CN103559684A - Method for restoring images based on smooth correction - Google Patents

Abstract

The invention discloses a method for restoring images based on smooth correction. The method includes the steps that noisy images are input, the similarity of elements x to be processed and reference pixels y in a search area is calculated, and weights of all reference pixel points in the search area are obtained; weighted averaging is conducted on all the pixel points in the search area according to the calculated weights of all the reference pixels in the search area to obtain gray values of the corrected pixel points; after all the pixels in the noisy images are processed, the gray values of the corrected pixel points are utilized to replace gray values of the pixel points in the noisy images to obtain observation images; an estimated state equation and an observation equation of the images are built, and a two-dimensional block Kalman filter and front feedback smoothing method is utilized to denoise the observation images to obtain the denoising images. According to the method for restoring the images, after an estimated value of a true value at the n+1 position is obtained, the estimated value at the position before the n+1 position is corrected through the smooth and feedback thought, and the restored quality of the images can be improved on the premise that calculation complexity is not increased.

Description

Image recovery method based on level and smooth correction

Technical field

The invention belongs to Computer Image Processing field, particularly a kind of image recovery method based on level and smooth correction.

Background technology

Digital picture can be subject to the pollution of noise in the process that gathers, changes and transmit.It is one of main contents of Computer Image Processing that image recovers (recovery), and it is degradation phenomena that its object is to eliminate or alleviate the image quality decline causing in Image Acquisition and transmitting procedure, the true colours of Recovery image.

Traditional denoising method roughly can be divided into two classes, and a class is the method based on spatial domain, and a class is the method based on transform domain.In the denoising method of spatial domain, more classical method has gaussian filtering, medium filtering, bilateral filtering etc.The method in spatial domain is all directly the gray scale of image to be processed.The method of transform domain is all that image is changed, as Fourier transform, and wavelet transformation, bent wave conversion, profile wave convert etc.

Kalman (Kalman) filtering is an optimization autoregression data processing algorithm, and the most outstanding advantage is to process in real time fast problem.It is widely used in robot navigation, control, Data Fusion of Sensor, and even radar system and the guided missile of military aspect are followed the trail of etc.More be applied in recent years Computer Image Processing as image denoising, image restoration, recognition of face, image are cut apart, Image Edge-Detection etc.When traditional Kalman filtering is processed for image, just by the observation information at n place, position, position n+1 is estimated, then by the observation information at n+1 place, actual value is upgraded.Defect is that the observation information of n+1 and follow-up location is not by n and reference by location in the past.The present invention uses for reference the thought of feedback, after the estimated value of actual value that has obtained n+1 position, by thought level and smooth and feedback, the estimated value of anterior locations is corrected.Improvement based on level and smooth can improve the quality that image recovers under the prerequisite that does not increase computation complexity.

And Kalman filtering effect relies on very large to observed image used, observed image used is better, and Kalman filtering is better for the recovery effects of image.In order to obtain good observed image, first take a kind of denoising method of non-local mean to carry out pre-service to image, obtain high-quality observed image.The essential idea of NLM is in entire image, to find more reference point, has good denoising performance.But still there is to a certain degree fuzzy in the edge of image and details.In order to preserve good marginal information characteristic, similarity is redefined.A little micro-slip window L and overall window O have been set, at local window, by method that can keep the edge information characteristic, calculate weights, in O-L (be illustrated in overall window, and outside micro-slip window) with block-based similarity measurement, calculate weights.This improvement fully combines Bao Bian and overall thought, can either keep the edge information characteristic, can find again plurality object reference block.

Summary of the invention

The problems referred to above that exist in image recovery process for legacy card Kalman Filtering, the invention provides a kind of improved Kalman filter image restoration technology based on local smoothing method, first use a kind of non-local mean algorithm to carry out pre-service to original image, using the high quality graphic obtaining as observed image, then by improved Kalman filtering, image is processed.

