CN103093428A - Space-time united image sequence multi-scale geometric transformation denoising method - Google Patents

Abstract

The invention discloses a space-time united image sequence multi-scale geometric transformation denoising method. By that an image multi-scale geometric analysis is introduced into the image denoising process, and image sequence space-time relevant information is united, a statistical distribution model of an image multi-scale geometric transformation domain coefficient, the built image statistical model serves as priori knowledge, a Bayesian lest square estimation method is adopted to obtain an optimal estimation result of non-noise-pollution image signals, and the problems that the situation that an image detail coefficient and image noise are difficult to distinguish often occurs in the denoising process of a conventional wavelet domain are solved. Meanwhile, plenty of image samples which are the same to a to-be-processed image in scene are collected and image statistical distribution modeling is conducted on the image samples, the statistical distribution model of the image multi-scale geometric transformation domain coefficient directly reflects statistical distribution features of texture details of edges and surface of the to-be-processed image and provides reliable priori distribution knowledge for Bayesian lest square estimation of the image, and space-time information united image sequence non-noise image signal estimation is achieved. A denoising effect of the image is improved, at the same time, image details are kept to a great extent.

Description

The multiple dimensioned geometric transformation denoising method of a kind of image sequence of space-time unite

Technical field

The invention belongs to technical field of image processing, be specially a kind of multiple dimensioned geometric transformation denoising method of image sequence of space-time unite.

Background technology

Intelligent vision occupies more and more consequence at aspects such as modern industry manufacturing and security monitorings.Realizing target object and the natural scene taken in the visual field are carried out automatic analysis and intelligent monitoring by computer image processing technology, is a kind of innovation to traditional industry process automation and security monitoring idea.Effective processing of visual pattern and the accurate extraction of Image Visual Feature are the keys of intelligent visual surveillance system success.Yet the industry spot image capture environment is often more abominable, and is many such as uneven illumination, on-the-spot dust, water smoke heavy, and is accompanied by the electromagnetic interference (EMI) of other equipment, and picture signal inevitably is subject to the interference of noise in collection and transmission.The existence of noise has greatly affected follow-up higher level image processing and scene is understood, and further applies in industrial monitoring thereby affected machine vision.Therefore, Image Denoising Technology is the hot issue of image pre-service aspect always.

For the characteristics of different application scenarioss with the picture noise of correspondence; researchers have proposed multiple Digital Image Noise method; wherein foremost is image wavelet territory threshold value shrinkage de-noising method and based on the various Innovative methods of this thought; because these methods directly are set to zero by the predefine rule coefficient that some amplitude is little; can't effectively separate the difference of picture signal coefficient and noise figure; often can cause the fuzzy of image border; denoising has reduced the visual quality of image simultaneously, even also can introduce some artificial pseudo-shadows.

Along with the further investigation and further understanding of researcher to image coefficient (such as the wavelet transformation domain coefficient) statistical model; image wavelet territory denoising method based on Bayesian Estimation more and more is subject to people's attention; but; be rich in the edge singular curve, divide and the whole shooting visual field shows the image of complex texture details without the prospect background area for imaging surface, the present image Bayesian denoising technology based on wavelet field still is difficult to solve picture noise and removes contradiction between protecting with the imaging surface details.Wherein topmost reason is that image detail and noise are difficult to effective differentiation at the thin yardstick of image wavelet decomposition.

At present, denoising method based on the single-frame images information modeling, owing to having ignored image sequence interframe time domain relevant information, when the erroneous judgement of noise signal and image detail signal occurs when, can't proofread and correct in conjunction with the time domain relevant information, keep to the utmost boundary curve and the superficial makings details of image when being difficult to noise is carried out effectively elimination, even may produce artificial pseudo-shadow, had a strong impact on follow-up image and processed and higher level visual analysis result.

Summary of the invention

The invention provides a kind of multiple dimensioned geometric transformation denoising method of image sequence of space-time unite, its purpose is by joint image time-space domain relevant information, effectively overcoming in prior art can't the differentiate between images edge and superficial makings minutia and the picture noise false border of causing and the problem of surperficial singular point, thereby the raising image denoising effect can keep image detail simultaneously greatly.

The multiple dimensioned geometric transformation denoising method of a kind of image sequence of space-time unite, at first treat the denoising image and carry out multiple dimensioned geometric transformation, Gauss's yardstick is mixed (GSM) model be applied to Image Multiscale geometric transformation territory, image transform domain is carried out the coefficients statistics modeling, take the coefficients statistics model that obtained as priori, by Bayes's least-squares estimation, obtain the image conversion domain coefficient optimal estimation based on spatial information statistical distribution in picture frame; Then introduce image sequence interframe weighting factor according to the correlativity of motion compensation principle and image sequence interframe sub-block, process by weighting the relevant optimum coefficient of time domain that image sequence interframe sub-block coefficient obtains pending picture frame, by Image Multiscale geometric analysis inverse transformation, obtain the denoising image of high s/n ratio at last.

