CN103310424A - Image denoising method based on structural similarity and total variation hybrid model - Google Patents

Abstract

The invention discloses an image denoising method based on a structural similarity and total variation hybrid model. The method comprises (1), designing a functional E (u); (2), introducing a new auxiliary variable to the E (u) and turning the original model into two simple sub-models by using an alternate iterative method; (3), performing numerical solution on the two sub-models respectively by using a gradient descent method and a chambolle projection method to obtain a discrete mathematical model; (4), inputting a noisy image f; (5), performing iteration denoising on the f by using the discrete mathematical model; and (6), stopping until the iteration reaches set end conditions and outputting the denoised image. By means of the image denoising method, structural information of images can be well maintained while denoising is performed effectively, visual effects of the images are improved, and the method is applicable to denoising of natural images.

Description

A kind of image de-noising method based on structural similarity and total variation mixture model

Technical field

The present invention relates to the image technique process field, be specifically related to a kind of image de-noising method based on structural similarity and total variation mixture model, be applicable to the noise remove of natural image.

Background technology

Image form and transmission course in because interference of noise causes quality to descend, this has had a strong impact on the correct understanding that people convey a message to image, so before image carried out subsequent treatment, must first carry out denoising to image.

The method of relevant image denoising has a lot, roughly can be divided into two big classes: spatial domain denoising method and transform domain denoising method.The spatial domain denoising method is directly pixel to be handled, and representational algorithm has mean filter algorithm and middle finger filtering algorithm.The different characteristic that the transform domain denoising method mainly utilizes useful signal and noise signal to show in transform domain is removed noise effectively.Representational algorithm has based on the denoise algorithm of Fourier transform with based on the denoise algorithm of wavelet transformation.

At present, the airspace filter method has had very big development, many new methods occurred, as based on the method for fuzzy mathematics, based on method of partial differential equation etc.Particularly based on the method for partial differential equation, each image processing field such as cut apart at image denoising, image and obtained great success, become image handle with analyze in important tool and research focus.And wherein most typical representative is by ROF, and Osher and Fatemi propose the ROF model based on TV.The upsurge of image transaction module researchs such as this model started image denoising based on TV, cut apart, and become image and handle one of research focus.

Though the ROF model can keep edge of image preferably when carrying out denoising, two significant disadvantages are arranged also: the one, be easy to generate " staircase effect ", the 2nd, bad to detailed information such as the texture maintenance of image.At these problems, many scholars improve the ROF model, but these improvement great majority are the regular terms at the ROF model, and a loyal improved research is very limited for model.In fact the loyal item of ROF model uses L ²Modeling is carried out to " vibration " composition (comprising texture, noise) of image in the space, and uses L ²Tolerance is portrayed.In fact L ²Norm has only reflected the difference between image list pixel, and it is structural to have ignored image space.Yet natural image is highly structural, and the pixel that relatively approaches in the very strong relevance, particularly spatial domain is namely arranged between pixel, and this relevance is containing the important information of object structures in the visual scene.Therefore, use L ²Norm is as loyal of denoising model, and denoising result can not be preferably be consistent with the visual characteristic of human eye, thereby has reduced the visual effect of recovering image.

Summary of the invention

In view of the deficiencies in the prior art, the present invention aims to provide a kind of image denoising new method based on structural similarity and total variation mixture model.Specifically, the angle structural information that structural similarity is formed from image is defined as and is independent of brightness, contrast, and reflects the structure attribute of object in the image.It is the combination of brightness, contrast and three different factors of structure with distortion modeling, and with the estimation of average as brightness, the estimation that standard deviation is spent as a comparison, covariance is as the estimation of structural similarity.The present invention introduces structural similarity and replaces L in loyal of image denoising model ²Norm can make image keep original structure information better in the denoising process, improves the visual effect of recovering image.

