CN102547074B - Surfacelet domain BKF model Bayes video denoising method - Google Patents

Abstract

A Surfacelet domain BKF model Bayes video denoising method comprises the following steps: inputting a video to be denoised; acquiring a high frequency subband coefficient; evaluating a noise standard deviation; acquiring a Surfacelet domain high frequency subband BKF distribution shape parameter and a size parameter of the video to be denoised; judging the value of the BKF distribution shape parameter; acquiring a Surfacelet domain coefficient of the denoised video; and acquiring the denoised video. According to the method provided by the invention, the marginal distribution of the Surfacelet coefficient of the video is modeled by using the BKF function, so that by making full use of the correlation of the Surfacelet domain high frequency subband coefficient of a video image, marginal detail information of the video image can be kept well on the premise of effectively denoising.

Description

Surfacelet territory BKF model Bayes video denoising method

Technical field

The invention belongs to technical field of image processing, further relate to a kind of Surfacelet territory BKF model Bayes video denoising method in technical field of video processing.The present invention can be applicable to the removal of video image additive noise.

Background technology

In the collection and transmitting procedure of video image, the introducing of noise is inevitable.Because video image has very large correlation at neighbor and interframe, and noise is random and incoherent, and this provides theoretical foundation for the noise remove of video image in time-space domain.Because noisy video image is after wavelet transformation, Surfacelet conversion, video image and noise have different characteristics at transform domain, coefficient in transform domain has certain regularity of distribution, according to the coefficient feature of domain of variation and the regularity of distribution, carries out denoising, can obtain good denoising effect.

Patent application " the non-local mean space domain time varying video filtering method " (number of patent application 200910219213.2 that Xian Electronics Science and Technology University proposes, publication number CN101742088A) disclose a kind of non-local mean space domain time varying video filtering method, mainly solved the large and limited problem of range of application of the amount of calculation of existing non-local mean space domain time varying filter.The filtering of the method is: the weights normalization coefficient of initialization current frame image all points and non-normalized filtered value are 0; For each coordinate biasing in region of search, respectively all pixels of current frame image are carried out to unified preliminary treatment, then calculate fast all pixels of current frame image at the Weighted Kernel weights at this region of search coordinate place; According to these Weighted Kernel weights, upgrade weights normalization coefficient and non-normalized filtered value; According to weights normalization coefficient and non-normalized filtered value, calculate filtered image.Although the method has greatly reduced the computation complexity of existing non-local mean space domain time varying filtering method, obtain good denoising effect, but the deficiency still existing is, the method has only been considered the correlation between pixel in present frame, do not utilize the correlation of video image interframe, can not effectively improve the denoising effect of video image.

Patent application " the spatially adaptive threshold video denoising method based on Surfacelet the transform domain " (number of patent application 201110081454.2 that Xian Electronics Science and Technology University proposes, publication number CN102158637A) a kind of spatially adaptive threshold video denoising method based on Surfacelet transform domain is disclosed, mainly solve that video denoising effect is undesirable, denoising process complexity is excessive and video denoising in there is the problems such as artifact, pseudo-Gibbs' effect.The implementation procedure of the method is: input is treated denoising video and done Surfacelet conversion; Coefficient estimating noise in the directional subband respectively each Surfacelet being decomposed; Usage factor dimensional energy value is calculated adaptive threshold; Usage factor neighborhood information is adjusted above-mentioned threshold value; Utilize threshold function table to carry out denoising; Coefficient after denoising is reconstructed, obtains denoising rear video.Although the method can improve video denoising effect by usage factor neighborhood relationships, the detailed information that effectively keeps video, obtain good video denoising effect, but the deficiency still existing is, the method has only been utilized a small amount of neighborhood information of coefficient, do not make full use of the Relationship of Coefficients outside neighborhood, denoising effect has much room for improvement.