Described Image Multiscale geometric transformation refers to, adopt Second Generation Curvelet Transform to carry out Image Multiscale geometric transformation, the scale parameter that the Curvelet conversion is decomposed is 4, the Directional Decomposition number of each yardstick is respectively 32,32,64 and 64, image is transformed in the subband figure that obtains after decomposition, comprises the image high-frequency sub-band figure that comprises the image general profile and the image low frequency sub-band figure that comprises image detail.

Described image transform domain coefficients statistics is modeled as and adopts the GSM model to carry out spatial information statistical distribution modeling in picture frame, specifically carries out following steps:

(1) basis treats that the denoising image has the visual characteristic of boundary curve and superficial makings details, collects to have a large amount of image I that are not subjected to noise pollution for the treatment of the identical visual characteristic of denoising image in identical photographed scene _iComposition diagram is as statistical distribution modeling sample storehouse { I _i, 1≤i≤m} is total to m width image, m 〉=10 in Sample Storehouse;

(2) to the arbitrary image I in image library _iAdopt Second Generation Curvelet Transform to obtain I _iCorresponding each high-frequency sub-band matrix of coefficients of Curvelet transform domain

J represents decomposition scale, and θ represents to decompose direction, and the scale parameter that image C urvelet conversion is decomposed is 4, and minute skill of the decomposition direction on each decomposition scale of image is respectively 32,32,64 and 64;

(3) local window coefficient sampling is to the matrix of coefficients of any HFS subband figure

In same subband figure, collect sampled point, the big or small local window coefficient as w*w of local window centered by any (kx, ky), w ∈ [5,7,9] processes by bilinear interpolation simultaneously, collects

With

Picture breakdown sub-band coefficients on middle same position (kx, ky) forms stochastic variable y, and the dimension of y is w*w+2;

(4) adopt the local window coefficient method of sampling described in (3), each HFS subband figure coefficient to image in Sample Storehouse carries out r sampling, sampling number satisfies 1024≤r＜M*N*m, M, N is respectively the wide and high of image, and size of coefficient vector composition that r sampling obtained is r*W stochastic variable matrix X, and the coefficient vector that the sampling of local window coefficient obtains is carried out in each behavior of X in image transform domain high-frequency sub-band figure, W=w*w+2, m are the amount of images of Sample Storehouse;

Wherein, in the subband figure that obtains after image is decomposed, comprise image low frequency sub-band image and image high-frequency sub-band figure, image low frequency sub-band figure comprises the general profile of image, and image high-frequency sub-band figure mainly comprises image detail;

(5) adopt the statistical distribution pattern of GSM models fitting Image Multiscale geometric transformation domain coefficient, namely the stochastic variable that consists of of the vectorial y of any row in X is carried out the statistical modeling analysis by the GSM model, and this statistical model represents by following formula:

$y=\sqrt{z}U---\left(1\right)$

Wherein z is the stochastic variable greater than zero, and U is that an average is zero Gaussian random variable, and z and U are separate, and the probability density function of y is:

$p_y\left(y\right)=\∫p\left(y\right|z)p_z\left(z\right)\mathrm{dz}=\∫\frac{\exp \left(\frac{-y^T{\left({\mathrm{zc}}_u\right)}^{-1}y}{2}\right)}{{\left(2\mathrm{\π}\right)}^{W/2}{\left|{\mathrm{zc}}_u\right|}^{1/2}}{p}_z\left(z\right)\mathrm{dz}---\left(2\right)$

C wherein _uBe the covariance matrix of U, adopt maximum likelihood to estimate the parameter z in model is carried out optimal estimation

$\hat{z}=\underset{z}{\max }\left\{\log p\left(y\right|z)\right\}=\underset{z}{\min }\{W\log \left(\sqrt{z}\right)+Y^T{C_u}^{-1}Y/\left(2z^2\right)\}=Y^T{C}_{u}Y/W---\left(3\right)$

Then the probability density that adopts Nonparametric Estimation to obtain z is estimated p _z|y(z|y)

$p_{z|y}\left(z\right|y)=\frac{1}{\mathrm{Wh}}\underset{i=1}{\overset{W}{\mathrm{\Σ}}}K\left(\frac{z-{\hat{z}}_i}{h}\right)---\left(4\right)$

Wherein h is bandwidth, and (MISE) can obtain bandwidth h by the minimized average integrated square error, and K () is gaussian kernel function.