To achieve these goals, the technical solution used in the present invention is as follows:

A kind of image de-noising method based on structural similarity and total variation mixture model has target image, said method comprising the steps of:

(1) design functional E (u);

(2) in described functional E (u), introduce auxiliary variable, obtain its equivalent form of value E ^*(u);

(3) utilization replaces alternative manner with described functional E ^*(u) be converted into two submodels, model 1 and model 2;

(4) use gradient descent method, model 2 to use the chambolle projecting method to carry out numerical solution, and obtain the discrete mathematics model to described model 1;

(5) input noise image f;

(6) utilize described discrete mathematics model that image f is carried out the iteration denoising;

When (7) reaching the iteration stopping condition, the image after the output denoising.

What need further specify is that described functional E (u) is E (u)=∫ _Ω(1-SSIM (f, u)) dxdy+ λ ∫ _Ω| ▽ u|dxdy, wherein, described ∫ _Ω| ▽ u|dxdy is regular terms, in order to represent the bound term of level and smooth of output image, described ∫ _Ω(1-SSIM (f, u)) dxdy is loyal, strengthens in order to the contrast of representing the initial observation image of output image u f, λ is regular parameter, in order to balance regular terms and loyal item, u (x, y) be in the Ω of image support territory, coordinate position is (x, the grey scale pixel value of y) locating.

What need further specify is described new functional E ^*(u) be:

${\∫}_{\mathrm{\Ω}}(1-\mathrm{SSIM}(f,u))\mathrm{dxdy}+\mathrm{\λ}{\∫}_{\mathrm{\Ω}}|\▿v|\mathrm{dxdy}+\frac{\mathrm{\μ}}{2}{\∫}_{\mathrm{\Ω}}{(u-v)}^2\mathrm{dxdy};$

Wherein, the auxiliary variable of v for introducing, μ is the parameter of penalty, is used for guaranteeing that u and v are fully approaching.

Need to prove that described model 1 is respectively with model 2:

$u^{n+1}=\underset{u}{\arg \min {\∫}_{\mathrm{\Ω}}}(1-\mathrm{SSIM}(f,u))\mathrm{dxdy}+\frac{\mathrm{\μ}}{2}{\∫}_{\mathrm{\Ω}}{(u-v^n)}^2\mathrm{dxdy}---\left(1\right);$

$v^{n+1}=\underset{v}{\arg \min }\mathrm{\λ}{\∫}_{\mathrm{\Ω}}|\▿v|\mathrm{dxdy}+\frac{\mathrm{\μ}}{2}{\∫}_{\mathrm{\Ω}}{(u^n-v)}^2\mathrm{dxdy}---\left(2\right).$

Need to prove, described use gradient descent method solving model 1, corresponding Eulerian equation is: $-{\stackrel{\→}{\▿}}_u\mathrm{SSIM}(f,u)+\mathrm{\μ}(u-v)=0.$

Need to prove, described For:

${\stackrel{\→}{\▿}}_u\mathrm{SSIM}(f,u)=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\frac{2}{m{B}_1^2{B}_2^2}[A_1{B}_1(B_{2}x-A_{2}y)+B_1{B}_2(A_2-A_1){\mathrm{\μ}}_{x}1+A_1{A}_2(B_1-B_2){\mathrm{\μ}}_{y}1]$

Wherein, x, y represent respectively to make the column vector with same dimension from the image block that the same spatial location of image f and u is extracted, the sum of M presentation video piece, and m represents the number of pixels of topography's piece, 1 each element of expression all is 1 column vector.

Need to prove described A ₁, A ₂, B ₁, B ₂Be respectively

A ₁＝2μ _xμ _y+C ₁，A ₂＝2σ _xy+C ₂， $B_1={\mathrm{\μ}}_x^2+{\mathrm{\μ}}_y^2+C_1,$ $B_2={\mathrm{\σ}}_x^2+{\mathrm{\σ}}_y^2+C_2;$

Wherein, μ _x, μ _yThe average of representing x and y respectively, σ _x, σ _yRepresent x and y standard deviation respectively, σ _XyThe covariance of expression x and y, C ₁, C ₂Be constant.