Summary of the invention

The present invention is directed to above-mentioned the deficiencies in the prior art, with Surfacelet coefficient, video image and noise are described, according to the feature of video image Surfacelet coefficient edge distribution, utilize Bezier K distribution function to carry out modeling to Surfacelet coefficient edge distribution, effectively utilized the relation between all coefficients in subband, propose a kind of Surfacelet territory BKF model Bayes video denoising method, can effectively noise be removed from video image.

Concrete steps of the present invention are as follows:

(1) denoising video is treated in one of input.

(2) obtain and treat denoising video Surfacelet domain coefficient

Call Surfacelet kit and treat denoising video and do Surfacelet conversion, obtain the Surfacelet territory high-frequency sub-band coefficient for the treatment of denoising video.

(3) with the estimation of noise estimation formulas, treat that the noise criteria of denoising video is poor.

(4) obtain according to the following formula the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band:

$p=\frac{3\×\max {({\hat{c}}_2-{\mathrm{\σ}}^2,0)}^2}{{\hat{c}}_4}$

Wherein, p is the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band;

Max () is for getting max function;

for treating the second-order cumulant of denoising video Surfacelet territory high-frequency sub-band;

σ treats that the noise criteria of denoising video is poor;

for treating the fourth order cumulant of denoising video Surfacelet territory high-frequency sub-band.

(5) obtain according to the following formula the Bezier K distribution scale parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band:

$c=\frac{\max ({\hat{c}}_2-{\mathrm{\σ}}^2,0)}{p}$

Wherein, c is the Bezier K distribution scale parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band;

Max () is for getting max function;

for treating the second-order cumulant of denoising video Surfacelet territory high-frequency sub-band;

σ treats that the noise criteria of denoising video is poor;

P is the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band.

(6) size of the Bezier K distribution shape parameter of denoising video Surfacelet territory high-frequency sub-band is treated in judgement, if be greater than 1, carries out next step, otherwise execution step (10).

(7) obtain according to the following formula denoising video Surfacelet domain coefficient:

${\hat{c}}_{\mathrm{ijk}}=\frac{{\mathrm{\σ}}_g^2}{{\mathrm{\σ}}_g^2+{\mathrm{\σ}}^2}\×c_{\mathrm{ijk}}$

Wherein,

for denoising video Surfacelet domain coefficient;

I is the coefficient index of k subband of j the yardstick in denoising video Surfacelet territory;

J is for treating j, territory of denoising video Surfacelet yardstick;

K is k subband treating j the yardstick in denoising video Surfacelet territory;

σ _gfor treating denoising video Surfacelet territory high-frequency sub-band coefficient standard deviation;

σ treats that the noise criteria of denoising video is poor;

C _ijkfor treating i coefficient of k subband of j the yardstick in denoising video Surfacelet territory.

(8) obtain according to the following formula denoising video Surfacelet domain coefficient:

${\hat{c}}_{\mathrm{ijk}}=\frac{\underset{-\∞}{\overset{+\∞}{\∫}}x\·f(c_{\mathrm{ijk}}-x)\·p\left(x\right)\mathrm{dx}}{\underset{-\∞}{\overset{+\∞}{\∫}}f(c_{\mathrm{ijk}}-x)\·p\left(x\right)\mathrm{dx}}$

Wherein,

for i coefficient of k subband of j the yardstick in denoising video Surfacelet territory;

I is the coefficient index of k subband of j the yardstick in denoising video Surfacelet territory;

J is for treating j, territory of denoising video Surfacelet yardstick;

K is k subband treating j the yardstick in denoising video Surfacelet territory;

X is integration variable;

F () is the Gaussian function of zero-mean;

C _ijkfor treating i coefficient of k subband of j the yardstick in denoising video Surfacelet territory;

P () is Bezier K distribution function.

(9) obtain denoising video

By calling Surfacelet kit, Surfacelet inversion is done in denoising video Surfacelet territory bring and obtain denoising video.