Described image conversion domain coefficient optimal estimation based on spatial information statistical distribution in picture frame refers to, represents not to be subjected to the arbitrfary point x in each HFS subband of image figure of noise pollution by the GSM model _cThe statistical distribution of the random vector x that forms of local window coefficient, the image observation coefficient y that be subjected to noise pollution corresponding with x is expressed as:

$y\stackrel{d}{=}x+\mathrm{\ω}\stackrel{d}{=}\sqrt{z}u+\mathrm{\ω}---\left(5\right)$

Wherein ω is the picture noise of Gaussian distributed, and x is the multiple dimensioned geometric transformation territory high-frequency sub-band coefficient that is not subjected to the picture signal of noise pollution, and y is the make an uproar multiple dimensioned geometric transformation territory high-frequency sub-band coefficient of observation signal of the band corresponding with x,

The statistical distribution that the variable of expression equation both sides is corresponding equates;

In order to obtain the optimal estimation of the original image that is not subjected to noise pollution, need to process each high-frequency sub-band coefficient pointwise of band noise image transform domain.At first, with arbitrfary point in the image conversion domain coefficient of noise (such as with x _cCentered by) local window coefficient x(the same with the local window coefficient sampling process described in (3)), can set up its statistical distribution pattern by GSM, namely

But actual observation to the image y(coefficient corresponding with x) be with noise, namely be equivalent to the ω that superposeed on the basis of x, as shown in Equation (5).

Be not subjected to the centre of neighbourhood coefficient x of noise pollution _cAdopt Bayes's criterion of least squares to carry out the optimal estimation result that maximum a posteriori estimates to obtain the image conversion domain coefficient

${\hat{x}}_c=E\left\{x_c\right|y\}=\underset{0}{\overset{\∞}{\∫}}p\left(z\right|y)E\{y_c|y,z\}\mathrm{dz}---\left(6\right)$

P in following formula (z|y) adopts formula (4) to estimate, E{x _c| y, z}=zC _u(zC _u+ C _w) ^-1y。

The motion compensation of described image sequence inter-frame information refers to adopt cross-correlation method to obtain the motion estimation result of consecutive frame image subblock, and computing method are:

If image subblock f ₁(v) and f ₂(v) displacement of Δ v occurs in consecutive frame, its movement representation is

f ₂(v)＝f ₁(v-Δv) （7）

Like this, motion vector Δ v is estimated by following formula

$\mathrm{\Δ}\hat{v}=\underset{v}{\arg \max }{k}_{\mathrm{cc}}\left(v\right)=\arg \max \left\{F^{-1}\left(Y\left(\mathrm{\ω}\right)\right)\right\}---\left(8\right)$

Wherein

F ₁(ω) and F ₂(ω) difference presentation video sub-block f ₁(v) and f ₂(v) Fourier transform,

Expression F ₂Complex conjugate (ω).

Weighting is processed image sequence interframe sub-block coefficient and is referred to, image conversion domain coefficient optimal estimation result based on spatial information statistical distribution in picture frame is weighted summation, obtain the image transform domain optimum coefficient estimated result of image sequence Spatial-temporal Information Fusion, that is:

${\hat{x}}_t=\underset{k\∈I}{\mathrm{\Σ}}\mathrm{\λ}\left(k\right){\hat{x}}_{c_k}---\left(9\right)$

Wherein,

Refer to the k two field picture coefficient in transform domain optimal estimation result based on spatial information statistical distribution in picture frame that obtains by formula (6) node-by-node algorithm, I needs the image sequence considered before and after pending image t, the sequence number is N=i+j+1 (i two field picture before t, j frame after t), λ (k) is the weighting factor of influence, relevant with the similarity of local neighborhood corresponding between image, the t two field picture local neighborhood similarity degree corresponding with the t+i two field picture passes through Euclidean distance || v _t-v _t+i‖ ²Weigh, the weight of λ (k) is calculated as follows

$\mathrm{\λ}\left(k\right)=\frac{1}{C\left(i\right)}\exp (-{\left|\right|v_k-v_i\left|\right|}^2)---\left(10\right)$

In formula, $C\left(i\right)=\underset{k\∈I}{\mathrm{\Σ}}\exp (-{\left|\right|v_k-v_i\left|\right|}^2),$ Play the normalization effect.

Use the optimal coefficient in multi-scale transform territory that said method obtains the Spatial-temporal Information Fusion of each picture frame and estimate, then by Image Multiscale geometric analysis inverse transformation, obtain the denoising result of whole image sequence.

Beneficial effect

The invention provides a kind of multiple dimensioned geometric transformation denoising method of image sequence of space-time unite, by the Image Multiscale geometric analysis being incorporated in the image denoising processing, by joint image temporal and spatial correlations information, set up the statistical distribution pattern of Image Multiscale geometric transformation domain coefficient, take the image statistics model set up as priori, adopt Bayes's the least square estimation method to obtain the optimal estimation result of the picture signal of noise-less pollution.

Edge geometric properties by taking into full account pending picture signal and the statistical distribution characteristics of superficial makings minutia, the Image Multiscale geometric analysis is applied in the optimum expression of the image with complex edge and superficial makings details, has solved the difficult problem that the image detail coefficient that often runs into and picture noise are difficult to distinguish in conventional wavelet field denoising process; And carry out image statistics distribution modeling with image pattern pending image same scene in a large number by collecting, the Image Multiscale geometric transformation territory statistical distribution pattern of setting up has directly embodied the edge of pending image and the statistical distribution characteristics of superficial makings details, for image Bayes least-squares estimation provides reliable prior distribution knowledge.