Need to prove described μ _x, μ _y, σ _x, σ _y, σ _Xy, C ₁, C ₂Be respectively:

${\mathrm{\μ}}_x=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{x}_i,$ ${\mathrm{\μ}}_y=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{x}_i,$ ${\mathrm{\σ}}_x=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{(x_i-{\mathrm{\μ}}_x)}^2},$ ${\mathrm{\σ}}_y=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{(x_i-{\mathrm{\μ}}_y)}^2},$ ${\mathrm{\σ}}_{\mathrm{xy}}=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i(x_i-{\mathrm{\μ}}_x)(y_i-{\mathrm{\μ}}_y)},$ C ₁＝(K ₁×L) ²，C ₂＝(K ₂×L) ²；

Wherein, x _i, y _i(i=1 2...N) is respectively the element of x and y, and N is the dimension of x and y, ω _iBe the weighting coefficient of i element and satisfy

K ₁=0.01, K ₂=0.03, L=255.

Need to prove that with chambolle projecting method solving model (2), the iterative formula that obtains is in the described step (3)

$v^n=u^n-\frac{\mathrm{\λ}}{\mathrm{\μ}}\mathrm{div}p,$

Wherein, $p^0=0,p^{k+1}=\frac{p^k+\mathrm{\τ}\▿({\mathrm{div}p}^k-\frac{\mathrm{\μ}}{\mathrm{\λ}}{u}^n)}{1+\mathrm{\τ}|\▿({\mathrm{div}p}^k-\frac{\mathrm{\μ}}{\mathrm{\λ}}{u}^n)|},$ τ represents the iteration interval time parameter.

Beneficial effect of the present invention is:

1, because the present invention introduces structural similarity in loyal of denoising model, to replace original L ²Norm, the visual effect of image improves so that image can keep original structural information preferably in the denoising process in institute;

2, the present invention utilizes alternately process of iteration in the model solution process, and two variable mutual restriction on calculating influence each other like this, alternately calculate, and makes reconstructed image develop to more excellent direction, till obtaining a better image;

3, the iteration stopping principle is to recover image u at L among the present invention ²Fully near initial observation image f, make this model have structural similarity and L concurrently like this under the norm meaning ²Norm advantage separately, the denoising effect of image is more excellent.

Description of drawings

Fig. 1 is the process flow diagram of image de-noising method of the present invention;

Fig. 2 is the original test sample figure of image de-noising method of the present invention;

Fig. 3 is the exemplary plot behind the interpolation white Gaussian noise of image de-noising method of the present invention;

Fig. 4 is ROF model denoising exemplary plot in the prior art;

Fig. 5 is the denoising exemplary plot of image de-noising method of the present invention.

Embodiment

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

As shown in Figure 1, the present invention is a kind of image de-noising method based on structural similarity and total variation mixture model, has target image, said method comprising the steps of:

Step 1, design functional E (u);

Need to prove that for convenience of description, present embodiment is at a width of cloth digital picture, (x y) is illustrated in the Ω of image support territory u, and coordinate is (x, the grey scale pixel value of y) locating.

Wherein, ▽ u presentation video u (x, gradient fields y): ▽ u=(u _x, u _y);

▽ u has reflected near the situation of change any point in the image, and gradient magnitude is represented the speed that changes, the direction that the direction indication of gradient changes.

SSIM (f, u) the structural similarity degree of presentation video f and u also is structural similarity:

$\mathrm{SSIM}(f,u)=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\mathrm{SSIM}(x,y);$

Wherein, x, y represent respectively to make the column vector with same dimension from the image block that the same spatial location of f and u is extracted, and M represents the sum of topography's piece.SSIM (x y) is defined as:

$\mathrm{SSIM}(x,y)=\frac{(2{\mathrm{\μ}}_x{\mathrm{\μ}}_y+C_1)({2\mathrm{\σ}}_{\mathrm{xy}}+C_2)}{({\mathrm{\μ}}_x^2+{\mathrm{\μ}}_y^2+C_1)({\mathrm{\σ}}_x^2+{\mathrm{\σ}}_y^2+C_2)}$

