present invention and gradient restrict is:

1, in conjunction with Bayesian frame and image correlated characteristic, mathematically derive and set up Image restoration

Usually, image degradation model is Y=h*X+n, and wherein Y is the observed image of input, and X is ideal image, and * is convolution symbol, and n is additive Gaussian noise, and h is blur degradation function-as point spread function.Generally, above formula can simply be write vector and matrix form by us, is Y=HX+n, and H corresponds to h, is circular matrix.

Need to remove fuzzy and restraint speckle from observed image Y, recover ideal image X.According to bayesian theory, use maximization posterior probability to be equivalent to the mathematical principle minimizing cost function, cost function/penalty that construct image is recovered, and modeling is carried out to the various piece of cost function, to facilitate follow-up global optimization.

For structure cost function, first consider must be minimum, namely noise energy is minimum, in this || || ₂represent second order norm; Secondly, be auxiliary recovery detailed information, adopt the mode of gradient constraint, so also must be minimum, for difference operator, such as can be the horizontal difference operator of single order, for the vertical difference operator of single order etc., how much it can determine according to practical matter; Finally, for suppressing the ringing ripples that produces in rejuvenation and noise, structure weight factor matrix of coefficients M _i, constraint gradient, so must make minimum, for different difference operators different M can be had _i.

Finally, the cost function of the Image restoration that construction complete restricts in conjunction with weight factor and gradient, $J\left(X\right)=\arg {\min }_X{\left|\right|Y-\mathrm{HY}\left|\right|}_2^2+\mathrm{\λ\Σ}{\left|\right|{\left({\∂}_{i}X\right)}_{M_i}\left|\right|}_2^2,$ Establish Image restoration.

2, optimize and ask for optimal recovery image.

According to the cost function equation of J (X) this Restoration model, we can utilize Suzanne Lenglen day theorem, to X carry out partial differential ask extreme value and order be 0, namely thus structure and acquisition optimization method, finally ask for the optimum solution meeting cost function.

Here the optimum solution obtained is the optimal result of Postprocessing technique.

In conjunction with the image recovery method that weight factor and gradient restrict, comprise the steps:

(1), derive and set up Image restoration

According to bayesian probability model, from this degradation model of Y=HX+n, the thinking obtaining best X is guided to be probability X=arg max p (X/Y) that satisfies condition.According to Bayes' theorem, there is p (X/Y) ∝ p (Y/X) p (X), so X=arg max p (Y/X) p (X).

For structure cost function, first consider must be minimum, namely noise energy is minimum, in this || || ₂represent second order norm.So, namely energy is minimum corresponds to maximum probability, namely $J_1\left(X\right)={\left|\right|Y-\mathrm{HY}\left|\right|}_2^2=-\ln p(Y/X);$

In addition, be auxiliary recovery detailed information, adopt the mode of gradient constraint, so also must be minimum, for difference operator, such as can be the horizontal difference operator of single order, for the vertical difference operator of single order etc., how much it can determine according to practical matter; Finally, for suppressing the ringing ripples that produces in rejuvenation and noise, structure weight factor matrix of coefficients M _i, constraint gradient, so must make minimum, for different difference operators different M can be had _i.So have $J_2\left(X\right)=\mathrm{\Σ}{\left|\right|{\left({\∂}_{i}X\right)}_{M_i}\left|\right|}_2^2=-\ln p\left(X\right).$

So X=arg max p (Y/X) p (X) is maximum probability, minimum corresponding to energy, then correspond to following formula:

$X=\arg {\min }_{X}J\left(X\right)=\arg {\min }_X[J_1\left(X\right)+\mathrm{\λ}{J}_2\left(X\right)]=\arg {\min }_X{\left|\right|Y-\mathrm{HX}\left|\right|}_2^2+\mathrm{\λ\Σ}{\left|\right|{\left({\∂}_{i}X\right)}_{M_i}\left|\right|}_2^2$

λ is Regularization coefficient, and in order to balance two, front and back, last item signal fidelity, latter one is Hemifusus ternatanus degree.