Utilize the time domain relevant information of image sequence interframe, carry out the relevant image sequence interframe sub-block weighting of time domain by the motion compensation of image sequence interframe sub-block in conjunction with the correlativity of interframe sub-block and process, realized the optimum noise-free picture Signal estimation of image sequence of Spatial-temporal Information Fusion.

Kept greatly image detail when improving image denoising effect.

Description of drawings

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is estimation schematic diagram between picture frame;

Fig. 3 is for treating the denoising experimental image;

Fig. 4 is for using this method and additive method Fig. 3 to be carried out the effect contrast figure of denoising experiment, the row at the 5 places representatives noisy image of the poor Gaussian noise of various criterion that superposeed on Fig. 3 wherein, comprise figure (a), figure (d), figure (g) is (15 to the standard deviation level of Fig. 3 superimposed noise respectively, 30, 60), the image column at 7 places comprises figure (c), figure (f), figure (i) is respectively and adopts step 1 of the present invention ~ step 6 to carry out the result of the multiple dimensioned geometric transformation denoising of space time information joint image, the image column figure at 6 places (b), figure (e), figure (h) is respectively and adopts traditional small wave converting method to carry out the result of image denoising.

Embodiment

The present invention will be further described below in conjunction with accompanying drawing.

as shown in Figure 1, process flow diagram for the multiple dimensioned geometric transformation denoising method of a kind of image sequence of space-time unite, this denoising method has taken into full account the space-time sequence image in the statistic correlation of the relevant Image Multiscale geometric transformation domain coefficient of shutting mutually with temporal information of spatial information, by Bayes's least-squares estimation, acquisition is based on the picture signal optimal estimation of spatial information statistical distribution in frame, then, motion estimation result between the recycling picture frame, by information weighting between picture frame, the optimum coefficient that obtains pending picture frame time domain relevant multiple dimensioned geometric transformation territory is estimated, obtain the high denoising image of signal to noise ratio (S/N ratio) by the multi-scale geometric analysis inverse transformation at last.

Implementation step is as follows:

Step 1: set up the statistical distribution pattern of Image Multiscale geometric transformation domain coefficient, concrete operation step is as follows:

(1) the complex texture image clear, that be not subjected to noise pollution of collecting under a large amount of pending image same scene forms training sample database, for the image statistics modeling analysis of back is prepared.

(2) adopt Second Generation Curvelet Transform to training the image pattern in the storehouse to carry out the Image Multiscale geometric analysis, the optimization that realizes image pattern storehouse complex texture image border curve and surface details represents, the scale parameter that image C urvelet conversion is decomposed is 4, minute skill of the decomposition direction of each yardstick is respectively 32,32,64 and 64, after image is carried out multiple dimensioned geometry decomposition, the high-frequency sub-band figure that obtains to comprise the low frequency sub-band figure of image general profile and comprise image detail.

(3) collect the local window coefficient composition stochastic variable X of Image Multiscale geometric transformation territory high-frequency sub-band in training sample database, the method of sampling of X is: to the carrying out in Sample Storehouse the arbitrary image sample after multiple dimensioned geometric transformation, random selected position is as the sampling center in any high-frequency sub-band figure, collection is centered by this position, the local window size is the local window coefficient of w*w, process by bilinear interpolation simultaneously, collect the image transform domain sub-band coefficients on the same position on adjacent two decomposition scales of equidirectional, the local window coefficient that collects, comprise and have the dependent Image Sub-Band coefficient of statistics between the local window coefficient decomposition scale adjacent with equidirectional in same subband figure, be total to w*w+2 coefficient, w ∈ [5, 7, 9], through r local window coefficient sampling, the size of X is r*W, r represents to carry out the number of times of local window coefficient sampling, r satisfies 1024≤r＜M*N*t, M wherein, N is respectively the wide and high of image, m is the number of image pattern in the statistical modeling training sample database, W=w*w+2 represents the dimension of the random vector that the local window coefficient forms.

(4) adopt the statistical distribution of the vectorial y of any row in GSM models fitting X, this model can represent by following formula:

$y=\sqrt{z}U---\left(1\right)$

Wherein z is the stochastic variable greater than zero, and U is the Gaussian random variable of a zero-mean, and z and U are separate; The probability density function of y is so

$p_y\left(y\right)=\∫p\left(y\right|z)p_z\left(z\right)\mathrm{dz}=\∫\frac{\exp \left(\frac{-y^T{\left({\mathrm{zc}}_u\right)}^{-1}y}{2}\right)}{{\left(2\mathrm{\π}\right)}^{W/2}{\left|{\mathrm{zc}}_u\right|}^{1/2}}{p}_z\left(z\right)\mathrm{dz}---\left(2\right)$

C wherein _uCovariance matrix for U.