Image recovery method based on level and smooth correction provided by the invention, comprises the following steps:

S1, input noisy image, using the noisy image inputted as overall window O, set a micro-slip window L(centered by pending pixel x as shown in Figure 2); Calculate pending element x in this noisy image and the similarity of the reference pixel y in Search Area, obtain the weights of all reference image vegetarian refreshments in Search Area

$w(x,y)=\left\{\begin{array}{cc}{w}_1(x,y)& y\∈L\\ w_2(x,y)& y\∈O-L\end{array}\right.$

Wherein, O-L is illustrated in overall window, but the region in micro-slip window not, weight w ₁(x, y) represents to be positioned at the reference pixel y of micro-slip window and the similarity of pending pixel x; Weight w ₂(x, y) represents to be positioned at outside micro-slip window, but reference pixel y in overall window and the similarity of pending pixel x; This weight w (x, y) meets: 0≤w (x, y)≤1, ∑ _{y ∈ O}w (x, y)=1.

Above-mentioned weight w ₁the formula of (x, y) is:

$w_1(x,y)=\frac{1}{2Z_1}{g}_{{\mathrm{\σ}}_{s,y}}\left({\left|\right|x-y\left|\right|}_2\right)*g_{{\mathrm{\σ}}_{r,y}}(I\left(x\right)-I\left(y\right))$

In formula, I (x) and I (y) represent to be positioned at the grey scale pixel value at x and y place,

σ _s,yand σ _r,yrespectively the coefficient in spatial domain and gray scale territory, ‖ ‖ ₂represent l ₂norm, Z ₁it is normalization coefficient

$Z_1={\mathrm{\Σ}}_{y\∈L}{g}_{{\mathrm{\σ}}_{s,y}}\left({\left|\right|x-y\left|\right|}_2\right)*g_{{\mathrm{\σ}}_{s,y}}(I\left(x\right)-I\left(y\right)).$

Above-mentioned weight w ₂the formula of (x, y) is:

$w_2(x,y)=\frac{1}{2Z_2}\exp (-\frac{{\left|\right|v\left(x\right)-v\left(y\right)\left|\right|}^2}{h^2})$

In formula, v (x) and v (y) represent respectively with x, the image block that the size centered by y is n*n; H smoothly controls parameter, h=kn δ ₀; δ ₀it is the standard deviation of image institute Noise; K is constant, in experiment, often gets between 0.5～2; Z ₂normalization coefficient,

$Z_2={\mathrm{\Σ}}_{y\∈O-L}\exp (-\frac{{\left|\right|v\left(x\right)-v\left(y\right)\left|\right|}^2}{h^2}).$

In the Search Area that S2, basis calculate, the weights of all reference pixels, are weighted on average all pixels in Search Area, obtain the revised gray-scale value of pixel

I′(x)=∑ _y∈OI(y)w(x，y)。

S3, with step S1, S2, handle in noisy image after all pixels, with the gray-scale value (being the gray-scale value that weighting obtains) of pixel after revising, replace the gray-scale value of pixel in noisy image, obtain high-quality observed image;

S4, state variable are made as the pixel value of image, set up Kalman state equation and observation equation that observed image is estimated, adopt conventional two-dimensional piece Kalman filtering method to go dry processing to observed image; Then, by front feedback smoothing method, image is carried out to smoothing processing, by the estimated value of the actual value of current block image, the estimated value of piece image is above corrected, the image after smoothing processing is last removal noise image.

In above-mentioned steps S4, selection rectangular area is as shown in Figure 3 as processing unit, and the state equation of observed image and observation equation are respectively:

Y(n)=MX(n)+ε(n)

Wherein, X (n) and X (n+1) are adjacent image blocks, the image block in Y (n) observed image;

be state-transition matrix, reacted the relation between adjacent image piece,

M is observing matrix, the relation between reaction true picture and observed image;

δ (n+1) is system noise, and ε (n) is observation noise, is generally additive white noise.