Wherein, μ _x, μ _yThe average of representing x and y respectively, σ _x, σ _yRepresent x and y standard deviation respectively, σ _XyThe covariance of expression x and y, C ₁, C ₂Be constant.Their concrete computing formula is as follows:

${\mathrm{\μ}}_x=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{x}_i,$ ${\mathrm{\μ}}_y=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{x}_i,$ ${\mathrm{\σ}}_x=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{(x_i-{\mathrm{\μ}}_x)}^2},$ ${\mathrm{\σ}}_y=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{(x_i-{\mathrm{\μ}}_x)}^2},$ ${\mathrm{\σ}}_{\mathrm{xy}}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i(x_i-{\mathrm{\μ}}_x)(y_i-{\mathrm{\μ}}_y),$ C ₁＝(K ₁×L) ²，C ₂＝(K ₂×L) ²；

Wherein, x _i, y _i(i=1 2...N) is respectively the element of x and y, and N is the dimension of x and y, ω _iBe the weighting coefficient of i element and satisfy

K ₁=0.01, K ₂=0.03, L=255.

From the definition of structural similarity as can be seen, SSIM (f, value u) between-1 to 1, and SSIM (f, value u) is the bigger the better.

Take all factors into consideration the flatness of image and the maximum of original structure information is kept, structural similarity maximum at target image u and noise image f, perhaps (1-SSIM (f, u)) under the least meaning, make the regular terms minimum of image smoothing item, namely seek to strengthen image u, make functional E (u) minimum: E (u)=∫ _Ω(1-SSIM (f, u)) dxdy+ λ ∫ _Ω| ▽ u|dxdy;

Wherein, $\▿u=(\frac{\∂u}{\∂x},\frac{\∂u}{\∂y}),$

$|\▿u|=\sqrt{u_x^2+u_y^2},$

▽ u represents the gradient of noise image u,

With Be respectively image at the single order partial derivative of x and y direction.

Above-mentioned functional comprises two parts, regular terms and loyal item, wherein, ∫ _Ω| ▽ u|dxdy is regular terms, the bound term that the expression output image is level and smooth, ∫ _Ω(1-SSIM (f, u)) dxdy is loyal of the noise image f of output image u.This loyalty item requires image after the denoising and input picture that similarity on structure and the content should be arranged, and regular parameter λ plays important equilibrium activity between regular terms and loyal.

Step 2 is introduced auxiliary variable v in functional E (u), obtain its equivalent form of value E ^*(u).

$E*\left(u\right)={\∫}_{\mathrm{\Ω}}(1-\mathrm{SSIM}(f,u))\mathrm{dxdy}+\mathrm{\λ}{\∫}_{\mathrm{\Ω}}|\▿v|\mathrm{dxdy}+\frac{\mathrm{\μ}}{2}{\∫}_{\mathrm{\Ω}}{(u-v)}^2\mathrm{dxdy};$

Wherein, μ is the parameter of penalty, is used for guaranteeing that u and v are fully approaching.

The minimal value of functional E (u) found the solution change into functional E of equal valuely ^*Finding the solution (u).

Step 3 is utilized alternately iterative strategy E ^*(u) be following two simple submodels, model 1 and model 2:

$u^{n+1}=\underset{u}{\arg \min {\∫}_{\mathrm{\Ω}}}(1-\mathrm{SSIM}(f,u))\mathrm{dxdy}+\frac{\mathrm{\μ}}{2}{\∫}_{\mathrm{\Ω}}{(u-v^n)}^2\mathrm{dxdy}---\left(1\right)$

$v^{n+1}=\underset{v}{\arg \min }\mathrm{\λ}{\∫}_{\mathrm{\Ω}}{|\▿v|}_1\mathrm{dxdy}+\frac{\mathrm{\μ}}{2}{\∫}_{\mathrm{\Ω}}{(u^n-v)}^2\mathrm{dxdy}---\left(2\right)$

Wherein, n is the iterations of variable.