The present invention has the following advantages compared with prior art:

First, the present invention adopts the method that denoising video is made disposed of in its entirety for the treatment of, make the present invention make full use of between video image pixel and correlation that interframe exists, overcome and in prior art, only considered the correlation between pixel in present frame, do not utilize the shortcoming of the correlation of video image interframe, effectively improved the denoising effect of video image.

Second, the present invention adopts the method for Surfacelet territory BKF model Bayes denoising, utilize Bezier K distribution function to carry out modeling to video Surfacelet coefficient edge distribution, effectively utilized the relation between all coefficients in subband, overcome Relationship of Coefficients in prior art and utilized inadequate shortcoming, made the present invention can more effective removal noise and keep the edge details information of video.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention;

Fig. 2 is design sketch of the present invention.

Embodiment

Below in conjunction with accompanying drawing 1, the present invention will be further described.

Step 1, inputs one and treats denoising video, and its video size is 192 * 192 * 192 pixels, and institute's plus noise is white Gaussian noise.

Step 2, obtains the Surfacelet domain coefficient for the treatment of denoising video.

Call Surfacelet kit and treat denoising video and do Surfacelet conversion, obtain the Surfacelet territory high-frequency sub-band coefficient for the treatment of denoising video.

Step 3, treats that with the estimation of noise estimation formulas the noise criteria of denoising video is poor.

In the high frequency detail subbands in the Surfacelet territory of noisy video, its energy is mainly provided by noise, noise is independent identically distributed white Gaussian noise in Surfacelet territory, and noise variance is constant, so Donoho proposes to carry out estimating noise standard deviation by robust intermediate value.

The poor estimation formulas of noise criteria is:

σ＝midean(abs(C))/0.6725

Wherein, σ treats that the noise criteria of denoising video is poor;

Median () is for getting median function;

Abs () is the symbol that takes absolute value;

C is for treating denoising video Surfacelet territory high-frequency sub-band coefficient sets.

Step 4, obtains the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band.

The Bezier K distribution shape parameter p of high-frequency sub-band has been described the shape of coefficient distributed model, when p is 1, coefficient is distributed as two exponential distribution, when p is greater than 1, coefficient is distributed as Gaussian Profile, and when p is between 0 and 1, Bezier K distributed model can better be described coefficient distribution situation.P major part in the present invention is between 0 and 1.

First obtain second-order cumulant and the fourth order cumulant for the treatment of denoising video Surfacelet territory high-frequency sub-band, the computing formula of second-order cumulant is:

${\hat{c}}_2=\frac{n}{n-1}\×{\hat{M}}_2$

Wherein,

for treating the second-order cumulant of the Surfacelet territory high-frequency sub-band of denoising video;

N is the coefficient number for the treatment of the Surfacelet territory high-frequency sub-band of denoising video;

for treating the second order sample central moment of the Surfacelet territory high-frequency sub-band of denoising video;

The computing formula of fourth order cumulant is:

${\hat{c}}_4=\frac{n^2\×[(n+1)\×{\hat{M}}_4-3\×(n-1)\×{\hat{M}}_2]}{(n-1)\×(n-2)\×(n-3)}$

Wherein,

for treating the fourth order cumulant of denoising video Surfacelet territory high-frequency sub-band;

N is the coefficient number for the treatment of denoising video Surfacelet territory high-frequency sub-band;

for treating the quadravalence sample central moment of denoising video Surfacelet territory high-frequency sub-band;

for treating the second order sample central moment of denoising video Surfacelet territory high-frequency sub-band;

Then obtain according to the following formula the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band:

$p=\frac{3\×\max {({\hat{c}}_2-{\mathrm{\σ}}^2,0)}^2}{{\hat{c}}_4}$

Wherein, p is the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band;

Max () is for getting max function;

for treating the second-order cumulant of denoising video Surfacelet territory high-frequency sub-band;

σ treats that the noise criteria of denoising video is poor;

for treating the fourth order cumulant of denoising video Surfacelet territory high-frequency sub-band.