(5) according to the GSM model of upper step definition, in the known situation of z, y Normal Distribution obviously, namely p (y|z) represents with following formula:

$p\left(y\right|z)=\frac{1}{\sqrt{{\left(2\mathrm{\&pi;}\right)}^N{C}_{y|z}}}{e}^{\frac{-y^T{C_{y|z}}^{-1}\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA00002768893500012.png"\; state="\{\{state\}\}">y</figure-callout>}}{2}}$

So, adopt maximum likelihood to estimate to obtain the optimal estimation of z:

$\hat{z}=\underset{z}{\max }\left\{\log p\left(y\right|z)\right\}=\underset{z}{\min }\{W\log \left(\sqrt{z}\right)+Y^T{C_u}^{-1}Y/\left(2z^2\right)\}=Y^T{C}_{u}Y/W---\left(3\right)$

All row in X are carried out same processing, obtain a large amount of estimated value of variable z

Afterwards, obtain the probability density estimation p of z by non-parametric estmation _z|y(z|y)

$p_{z|y}\left(z\right|y)=\frac{1}{\mathrm{Wh}}\underset{i=1}{\overset{W}{\mathrm{\&Sigma;}}}K\left(\frac{z-{\hat{z}}_i}{h}\right)---\left(4\right)$

Wherein h is bandwidth, and (MISE) can obtain bandwidth h by the minimized average integrated square error, and K () is gaussian kernel function, and this probability density is to carry out the basis that successive image signal Bayes Optimum is estimated.

Step 2: treat the preparation of denoising picture frame, establish and treat that the denoising picture frame is t, collect simultaneously the front n two field picture of picture frame t, and the rear n two field picture of picture frame t, 10 〉=n 〉=1.

Step 3: the image coefficient transform domain statistical distribution pattern of being set up take step 1 is as priori, adopt the denoising sequence of image frames for the treatment of of preparing in the Curvelet transfer pair step 2 of the second generation to carry out Image Multiscale geometric transformation, frame by frame the high-frequency sub-band coefficient of the pending image sequence of preparation in step 2 is processed by Bayes's least-squares estimation, keep image low frequency sub-band coefficient constant, acquisition is based on the picture signal optimal estimation of spatial information statistical distribution in frame, and concrete steps are as follows:

Be not subjected to the vector x of the image transform domain high-frequency sub-band local neighborhood window coefficient composition of noise pollution to represent its statistical distribution with the GSM model, the image observation coefficient y that is subjected to noise pollution of its correspondence can be expressed as a stochastic variable of obeying the GSM model and be superimposed with corresponding picture noise variable so, namely

$y\stackrel{d}{=}x+\mathrm{\&omega;}\stackrel{d}{=}\sqrt{z}u+\mathrm{\&omega;}---\left(5\right)$

Wherein, ω is the picture noise of Gaussian distributed, and x is the multiple dimensioned geometric transformation territory high-frequency sub-band coefficient that is not subjected to the picture signal of noise pollution, and y is the make an uproar multiple dimensioned geometric transformation territory high-frequency sub-band coefficient of observation signal of the band corresponding with x,

The statistical distribution that the variable of expression equation both sides is corresponding equates; Be not subjected to the centre of neighbourhood coefficient x of the picture signal x of noise pollution _cCan utilize and be with the observed differential y that makes an uproar to carry out the maximum a posteriori estimation by Bayes's criterion of least squares, method of estimation is as follows:

If adopt

The error cost function that Image Sub-Band coefficient x is estimated is

And establish evaluated error corresponding to whole image and be

So

Can adopt following formula to calculate,

Wherein

P _X,Y(x, y) is subjected to the joint probability density function of the picture signal coefficient of noise pollution for make an uproar observed differential and former beginning and end of picture strip.Come optimal estimation not to be subjected to the image coefficient x of noise pollution by observed differential y, namely by minimizing evaluated error

Obtain x _cOptimal estimation.

By right Differentiate, and make that its derivative is zero, can obtain x _cThe optimal estimation value

Namely

${\hat{x}}_c=E\left\{x_c\right|y\}=\underset{0}{\overset{\&infin;}{\&Integral;}}p\left(z\right|y)E\{y_c|y,z\}\mathrm{dz}---\left(6\right)$

P in following formula (z|y) adopts formula (3) and (4) to estimate, and E{x _c| y, z} are actually in the situation that y, z are known, and the optimal estimation of x can estimate to calculate by maximum likelihood E{x _c| y, z}=zC _u(zC _u+ C _w) ^-1y。

Step 4: adopt cross-correlation method to carry out estimation between picture frame.The image cross-correlation method carries out interframe movement and estimates schematic diagram as shown in Figure 2, and in Fig. 2,1 and 2 represent the consecutive frame image, 2 representative image sub-block simple crosscorrelation peaks, and 3 represent final interframe movement vector estimated result.

If image subblock f ₁(v) and f ₂(v) displacement of Δ v occurs in consecutive frame, its motion can be expressed as

f ₂(v)＝f ₁(v-Δv) （7）

Like this, motion vector Δ v is calculated by following formula

$\mathrm{\&Delta;}\hat{v}=\underset{v}{\arg \max }{k}_{\mathrm{cc}}\left(v\right)=\arg \max \left\{F^{-1}\left(Y\left(\mathrm{\&omega;}\right)\right)\right\}---\left(8\right)$

Wherein

F ₁(ω) and F ₂(ω) difference presentation video sub-block f ₁(v) and f ₂(v) Fourier transform, Expression F ₂Complex conjugate (ω).