(2), weight factor matrix of coefficients is designed

Mention in step 1, for different difference operators different M can be had _i.In common model, at least adopt two class difference operators, i.e. the horizontal operator of single order [1-1] and the vertical operator [1 of single order;-1], we write a Chinese character in simplified form into with .So design weight factor matrix of coefficients is:

wherein α and ε is two constant parameter, and the former is for controlling the degree of graded, and the latter is in order to prevent the generation of morbid state.

If there is other difference operator to introduce, also more weight factor matrix of coefficients M can be designed by similar method.

(3), optimize and ask for optimal recovery image

Cost function equation for Restoration model is:

$X=\arg {\min }_{X}J\left(X\right)=\arg {\min }_X{\left|\right|Y-\mathrm{HX}\left|\right|}_2^2+\mathrm{\λ\Σ}{\left|\right|{\left({\∂}_{i}X\right)}_{M_i}\left|\right|}_2^2,$

According to Lagrange's theorem, best X meets following formula:

$\frac{\∂J\left(X\right)}{\∂X}=0$

Can X be solved thus, namely meet following formula:

$\frac{\∂\left\{{(Y-\mathrm{HX})}^T(Y-\mathrm{HX})\right\}}{\∂X}+\mathrm{\λ}\frac{\∂\left\{\mathrm{\Σ}\left({\left({\∂}_{i}X\right)}^T{M}_i\left({\∂}_{i}X\right)\right)\right\}}{\∂X}=0$

So, according to matrix and differential of vector principle, acquisition of finally deriving:

$[H^{T}H+\mathrm{\λ\Σ}\left({\∂}_i^T{M}_i{\∂}_i\right)]X=H^{T}Y,$

Namely optimum solution X is: $X=[{[H^{T}H+\mathrm{\λ\Σ}\left({\∂}_i^T{M}_i{\∂}_i\right)]}^{-1}{H}^{T}Y,$

Here the X obtained is best Postprocessing technique result.

The inventive method considers the requirement of signal fidelity and Hemifusus ternatanus degree in Postprocessing technique, the thinking high according to fidelity, Hemifusus ternatanus degree is good, the Postprocessing technique cost function based on energy minimization is proposed from the angle of Bayes's conditional probability, construct Image restoration, by the acquisition optimized and finally realize Postprocessing technique optimum solution of deriving.In the methods of the invention, input a width observation fuzzy noise image, and provide corresponding degenrate function, extraordinary restoration result can be obtained fast.The inventive method can be applicable to visible ray, the process such as image deblurring, denoising such as infrared, realizes Postprocessing technique fast.

Accompanying drawing explanation

Fig. 1 is the operating process block diagram of the inventive method;

Fig. 2 a is the former figure that embodiment tests a width figure used;

Fig. 2 b is the recovery figure that embodiment tests a width figure used.

Embodiment

Fuzzy noise degraded image is used directly to test the validity of this algorithm as specific experiment object.

Utilize the inventive method process image, as shown in Figure 1, input former figure (fuzzy noise Degenerate Graphs), can be restored image.For Fig. 2 a:

If Fig. 2 a is Y, need to obtain recovery figure X.

According to the cost function of the Image restoration set up, the equation asking for X meets:

$\begin{array}{c}X=\arg {\min }_{X}J\left(X\right)\\ =\arg {\min }_X{\left|\right|Y-\mathrm{HY}\left|\right|}_2^2+\mathrm{\λ\Σ}{\left|\right|{\left({\∂}_{i}X\right)}_{M_i}\left|\right|}_2^2\end{array}$

λ is Regularization coefficient, and in order to balance two, front and back, last item signal fidelity, latter one is Hemifusus ternatanus degree.

For this embodiment, we adopt two class difference operators, i.e. the horizontal operator of single order [1-1] and the vertical operator [1 of single order;-1], we write a Chinese character in simplified form into with .So design weight factor matrix of coefficients is:

wherein α and ε is two constant parameter, and the former is for controlling the degree of graded, and the latter is in order to prevent the generation of morbid state.