Step 5, obtains the Bezier K distribution scale parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band.

What Bezier K distribution scale parameter was described is the details in Bezier K distribution curve, obtains according to the following formula the Bezier K distribution scale parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band:

$c=\frac{\max ({\hat{c}}_2-{\mathrm{\σ}}^2,0)}{p}$

Wherein, c is the Bezier K distribution scale parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band;

Max () is for getting max function;

for treating the second-order cumulant of denoising video Surfacelet territory high-frequency sub-band;

σ treats that the noise criteria of denoising video is poor;

P is the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band.

Step 6, the size of the Bezier K distribution shape parameter of denoising video Surfacelet territory high-frequency sub-band is treated in judgement, if be greater than 1, carries out next step, otherwise execution step (8).

When form parameter is greater than 1, treat denoising video Surfacelet territory high-frequency sub-band coefficient Gaussian distributed, we adopt the method denoising of step (7); When form parameter is less than 1, treat that denoising video Surfacelet territory high-frequency sub-band coefficient obedience Bezier K distributes, we adopt the method denoising of step (8).

Step 7, obtains denoising video Surfacelet domain coefficient.

Obtain according to the following formula denoising video Surfacelet domain coefficient:

${\hat{c}}_{\mathrm{ijk}}=\frac{{\mathrm{\σ}}_g^2}{{\mathrm{\σ}}_g^2+{\mathrm{\σ}}^2}\×c_{\mathrm{ijk}}$

Wherein,

for denoising video Surfacelet domain coefficient;

I is the coefficient index of k subband of j the yardstick in denoising video Surfacelet territory;

J is for treating j, territory of denoising video Surfacelet yardstick;

K is k subband treating j the yardstick in denoising video Surfacelet territory;

σ _gfor treating denoising video Surfacelet territory high-frequency sub-band coefficient standard deviation;

σ treats that the noise criteria of denoising video is poor;

C _ijkfor treating i coefficient of k subband of j the yardstick in denoising video Surfacelet territory.

Step 8, obtains denoising video Surfacelet domain coefficient.

Obtain according to the following formula denoising video Surfacelet domain coefficient:

${\hat{c}}_{\mathrm{ijk}}=\frac{\underset{-\∞}{\overset{+\∞}{\∫}}x\·f(c_{\mathrm{ijk}}-x)\·p\left(x\right)\mathrm{dx}}{\underset{-\∞}{\overset{+\∞}{\∫}}f(c_{\mathrm{ijk}}-x)\·p\left(x\right)\mathrm{dx}}$

Wherein,

for i coefficient of k subband of j the yardstick in denoising video Surfacelet territory;

I is the coefficient index of k subband of j the yardstick in denoising video Surfacelet territory;

J is for treating j, territory of denoising video Surfacelet yardstick;

K is k subband treating j the yardstick in denoising video Surfacelet territory;

X is integration variable;

F () is Gaussian function;

C _ijkfor treating i coefficient of k subband of j the yardstick in denoising video Surfacelet territory;

P () is Bezier K function.

Step 9, obtains denoising video.

By calling Surfacelet kit, Surfacelet inversion is done in denoising video Surfacelet territory bring and obtain denoising video.

Below in conjunction with 2 pairs of effects of the present invention of accompanying drawing, be further described.

Fig. 2 (a) is that size is 192 * 192 * 192 pixels without making an uproar sequence of video images Mobile; Fig. 2 (b) is for adding that to Fig. 2 (a) standard deviation is the video image after Gauss's additive white noise of 20; Fig. 2 (c) is for being used the design sketch after Visual shrinkage method of the prior art is processed Fig. 2 (b); Fig. 2 (d) is for being used the design sketch after the 3D-CMST method based on hard-threshold function of the prior art is processed Fig. 2 (b); Fig. 2 (e) is the design sketch after using NormalShrink method in non-downsampling Contourlet of the prior art to process Fig. 2 (b); Fig. 2 (f) is for being used the design sketch after the present invention processes Fig. 2 (b).