Step 4 is used gradient descent method and chambolle projecting method respectively to model 1 and model 2

Carry out numerical solution, obtain the discrete mathematics model.

Wherein use the Eulerian equation of gradient descent method solving model 1 correspondence to be:

$-{\stackrel{\→}{\▿}}_u\mathrm{SSIM}(f,u)+\mathrm{\μ}(u-v)=0;$

Wherein, x, y represent respectively to make the column vector with same dimension from the image block that the same spatial location of image f and u is extracted, the sum of M presentation video piece, and m represents the number of pixels of topography's piece, 1 each element of expression all is 1 column vector, and

${\stackrel{\→}{\▿}}_u\mathrm{SSIM}(f,u)=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\frac{2}{m{B}_1^2{B}_2^2}[A_1{B}_1(B_{2}x-A_{2}y)+B_1{B}_2(A_2-A_1){\mathrm{\μ}}_{x}1+A_1{A}_2(B_1-B_2){\mathrm{\μ}}_{y}1],$

A ₁＝2μ _xμ _y+C ₁，A ₂＝2σ _xy+C ₂， $B_1={\mathrm{\μ}}_x^2+{\mathrm{\μ}}_y^2+C_1,$ $B_2={\mathrm{\σ}}_x^2+{\mathrm{\σ}}_y^2+C_2;$

Wherein, μ _x, μ _yThe average of representing x and y respectively, σ _x, σ _yRepresent x and y standard deviation respectively, σ _XyThe covariance of expression x and y, C ₁, C ₂Be constant.Their computing formula is respectively: ${\mathrm{\μ}}_x=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{x}_i,$ ${\mathrm{\μ}}_y=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{x}_i,$ ${\mathrm{\σ}}_x=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{(x_i-{\mathrm{\μ}}_x)}^2},$ ${\mathrm{\σ}}_y=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i{(x_i-{\mathrm{\μ}}_y)}^2},$ ${\mathrm{\σ}}_{\mathrm{xy}}=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i(x_i-{\mathrm{\μ}}_x)(y_i-{\mathrm{\μ}}_y)},$ C ₁＝(K ₁×L) ²，C ₂＝(K ₂×L) ²；

Wherein, x _i, y _i(i=1 2...N) is respectively the element of x and y, and N is the dimension of x and y, ω _iBe the weighting coefficient of i element and satisfy

K ₁=0.01, K ₂=0.03, L=255.

Fixed variable v, according to the Eulerian equation of model 1, utilize the gradient descent method can obtain mathematical model:

$\frac{\∂u}{\∂t}={\stackrel{\→}{\▿}}_u\mathrm{SSIM}(f,u)+\mathrm{\μ}(v-u);$

Wherein, t represents the time.

And then derive its discrete mathematical model: $\frac{\∂u}{\∂t}=\frac{u^{n+1}-u^n}{\mathrm{\τ}}={\stackrel{\→}{\▿}}_u\mathrm{SSIM}(f,u)+\mathrm{\μ}(v-u^n),$ Namely

$u^{n+1}=u^n+\mathrm{\τ}({\stackrel{\→}{\▿}}_u\mathrm{SSIM}(f,u)+\mathrm{\μ}(v-u^n))---\left(3\right);$

Wherein, τ represents the iteration interval time parameter, and n represents the iterations parameter.

Utilize chambolle projecting method solving model (2), the solution formula that obtains is:

$v^n=u^n-\frac{\mathrm{\λ}}{\mathrm{\μ}}\mathrm{div}p---\left(4\right);$

Wherein, div () is divergence operator,

The iterative formula of p is

$p^0=0,p^{k+1}=\frac{p^k+\mathrm{\τ}\▿({\mathrm{div}p}^k-\frac{\mathrm{\μ}}{\mathrm{\λ}}{u}^n)}{1+\mathrm{\τ}|\▿({\mathrm{div}p}^k-\frac{\mathrm{\μ}}{\mathrm{\λ}}{u}^n)|};$

Utilize alternately iterative idea, obtained the iterative formula of u and v by (3) and (4).