Step 5: utilize that between picture frame, motion estimation result is weighted processing to the image conversion domain coefficient optimal estimation result based on spatial information statistical distribution in frame in step 3, obtain the relevant best denoising coefficient estimation in multiple dimensioned geometric transformation territory of time domain of pending picture frame t, its computing method are:

${\hat{x}}_t=\underset{k\&Element;I}{\mathrm{\&Sigma;}}\mathrm{\&lambda;}\left(k\right){\hat{x}}_{c_k}---\left(9\right)$

Wherein,

Refer to the k two field picture coefficient in transform domain optimal estimation result based on spatial information statistical distribution in picture frame that obtains by formula (6) node-by-node algorithm, I needs the image sequence considered before and after pending image t, the sequence number is N=i+j+1 (i two field picture before t, j frame after t).ω (k) is the weighting factor of influence corresponding with each coefficient, and is relevant with the similarity of inter frame image local neighborhood.The t two field picture local neighborhood similarity degree corresponding with the t+i two field picture passes through Euclidean distance || v _t-v _t+i‖ ²Weigh.The weight of ω (k) is calculated as follows

$\mathrm{\&omega;}\left(k\right)=\frac{1}{C\left(i\right)}\exp (-{\left|\right|v_k-v_i\left|\right|}^2)$

In formula, $C\left(i\right)=\underset{k\&Element;I}{\mathrm{\&Sigma;}}\exp (-{\left|\right|v_k-v_i\left|\right|}^2),$ Play the normalization effect.

Step 6: the final process result of step 5 is carried out the denoising result that how much inverse transformations of Image Multiscale obtain pending picture frame t.

Step 7: repeated execution of steps 2 ~ 6 obtains the denoising result of whole image sequence.

Being illustrated in figure 3 as the original image that carries out denoising experiment in this example, is an independent two field picture that has in the image sequence of complex edge curve and superficial makings details.In denoising experiment, by adding Gauss's white noise at Fig. 3 left-hand seat fold and considering each 3 two field pictures before and after pending picture frame, use pair the superposeed image of noise of step 1 ~ step 6 to carry out the denoising experiment.For the performance of checking image denoising, adopt the white Gaussian noise of the different noise levels that superpose on this picture frame, and adopted this method to carry out respectively the denoising experiment, the visual effect after denoising is as shown in Figure 4.

in Fig. 4, the superposeed noisy image of the poor Gaussian noise of various criterion of the row at 5 places representatives, this row image from top to bottom, figure (a), figure (d), figure (g) is (15 to the standard deviation level of Fig. 3 superimposed noise respectively, 30, 60), the image column at 7 places comprises figure (c), figure (f), figure (i) is respectively and adopts step 1 of the present invention ~ step 6 to carry out the result of the multiple dimensioned geometric transformation denoising of space time information joint image, the image column figure at 6 places (b), figure (e), figure (h) is respectively the result that adopts traditional wavelet-decomposing method to carry out denoising, wherein, the number of plies of wavelet decomposition is 4, small echo used is CDF9/7 biorthogonal wavelet base.

In Fig. 46 and 7 is the visual effect comparison diagram of image denoising, shows that this method can protect image border curve and superficial makings details better when removing picture noise, obtain denoising image more clearly.

In order further to verify the denoising performance of this method, 4 image sequences with complex edge and superficial makings details have been selected in addition, by the white Gaussian noise of the different noise levels of stack (different standard deviations) on selected image sequence, further carried out picture noise and removed the contrast experiment.The image de-noising method that compares experiment has: (1) is based on the image de-noising method (being abbreviated as SCD) of the multiple dimensioned geometric transformation of single image, compare with this method, when being equivalent to adopt the method to carry out the image denoising processing, the number of image frames of selecting before and after pending image is zero, does not namely consider the front and back frame image information that pending image time domain is relevant; (2) the image wavelet transform denoising method (being abbreviated as MWD) of joint image space time information, this denoising method is compared unique not being both and has been adopted traditional wavelet to carry out picture breakdown with this method, the number of plies of wavelet decomposition is 4, and small echo used is CDF9/7 biorthogonal wavelet base; (3) image de-noising method proposed by the invention.Wherein, before and after (2) and (3) have all chosen pending picture frame, each 3 two field pictures carry out the image denoising processing.Table 1 has shown and adopts this several method image sequence to be carried out average peak signal to noise ratio (PSNR) result of denoising, as can be seen from Table 1, this method and other denoising method specific energy mutually obtain higher Y-PSNR, obtain better image denoising and process visual effect.