According to Lagrange's theorem, best X meets following formula:

$\frac{\∂J\left(X\right)}{\∂X}=0$

Can X be solved thus, namely meet following formula:

$\frac{\∂\left\{{(Y-\mathrm{HX})}^T(Y-\mathrm{HX})\right\}}{\∂X}+\mathrm{\λ}\frac{\∂\left\{\mathrm{\Σ}\left({\left({\∂}_{i}X\right)}^T{M}_i\left({\∂}_{i}X\right)\right)\right\}}{\∂X}=0$

So, according to matrix and differential of vector principle, acquisition of finally deriving:

$[H^{T}H+\mathrm{\λ\Σ}\left({\∂}_i^T{M}_i{\∂}_i\right)]X=H^{T}Y,$

Namely optimum solution X is: $X=[{[H^{T}H+\mathrm{\λ\Σ}\left({\∂}_i^T{M}_i{\∂}_i\right)]}^{-1}{H}^{T}Y,$

Here the X obtained is best Postprocessing technique result, so Fig. 2 b (being X) that is restored.

Contrast former figure, find to utilize the method effectively can realize Postprocessing technique.

At Intel double-core 2.7Ghz, under inside saving as the operating environment of 2G, for this 512 × 512 image, working time is about 200ms, and efficiency is high.

Claims (1)

1., in conjunction with the image recovery method that weight factor and gradient restrict, it is characterized in that, comprise the steps:

(1) derive and set up Image restoration

If Y is the observed image of input, X is the ideal image needing to obtain; So from Bayes' theorem, maximize according to conditional probability and be equal to energy minimization, devising Restoration model cost function is J (X), obtains best X and namely meets formula: X=argmin _xj (X);

(2) weight factor matrix of coefficients is designed

Cost function equation for the Image restoration in (1) is:

$J\left(X\right)=\arg m{\mathrm{in}}_X{\left|\right|Y-\mathrm{HX}\left|\right|}_2^2+\mathrm{\λ\Σ}{\left|\right|{\left({\∂}_{i}X\right)}_{M_i}\left|\right|}_2^2$

λ is Regularization coefficient, and H is circular matrix;

For suppressing the ringing ripples that produces in rejuvenation and noise, the weight factor matrix of coefficients Mi of structure is used for retraining gradient, for different difference operators there is different M _i(i=1,2...);

For different difference operators different M can be had _i; In common model, at least adopt two class difference operators (i=1,2), i.e. the horizontal operator of single order [1-1] and the vertical operator [1 of single order;-1], we write a Chinese character in simplified form into with namely here so design weight factor matrix of coefficients is: wherein α and ε is two constant parameter, and the former is for controlling the degree of graded, and the latter is in order to prevent the generation of morbid state;

(3) optimize and ask for optimal recovery image

Cost function equation for Restoration model is:

$X=\arg m{\mathrm{in}}_{X}J\left(X\right)={\arg \min }_X{\left|\right|Y-\mathrm{HX}\left|\right|}_2^2+\mathrm{\λ\Σ}{\left|\right|{\left({\∂}_{i}X\right)}_{M_i}\left|\right|}_2^2,$

According to Lagrange's theorem, best X meets following formula:

$\frac{\∂J\left(X\right)}{\∂X}=0$

Can X be solved thus, namely meet following formula:

$\frac{\∂\left\{{(Y-\mathrm{HX})}^T(Y-\mathrm{HX})\right\}}{\∂X}+\mathrm{\λ}\frac{\∂\left\{\mathrm{\Σ}\left({\left({\∂}_{i}X\right)}^T{M}_i\left({\∂}_{i}X\right)\right)\right\}}{\∂X}=0$

So, according to matrix and differential of vector principle, acquisition of finally deriving:

$[H^{T}H+\mathrm{\λ}\mathrm{\Σ}\left({\∂}_i^T{M}_i{\∂}_i\right)]X=H^{T}Y,$

Namely optimum solution X is: $X=[[H^{T}H+\mathrm{\λ}\mathrm{\Σ}\left({\∂}_i^T{M}_i{\∂}_i\right){]}^{-1}{H}^{T}Y,$

Here the X obtained is best Postprocessing technique result, T representing matrix transposition.