Step 5 is imported the original denoising image f that treats;

Step 6 utilizes the discrete mathematics model that image f is carried out the iteration denoising, obtains denoising image u one time;

Step 7 is proceeded the iteration denoising to image u, up to reaching the iteration stopping condition, the image u after the output denoising.

Finish an iteration denoising of this method by above-mentioned steps (1) to step (6).Need to prove that along with the increase of iterations, it is smooth that image more and more is tending towards.But iterations is too much, and image is too smooth, causes image blurring.Therefore, set the iteration stopping condition:

$\sqrt{\mathrm{\&Sigma;}{(u^{n+1}(i,j)-u^n(i,j))}^2}<\mathrm{\&epsiv;};$

Wherein, ε is very little constant.

Further understand technical scheme of the present invention and effect by following experiment.

Experiment condition and content

Experiment condition: test employed input picture as shown in Figure 2, wherein, figure (2a) is test pattern House, and figure (2b) is test pattern Pepper, and Fig. 3 is that figure (2a) adding standard deviation is 20 noise image.

Experiment content: under above-mentioned experiment condition, select the comparison that experimentizes of existing ROF denoise algorithm and the inventive method for use.The objective evaluation index of denoising result is weighed with Y-PSNR PSNR and structural similarity SSIM.

Experiment 1 is carried out denoising with existing ROF method to figure (3), and what numerical solution adopted is the algorithm of chambolle projection, wherein, and regular parameter λ=18, iteration interval time parameter τ=0.005.As shown in Figure 4, the method possesses certain denoising ability, but it is undesirable to recover image visual effect, can not keep the original structure information of image well, and be easy to generate staircase effect.

Experiment 2 is carried out denoising, the parameter setting with the inventive method to figure (3): regular parameter λ=0.08, iteration interval time parameter τ=0.01, stop condition ε=10 ^-3As shown in Figure 5, the inventive method has significant noise inhibiting ability, and the image after the denoising seems smoother, nature, and the structural information of image keeps ground better, details is also more clear, and than existing ROF method, the visual effect of recovering image is greatly improved.

Experiment 3, it is 20,30,40,50 Gauss's additive white noises that image among figure (2a) and the figure (2b) is added noise criteria difference σ respectively, with PSNR and the SSIM evaluation index as denoising effect, existing ROF denoising method and method of the present invention are compared, and PSNR value and the SSIM value of two kinds of method denoising results are listed in table 1 and table 2 respectively.

The PSNR of two kinds of denoise algorithm (dB) value relatively in the table 1

The SSIM value of two kinds of denoise algorithm relatively in the table 2

Can draw denoising result of the present invention according to table 1 and table 2 and on PSNR and SSIM evaluation index, all make moderate progress, especially be significantly improved in the SSIM value.Table 1 and table 2 have objectively shown superiority of the present invention.

For a person skilled in the art, can make other various corresponding changes and distortion according to technical scheme described above and design, and these all changes and distortion should belong within the protection domain of claim of the present invention all.

Claims (9)

1. the image de-noising method based on structural similarity and total variation mixture model has target image, it is characterized in that, said method comprising the steps of:

(1) design functional E (u);

(2) in described functional E (u), introduce auxiliary variable, obtain its equivalent form of value E ^*(u);

(3) utilize the alternately described functional E of alternative mannerization ^*(u) be two submodels, model 1 and model 2;

(4) use gradient descent method, model 2 to use the chambolle projecting method to carry out numerical solution, and obtain the discrete mathematics model to described model 1;

(5) input noise image f;

(6) utilize described discrete mathematics model that image f is carried out the iteration denoising;

When (7) reaching the iteration stopping condition, the image after the output denoising.