Table 1: image denoising effect contrast

The present invention is not limited to aforesaid embodiment, can to correct or reselect someway in abovementioned steps, all can implement.The present invention expands to any new feature or any new combination that discloses in this manual, and the arbitrary new method that discloses or step or any new combination of process.The present invention is particularly suitable for having the Denoising processing of complex geometry boundary curve and superficial makings details.

Claims (6)

1. the multiple dimensioned geometric transformation denoising method of the image sequence of a space-time unite, it is characterized in that: at first treat the denoising image and carry out multiple dimensioned geometric transformation, Gauss's yardstick is mixed (GSM) model be applied to Image Multiscale geometric transformation territory, image transform domain is carried out the coefficients statistics modeling, take the coefficients statistics model that obtained as priori, by Bayes's least-squares estimation, obtain the image conversion domain coefficient optimal estimation based on spatial information statistical distribution in picture frame; Then introduce image sequence interframe weighting factor according to the correlativity of motion compensation principle and image sequence interframe sub-block, process by weighting the relevant optimum coefficient of time domain that image sequence interframe sub-block coefficient obtains pending picture frame, by how much inverse transformations of Image Multiscale, obtain the denoising image of high s/n ratio at last.

2. the multiple dimensioned geometric transformation denoising method of the image sequence of a kind of space-time unite according to claim 1, it is characterized in that: described Image Multiscale geometric transformation refers to, adopt Second Generation Curvelet Transform to carry out Image Multiscale geometric transformation, the scale parameter that image C urvelet conversion is decomposed is 4, Directional Decomposition number on each yardstick is respectively 32, 32, 64 and 64, image is transformed in the subband figure that obtains after decomposition, comprise image low frequency sub-band figure and high-frequency sub-band figure, image low frequency sub-band figure comprises the image general profile, image high-frequency sub-band figure mainly comprises image detail.

3. the multiple dimensioned geometric transformation denoising method of the image sequence of a kind of space-time unite according to claim 2, it is characterized in that: describedly image transform domain is carried out coefficients statistics be modeled as and adopt the GSM model to carry out spatial information statistical distribution modeling in picture frame, specifically carry out following steps:

(1) according to treat boundary curve that the denoising image has and the visual characteristic of superficial makings details, collect to have in identical photographed scene treat the identical visual characteristic of denoising image be not subjected in a large number the image I of noise pollution _i, composition diagram is as statistical distribution modeling sample storehouse { I _i, 1≤i≤m} is total to m width image, m 〉=10 in Sample Storehouse;

(2) to the arbitrary image I in image library _iAdopt Second Generation Curvelet Transform, obtain I _iCorresponding each high-frequency sub-band of Curvelet transform domain figure matrix of coefficients

J represents decomposition scale, and θ represents to decompose direction, and the scale parameter that image C urvelet conversion is decomposed is 4, and minute skill of the decomposition direction on each decomposition scale of image is respectively 32,32,64 and 64;

(3) local window coefficient sampling is to any high-frequency sub-band figure matrix of coefficients

Collection sampled point, window size centered by arbitrarily (kx, ky) are the local window coefficient of w*w, and w ∈ [5,7,9] processes by bilinear interpolation simultaneously, collection

With

Picture breakdown sub-band coefficients on middle same position (kx, ky) point forms stochastic variable y, and the dimension of y is w*w+2;

(4) adopt the local window coefficient method of sampling described in (3), each high-frequency sub-band figure matrix of coefficients to image in Sample Storehouse carries out r sampling, sampling number satisfies 1024≤r＜M*N*m, M, N is respectively the wide and high of image, and size of coefficient composition that r sampling obtained is r*W stochastic variable X, the coefficient vector that any row vector of X obtains for carry out the sampling of local window coefficient in image transform domain high-frequency sub-band figure, W=w*w+2, wherein m is the amount of images of Sample Storehouse;

Wherein, in the subband figure that obtains after image is decomposed, comprise image low frequency sub-band figure and high-frequency sub-band figure, image low frequency sub-band figure comprises the image general profile, and image high-frequency sub-band figure mainly comprises image detail;

(5) adopt the statistical distribution pattern of GSM models fitting Image Multiscale geometric transformation domain coefficient, namely the stochastic variable that consists of of the vectorial y of any row in X is carried out the statistical modeling analysis by the GSM model, and this statistical model represents by following formula: $y=\sqrt{z}U---\left(1\right)$

Wherein z is the stochastic variable greater than zero, and U is that an average is zero Gaussian random variable, and z and U are separate, and the probability density function of y is:

$p_y\left(y\right)=\&Integral;p\left(y\right|z)p_z\left(z\right)\mathrm{dz}=\&Integral;\frac{\exp \left(\frac{-y^T{\left({\mathrm{zc}}_u\right)}^{-1}y}{2}\right)}{{\left(2\mathrm{\&pi;}\right)}^{W/2}{\left|{\mathrm{zc}}_u\right|}^{1/2}}{p}_z\left(z\right)\mathrm{dz}---\left(2\right)$

C wherein _uBe the covariance matrix of U, adopt maximum likelihood to estimate the parameter z in model is carried out optimal estimation