According to the state equation of above-mentioned observed image and observation equation, obtain state vector predictive equation and observation renewal equation, they respectively:

$\hat{X}(n+1|n+1)=\hat{X}(n+1|n)+K(n+1)\·{\{Y(n+1)-M\hat{X}(n+1|n)\}}^{-1}$

In formula,

to have obtained the estimation to the actual value of n+1 piece image after the observed reading of n piece image,

be the estimated value having obtained after the actual value of n+1 piece image being upgraded after the observed reading of n+1 piece image, K (n+1) is kalman gain.

For predicted picture better, and then before adopting, feedback smoothing method carries out smoothing processing to image.The front feedback smoothing equation that this front feedback smoothing method represents based on following formula:

In formula,

the estimated value having obtained after the actual value of n piece image being upgraded after the observed reading of n piece image,

be the estimated value having obtained after level and smooth to the actual value of n piece image after the observed reading of n+1 piece image, P (n+1|n) is prior estimate covariance matrix, and P (n|n) is posteriority estimate covariance matrix.

The size of above-mentioned micro-slip window L is set to 5 * 5, and 7 * 7,9 * 9 all can.

The present invention can better keep and recover edge and the texture of natural image in pre-service.Fully combine Bao Bian and overall thought, can either keep the edge information characteristic, can find again plurality object reference block.

The present invention uses for reference the thought of feedback traditional Kalman filtering is improved, adopt conventional two-dimensional piece Kalman filtering and front feedback smoothing method to go dry processing to observed image, after the estimated value of actual value that has obtained n+1 position, by thought level and smooth and feedback, the estimated value of anterior locations is corrected.

The present invention is based on level and smooth image recovery method and can under the prerequisite that does not increase computation complexity, improve the quality that image recovers.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of a kind of image recovery method based on level and smooth correction of the present invention;

Fig. 2 is that the micro-slip window and the overall window that in image pre-service, adopt are divided schematic diagram;

Fig. 3 is Kalman's image block of dividing in concrete enforcement, and the pixel in each image block and the how mobile schematic diagram of image block.

Embodiment

Below in conjunction with accompanying drawing to the detailed description of the invention.

With reference to process flow diagram 1, the concrete steps of the image recovery method based on level and smooth correction are as follows:

Step 1, digital picture is gathering, and what in transmitting procedure, because being interfered, obtain is not often desirable image, but containing noisy image.Iteration selects element in noisy image as pending element.Window is divided as shown in Figure 2, usings the noisy image inputted as overall window O, sets a micro-slip window L centered by pending pixel x in overall window O.

Step 2, calculates pending element x in the noisy image of input and the similarity of the reference pixel y in Search Area, obtains the weights of all reference image vegetarian refreshments in Search Area

$w(x,y)=\left\{\begin{array}{cc}{w}_1(x,y)& y\∈L\\ w_2(x,y)& y\∈O-L\end{array}\right.$

Wherein, O-L is illustrated in overall window O, but the region in micro-slip window L not; Search Area comprises region in micro-slip window L and is positioned at overall window but not in the region of micro-slip window L.

Above-mentioned weight w ₁(x, y) represents to be positioned at the reference pixel y of micro-slip window and the similarity of pending pixel x, and computing formula is as follows:

$w_1(x,y)=\frac{1}{2Z_1}{g}_{{\mathrm{\σ}}_{s,y}}\left({\left|\right|x-y\left|\right|}_2\right)*g_{{\mathrm{\σ}}_{r,y}}(I\left(x\right)-I\left(y\right))$

In formula, I (x) and I (y) represent to be positioned at the grey scale pixel value at x and y place,

σ _s,yand σ _r,yrespectively the coefficient in spatial domain and gray scale territory, ‖ ‖ ₂represent l ₂norm, Z ₁it is normalization coefficient

$Z_1={\mathrm{\Σ}}_{y\∈L}{g}_{{\mathrm{\σ}}_{s,y}}\left({\left|\right|x-y\left|\right|}_2\right)*g_{{\mathrm{\σ}}_{s,y}}(I\left(x\right)-I\left(y\right)).$

Above-mentioned weight w ₂(x, y) represents to be positioned at outside micro-slip window, but reference pixel y in overall window and the similarity of pending pixel x, computing formula is as follows:

$w_2(x,y)=\frac{1}{2Z_2}\exp (-\frac{{\left|\right|v\left(x\right)-v\left(y\right)\left|\right|}^2}{h^2})$

In formula, v (x) and v (y) represent respectively with x, the image block that the size centered by y is n * n; H smoothly controls parameter, h=kn δ ₀; δ ₀be the standard deviation of image institute Noise, k is constant, in experiment, often gets between 0.5～2; Z ₂it is normalization coefficient

$Z_2=\underset{y\∈O-L}{\mathrm{\Σ}}\exp (-\frac{{\left|\right|v\left(x\right)-v\left(y\right)\left|\right|}^2}{h^2})$

Above-mentioned weight w (x, y) meets: 0≤w (x, y)≤1, ∑ _{y ∈ O}w (x, y)=1.

Step 3, according to the weights of all pixels in the Search Area calculating, is weighted on average all pixels in Search Area, obtains the revised gray-scale value of pixel

I′(x)=∑ _y∈OI(y)w(x，y)。

Step 4, gets back to step 1 and reselects pending element, until all processes pixel in noisy image are complete.After handling all pixels, with the gray-scale value I ' of pixel after revising, (x) replace the gray-scale value of pixel in the noisy image of inputting, obtain high-quality observed image.

Step 5, sets up Kalman state equation and observation equation for image denoising.

This method adopts two-dimensional block kalman filter method to carry out denoising to pending image.When utilizing two-dimensional block kalman filter method to process the noise problem of image, first need to set up the system model of image.According to the attribute of Kalman filter theory and image self, and the mode of computing machine processing image, adopt with the following method:

Image is carried out to piecemeal (every block size is 3 * 3).Pixel as shown in Figure 3 and vector space relation are the schematic diagram of piece Kalman filtering, wherein K _ithe width that represents each piece, K _jthe height that represents each piece, i, j denotation coordination axle, in Fig. 3, each bulk is comprised of 9 fritters, and each fritter represents the vector that 4 pixels form.Selecting the iterative window size of piece Kalman filtering is L=66(L=K _ik _j), definition X _i,j(n) and X (n) be respectively 41 and the vector of L1, wherein x _i,j(n) be that coordinate is the gray-scale value that (i, j) locates pixel, the locus " n " of vectorial X (n) wherein represents the n time corresponding locus of iteration in Kalman's iterative filtering, and the concrete form of the composition is as follows:

$\begin{array}{c}{X_{\mathrm{1,1}}\left(n\right)=x_{\mathrm{1,1}}\left(n\right),x_{2,1}\left(n\right),x_{\mathrm{1,2}}\left(n\right),x_{\mathrm{2,2}}\left(n\right)}^T\\ {X_{\mathrm{2,1}}\left(n\right)=x_{\mathrm{3,1}}\left(n\right),x_{\mathrm{4,1}}\left(n\right),x_{\mathrm{3,2}}\left(n\right),x_{\mathrm{4,2}}\left(n\right)}^T\\ {X_{\mathrm{3,1}}\left(n\right)=x_{\mathrm{5,1}}\left(n\right),x_{\mathrm{6,1}}\left(n\right),x_{\mathrm{5,2}}\left(n\right),x_{\mathrm{6,2}}\left(n\right)}^T\\ X_{\mathrm{1,2}}\left(n\right)=x_{\mathrm{1,3}}\left(n\right),x_{\mathrm{2,3}}\left(n\right),x_{\mathrm{1,4}}\left(n\right),x_{\mathrm{2,4}}\left(n\right)\\ {X_{\mathrm{2,2}}\left(n\right)=x_{\mathrm{3,3}}\left(n\right),x_{\mathrm{4,3}}\left(n\right),x_{\mathrm{3,4}}\left(n\right),x_{\mathrm{4,4}}\left(n\right)}^T\\ \·\\ \·\\ \·\\ {X_{\mathrm{3,3}}\left(n\right)=x_{\mathrm{5,5}}\left(n\right),x_{\mathrm{6,5}}\left(n\right),x_{\mathrm{5,6}}\left(n\right),x_{\mathrm{6,6}}\left(n\right)}^T\\ {X\left(n\right)=X_{\mathrm{1,1}}^T\left(n\right),X_{\mathrm{2,1}}^T\left(n\right),X_{\mathrm{3,1}}^T\left(n\right),X_{\mathrm{1,2}}^T\left(n\right),X_{\mathrm{2,2}}^T\left(n\right),\·\·\·,X_{\mathrm{3,3}}^T\left(n\right)}^T\end{array}$