Experiment simulation environment of the present invention is: MATLAB R2009b, CPU:AMD Athlon * 2 2.11GHz, internal memory 2G, Window XP Professional.

In order to show denoising effect of the present invention, to the sequence of video images of Fig. 2 (a), adding respectively noise criteria poor is Gauss's additive white noise of 30, use respectively Visual shrinkage method of the prior art, the 3D-CMST method based on hard-threshold function, the NormalShrink method in non-downsampling Contourlet and the present invention to carry out denoising to adding the video of making an uproar, denoising effect as shown in Figure 2.

By Fig. 2 (c) and Fig. 2 (f), can be found out, adopt Visual shrinkage denoising method of the prior art to carry out denoising, denoising rear video is image blurring, most grain details is smoothed to be fallen, adopt after denoising of the present invention, video image is clear, and grain details recovery situation is good.By Fig. 2 (d), Fig. 2 (e) and Fig. 2 (f), can be found out, adopt NormalShrink method and the present invention in 3D-CMST method based on hard-threshold function of the prior art, non-downsampling Contourlet to carry out denoising, the present invention more can preserve original feature of video image, the maintenance effect of edge details is more obvious, and the visual effect of video image is better.

In order to further illustrate denoising effect of the present invention, to the sequence of video images of Fig. 2 (a), adding respectively noise criteria poor is 20, 30, 40, Gauss's additive white noise of 50, use respectively Visual shrinkage method of the prior art, 3D-CMST method based on hard-threshold function, NormalShrink method and the present invention in non-downsampling Contourlet carry out denoising, the Y-PSNR PSNR value of denoising effect comparison is listed in following table, in following table, Mobile is sequence of video images, Visual-SH is Visual shrinkage method, 3D-CMST is the 3D-CMST method based on hard-threshold function, NSCT-NS is the NormalShrink method in non-downsampling Contourlet.

PSNR value in upper table is the mean value of each two field picture PSNR after sequence of video images denoising, as can be seen from the table, compares with various denoising methods of the prior art, and the PSNR value of the video image after denoising of the present invention all has raising by a relatively large margin.

Above result shows, the present invention has kept well the edge details information of video image when effectively removing noise, and denoising effect is good.

Claims (4)

1. a Surfacelet territory BKF model Bayes video denoising method, comprises the steps:

(1) denoising video is treated in one of input;

(2) obtain and treat denoising video Surfacelet domain coefficient

Call Surfacelet kit and treat denoising video and do Surfacelet conversion, obtain the Surfacelet territory high-frequency sub-band coefficient for the treatment of denoising video;

(3) with the estimation of noise estimation formulas, treat that the noise criteria of denoising video is poor;

(4) obtain according to the following formula the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band:

$p=\frac{3\×\max {({\hat{c}}_2-{\mathrm{\σ}}^2,0)}^2}{{\hat{c}}_4}$

Wherein, p is the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band;

Max () is for getting max function;

for treating the second-order cumulant of denoising video Surfacelet territory high-frequency sub-band;

σ treats that the noise criteria of denoising video is poor;

for treating the fourth order cumulant of denoising video Surfacelet territory high-frequency sub-band;

(5) obtain according to the following formula the Bezier K distribution scale parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band:

$c=\frac{\max ({\hat{c}}_2-{\mathrm{\σ}}^2,0)}{p}$

Wherein, c is the Bezier K distribution scale parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band;

Max () is for getting max function;

for treating the second-order cumulant of denoising video Surfacelet territory high-frequency sub-band;

σ treats that the noise criteria of denoising video is poor;

P is the Bezier K distribution shape parameter for the treatment of denoising video Surfacelet territory high-frequency sub-band;

(6) size of the Bezier K distribution shape parameter of denoising video Surfacelet territory high-frequency sub-band is treated in judgement, if be greater than 1, carries out next step, otherwise execution step (8);