$\hat{z}=\underset{z}{\max }\left\{\log p\left(y\right|z)\right\}=\underset{z}{\min }\{W\log \left(\sqrt{z}\right)+Y^T{C_u}^{-1}Y/\left(2z^2\right)\}=Y^T{C}_{u}Y/W---\left(3\right)$

Then basis

Characteristic distributions, the probability density that adopts Nonparametric Estimation to obtain z is estimated p _z|y(z|y)

$p_{z|y}\left(z\right|y)=\frac{1}{\mathrm{Wh}}\underset{i=1}{\overset{W}{\mathrm{\&Sigma;}}}K\left(\frac{z-{\hat{z}}_i}{h}\right)---\left(4\right)$

Wherein h is bandwidth, and (MISE) can obtain bandwidth h by the minimized average integrated square error, and K () is gaussian kernel function.

4. the multiple dimensioned geometric transformation denoising method of the image sequence of a kind of space-time unite according to claim 3, it is characterized in that: described image conversion domain coefficient optimal estimation based on spatial information statistical distribution in picture frame refers to, represent not to be subjected to the statistical distribution of the random vector x that in the image transform domain high-frequency sub-band figure of noise pollution, the local window coefficient forms by the GSM model, the image observation coefficient y that be subjected to noise pollution corresponding with x is expressed as:

$y\stackrel{d}{=}x+\mathrm{\&omega;}\stackrel{d}{=}\sqrt{z}u+\mathrm{\&omega;}---\left(5\right)$

Wherein ω is the picture noise of Gaussian distributed, and x is the multiple dimensioned geometric transformation territory high-frequency sub-band coefficient that is not subjected to the picture signal of noise pollution, and y is the make an uproar multiple dimensioned geometric transformation territory high-frequency sub-band coefficient of observation signal of the band corresponding with x,

The statistical distribution that the variable of expression equation both sides is corresponding equates;

Adopt Bayes's criterion of least squares to carry out the window center coefficient x that maximum a posteriori estimates to obtain local window coefficient x _cThe optimal estimation result

${\hat{x}}_c=E\left\{x_c\right|y\}=\underset{0}{\overset{\&infin;}{\&Integral;}}p\left(z\right|y)E\{y_c|y,z\}\mathrm{dz}---\left(6\right)$

P in following formula (z|y) adopts formula (4) to estimate, E{x _c| y, z}=zC _u(zC _u+ C _w) ^-1y。

5. the multiple dimensioned geometric transformation denoising method of the image sequence of a kind of space-time unite according to claim 4, it is characterized in that, the motion compensation of described image sequence inter-frame information refers to adopt cross-correlation method to obtain the motion estimation result of consecutive frame image subblock, and computing method are:

If image subblock f ₁(v) and f ₂(v) displacement of Δ v occurs in consecutive frame, its movement representation is

f ₂(v)＝f ₁(v-Δv) （7）

Like this, motion vector Δ v is estimated by following formula

$\mathrm{\&Delta;}\hat{v}=\underset{v}{\arg \max }{k}_{\mathrm{cc}}\left(v\right)=\arg \max \left\{F^{-1}\left(Y\left(\mathrm{\&omega;}\right)\right)\right\}---\left(8\right)$

Wherein

F ₁(ω) and F ₂(ω) difference presentation video sub-block f ₁(v) and f ₂(v) Fourier transform,

Expression F ₂Complex conjugate (ω).

6. the multiple dimensioned geometric transformation denoising method of the image sequence of a kind of space-time unite according to claim 5, it is characterized in that, described weighting is processed image sequence interframe sub-block coefficient and is referred to, image conversion domain coefficient optimal estimation result based on spatial information statistical distribution in picture frame is weighted summation, obtain the best denoising coefficient of the image transform domain estimated result of image sequence Spatial-temporal Information Fusion, that is:

${\hat{x}}_t=\underset{k\&Element;I}{\mathrm{\&Sigma;}}\mathrm{\&lambda;}\left(k\right){\hat{x}}_{c_k}---\left(9\right)$

Wherein,

Refer to the k two field picture coefficient in transform domain optimal estimation result based on spatial information statistical distribution in picture frame that obtains by formula (6) node-by-node algorithm, I needs the image sequence considered before and after pending image t, the sequence number is N=i+j+1 (i two field picture before t, j frame after t), λ (k) is the weighting factor of influence, relevant with the similarity of local neighborhood corresponding between image, the t two field picture local neighborhood similarity degree corresponding with the t+i two field picture passes through Euclidean distance || v _t-v _t+i‖ ²Weigh, the weight of λ (k) is calculated as follows:

$\mathrm{\&lambda;}\left(k\right)=\frac{1}{C\left(i\right)}\exp (-{\left|\right|v_k-v_i\left|\right|}^2)---\left(10\right)$

In formula, $C\left(i\right)=\underset{k\&Element;I}{\mathrm{\&Sigma;}}\exp (-{\left|\right|v_k-v_i\left|\right|}^2),$ Play the normalization effect.

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