Set up state equation as follows and observation equation,

Y(n)=MX(n)+ε(n)

Wherein,

and M is according to the matrix of the corresponding size that in image, the relation between each pixel is chosen.Y (n) is illustrated in the observed reading at n place, position, and ε (n) is for measuring noise.The form of Y in observation equation (n) is identical with X (n) form, and contained each element is also consistent with X (n) institute corresponding element.Regulation δ (n+1) and ε (n) are the white noises of 0 average.

Step 6, obtains the Two-Dimensional Kalman filtering equations of image by state equation and observation equation, iterative process is as follows:

（1）

（2）K(n+1)={P(n+1|n)MT}·{MP(n+1|n)M ^T+Q} ^-1

（3）

（4） $\hat{X}(n+1|n+1)=\hat{X}(n+1|n)+K(n+1)\·{\{Y(n+1)-M\hat{X}(n+1|n)\}}^{-1}$

（5） $P(n+1|n+1)=\{I-K(n+1)M\}P(n+1|n)$

(6) n=n+1 gets back to (1);

Above in formula, to have obtained the estimation to the actual value of n+1 piece image after the observed reading of n piece image;

it is the estimated value having obtained after the actual value of n+1 piece image being upgraded after the observed reading of n+1 piece image; P (n+1|n) is prior estimate covariance matrix, and P (n|n) is posteriority estimate covariance matrix, and K (n+1) is kalman gain.

When above-mentioned legacy card Kalman Filtering is processed for image, just by the observation information at n place, position, position n+1 is estimated, then by the observation information at n+1 place, actual value is upgraded.Defect is that the observation information of n+1 and follow-up location is not by n and reference by location in the past.For better predicted picture, after obtaining the more real informations of image, the present invention uses for reference the thought of feedback, after the estimated value of actual value that has obtained n+1 position, by thought level and smooth and feedback, the estimated value of anterior locations is corrected.Adopt conventional two-dimensional piece Kalman filtering method and front feedback smoothing method to go dry processing to observed image.

In the inventive method, added the iterative process of front feedback smoother equation as follows:

（1）

（2）K(n+1)={P(n1|n)M ^T}·{MP(n+1|n)M ^T+Q} ^-1

（3）

（4） $\hat{X}(n+1|n+1)=\hat{X}(n+1|n)+K(n+1)\·{\{Y(n+1)-M\hat{X}(n+1|n)\}}^{-1}$

（5）

（6）P(n+1|n+1)={I-K(n+1)M}P(n+1)n)

(7) n=n+1 gets back to (1);

In formula,

the estimated value having obtained after the actual value of n piece image being upgraded after the observed reading of n piece image,

it is the estimated value having obtained after level and smooth to the actual value of n piece image after the observed reading of n+1 piece image.

Image after level and smooth is as last removal noise image.