(7) obtain according to the following formula denoising video Surfacelet domain coefficient:

${\hat{c}}_{\mathrm{ijk}}=\frac{{\mathrm{\σ}}_g^2}{{\mathrm{\σ}}_g^2+{\mathrm{\σ}}^2}\×c_{\mathrm{ijk}}$

Wherein, for denoising video Surfacelet domain coefficient;

I is the coefficient index of k subband of j the yardstick in denoising video Surfaeelet territory;

J is for treating j, territory of denoising video Surfacelet yardstick;

K is k subband treating j the yardstick in denoising video Surfacelet territory;

σ _gfor treating denoising video Surfacelet territory high-frequency sub-band coefficient standard deviation;

σ treats that the noise criteria of denoising video is poor;

C _ijkfor treating i coefficient of k subband of j the yardstick in denoising video Surfacelet territory;

(8) obtain according to the following formula denoising video Surfacelet domain coefficient:

${\hat{c}}_{\mathrm{ijk}}=\frac{\underset{-\∞}{\overset{+\∞}{\∫}}x\·f(c_{\mathrm{ijk}}-x)\·p\left(x\right)\mathrm{dx}}{\underset{-\∞}{\overset{+\∞}{\∫}}f(c_{\mathrm{ijk}}-x)\·p\left(x\right)\mathrm{dx}}$

Wherein,

for i coefficient of k subband of j the yardstick in denoising video Surfacelet territory;

I is the coefficient index of k subband of j the yardstick in denoising video Surfacelet territory;

J is for treating j, territory of denoising video Surfacelet yardstick;

K is k subband treating j the yardstick in denoising video Surfacelet territory;

X is integration variable;

F () is the Gaussian function of zero-mean;

C _ijkfor treating i coefficient of k subband of j the yardstick in denoising video Surfacelet territory;

P () is Bezier K distribution function;

(9) obtain denoising video

By calling Surfacelet kit, Surfacelet inversion is done in denoising video Surfacelet territory bring and obtain denoising video.

2. Surfacelet according to claim 1 territory BKF model Bayes video denoising method, is characterized in that: the noise estimation formulas described in step (3) is:

σ=midean(abs(C))／0.6725

Wherein, σ treats that the noise criteria of denoising video is poor;

Median () is for getting median function;

Abs () is the symbol that takes absolute value;

C is for treating denoising video Surfacelet territory high-frequency sub-band coefficient sets.

3. Surfacelet according to claim 1 territory BKF model Bayes video denoising method, is characterized in that: the second-order cumulant of the Surfacelet territory high-frequency sub-band for the treatment of denoising video described in step (4) is:

${\hat{c}}_2=\frac{n}{n-1}\×{\hat{M}}_2$

Wherein,

for treating the second-order cumulant of the Surfacelet territory high-frequency sub-band of denoising video;

N is the coefficient number for the treatment of the Surfacelet territory high-frequency sub-band of denoising video;

for treating the second order sample central moment of the Surfacelet territory high-frequency sub-band of denoising video.

4. Surfacelet according to claim 1 territory BKF model Bayes video denoising method, is characterized in that: the fourth order cumulant for the treatment of denoising video Surfacelet territory high-frequency sub-band described in step (4) is:

${\hat{c}}_4=\frac{n^2\×[(n+1)\×{\hat{M}}_4-3\×(n-1)\×{\hat{M}}_2]}{(n-1)\×(n-2)\×(n-3)}$

Wherein,

for treating the fourth order cumulant of denoising video Surfacelet territory high-frequency sub-band;

N is the coefficient number for the treatment of denoising video Surfacelet territory high-frequency sub-band;

for treating the quadravalence sample central moment of denoising video Surfacelet territory high-frequency sub-band;

for treating the second order sample central moment of denoising video Surfacelet territory high-frequency sub-band.

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