Claims (6)

1. the image recovery method based on level and smooth correction, is characterized in that comprising the following steps:

S1, input noisy image, using the noisy image inputted as overall window O, set a micro-slip window L centered by pending pixel x; Calculate pending element x in noisy image and the similarity of the reference pixel y in Search Area, obtain the weights of all reference image vegetarian refreshments in Search Area

$w(x,y)=\left\{\begin{array}{cc}{w}_1(x,y)& y\∈L\\ w_2(x,y)& y\∈O-L\end{array}\right.$

Wherein, O-L is illustrated in overall window, but the region in micro-slip window not, weight w ₁(x, y) represents to be positioned at the reference pixel y of micro-slip window and the similarity of pending pixel x; Weight w ₂(x, y) represents to be positioned at outside micro-slip window, but reference pixel y in overall window and the similarity of pending pixel x; This weight w (x, y) meets: 0≤w (x, y)≤1, ∑ _{y ∈ O}w (x, y)=1;

In the Search Area that S2, basis calculate, the weights of all reference pixels, are weighted on average all pixels in Search Area, obtain the revised gray-scale value of pixel;

S3, with step S1, S2, handle in noisy image after all pixels, with the gray-scale value of pixel after revising, replace the gray-scale value of pixel in noisy image, as observed image;

S4, state variable are made as the pixel value of image, set up state equation and observation equation that observed image is estimated, adopt conventional two-dimensional piece Kalman filtering method to go dry processing to observed image;

Then by front feedback smoothing method, image is carried out to smoothing processing, by the estimated value of the actual value of current block image, the estimated value of piece image is above corrected, the image after smoothing processing is last removal noise image.

2. the method for claim 1, is characterized in that, in step S1,

Weight w ₁the formula of (x, y) is $w_1(x,y)=\frac{1}{2Z_1}{g}_{{\mathrm{\σ}}_{s,y}}\left({\left|\right|x-y\left|\right|}_2\right)*g_{{\mathrm{\σ}}_{r,y}}(I\left(x\right)-I\left(y\right)),$ Wherein I (x) and I (y) represent to be positioned at the grey scale pixel value at x and y place, σ _s,yand σ _r,yrespectively the coefficient in spatial domain and gray scale territory, ‖ ‖ ₂represent l ₂norm, Z ₁it is normalization coefficient $Z_1={\mathrm{\Σ}}_{y\∈L}{g}_{{\mathrm{\σ}}_{s,y}}\left({\left|\right|x-y\left|\right|}_2\right)*g_{{\mathrm{\σ}}_{s,y}}(I\left(x\right)-I\left(y\right));$

Weight w ₂the formula of (x, y) is

wherein, v (x) and v (y) represent respectively with x, the image block that the size centered by y is n*n; H smoothly controls parameter, h=kn δ ₀, δ ₀be the standard deviation of image institute Noise, k is constant, Z ₂it is normalization coefficient

3. method as claimed in claim 2, is characterized in that, described constant K is chosen between 0.5～2.

4. method as claimed in claim 1 or 2, is characterized in that, in step S4, the state equation of described observed image and observation equation respectively: with Y (n)=MX (n)+ε (n)

Wherein, X (n) and X (n+1) they are adjacent image blocks, the image block in Y (n) observed image,

be state-transition matrix, reacted the relation between adjacent image piece

M is observing matrix, the relation between reaction true picture and observed image; δ (n+1) is system noise, and ε (n) is observation noise.

5. method as claimed in claim 4, is characterized in that, the state vector predictive equation obtaining according to the state equation of described observed image and observation equation and observation renewal equation respectively:

$\hat{X}(n+1|n+1)=\hat{X}(n+1|n)+K(n+1)\·{\{Y(n+1)-M\hat{X}(n+1|n)\}}^{-1}$

In formula, to have obtained the estimation to the actual value of n+1 piece image after the observed reading of n piece image,

be the estimated value having obtained after the actual value of n+1 piece image being upgraded after the observed reading of n+1 piece image, K (n+1) is kalman gain;

The front feedback smoothing equation that described front feedback smoothing method represents based on following formula:

In formula,

the estimated value having obtained after the actual value of n piece image being upgraded after the observed reading of n piece image,

be the estimated value having obtained after level and smooth to the actual value of n piece image after the observed reading of n+1 piece image, P (n+1|n) is prior estimate covariance matrix, and P (n|n) is posteriority estimate covariance matrix.

6. the method for claim 1, is characterized in that, the size of the window of micro-slip described in step S1 L is set to 5 * 5,7 * 7 or 9 * 9.

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