2. image de-noising method according to claim 1 is characterized in that, described functional E (u) is E (u)=∫ _Ω(1-SSIM (f, u)) dxdy+ λ ∫ _Ω| ▽ u|dxdy, wherein, described ∫ _Ω| ▽ u|dxdy is regular terms, in order to represent the bound term of level and smooth of output image, described ∫ _Ω(1-SSIM (f, u)) dxdy is loyal, strengthens in order to the contrast of representing the initial observation image of output image u f, λ is regular parameter, in order to balance regular terms and loyal item, u (x, y) be in the Ω of image support territory, coordinate position is (x, the grey scale pixel value of y) locating.

3. image de-noising method according to claim 1 is characterized in that, described new functional E ^*(u) be ${\&Integral;}_{\mathrm{\&Omega;}}(1-\mathrm{SSIM}(f,u))\mathrm{dxdy}+\mathrm{\&lambda;}{\&Integral;}_{\mathrm{\&Omega;}}|\&dtri;v|\mathrm{dxdy}+\frac{\mathrm{\&mu;}}{2}{\&Integral;}_{\mathrm{\&Omega;}}{(u-v)}^2\mathrm{dxdy};$

Wherein, the auxiliary variable of v for introducing, μ is the parameter of penalty, is used for guaranteeing fully approaching of u and v.

4. image denoising new method according to claim 1 is characterized in that, described model 1 is respectively with model 2:

$u^{n+1}=\underset{u}{\arg \min {\&Integral;}_{\mathrm{\&Omega;}}}(1-\mathrm{SSIM}(f,u))\mathrm{dxdy}+\frac{\mathrm{\&mu;}}{2}{\&Integral;}_{\mathrm{\&Omega;}}{(u-v^n)}^2\mathrm{dxdy}---\left(1\right);$

$v^{n+1}=\underset{v}{\arg \min }\mathrm{\&lambda;}{\&Integral;}_{\mathrm{\&Omega;}}|\&dtri;v|\mathrm{dxdy}+\frac{\mathrm{\&mu;}}{2}{\&Integral;}_{\mathrm{\&Omega;}}{(u^n-v)}^2\mathrm{dxdy}---\left(2\right).$

5. image de-noising method according to claim 1 is characterized in that, described use gradient descent method solving model 1, and corresponding Eulerian equation is:

$-{\stackrel{\&RightArrow;}{\&dtri;}}_u\mathrm{SSIM}(f,u)+\mathrm{\&mu;}(u-v)=0.$

6. image de-noising method according to claim 5 is characterized in that, and is described ${\stackrel{\&RightArrow;}{\&dtri;}}_u\mathrm{SSIM}(f,u)$ For:

${\stackrel{\&RightArrow;}{\&dtri;}}_u\mathrm{SSIM}(f,u)=\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}\frac{2}{m{B}_1^2{B}_2^2}[A_1{B}_1(B_{2}x-A_{2}y)+B_1{B}_2(A_2-A_1){\mathrm{\&mu;}}_{x}1+A_1{A}_2(B_1-B_2){\mathrm{\&mu;}}_{y}1]$

Wherein, x, y represent respectively to make the column vector with same dimension from the image block that the same spatial location of image f and u is extracted, the sum of M presentation video piece, and m represents the number of pixels of topography's piece, 1 each element of expression all is 1 column vector.

7. image de-noising method according to claim 6 is characterized in that, described A ₁, A ₂, B ₁, B ₂Be respectively

A ₁＝2μ _xμ _y+C ₁，A ₂＝2σ _xy+C ₂， $B_1={\mathrm{\&mu;}}_x^2+{\mathrm{\&mu;}}_y^2+C_1,$ $B_2={\mathrm{\&sigma;}}_x^2+{\mathrm{\&sigma;}}_y^2+C_2;$

Wherein, μ _x, μ _yThe average of representing x and y respectively, σ _x, σ _yRepresent x and y standard deviation respectively, σ _XyThe covariance of expression x and y, C ₁, C ₂Be constant.

8. image de-noising method according to claim 7 is characterized in that, described μ _x, μ _y, σ _x, σ _y, σ _Xy, C ₁, C ₂Be respectively:

${\mathrm{\&mu;}}_x=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{x}_i,$ ${\mathrm{\&mu;}}_y=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{x}_i,$ ${\mathrm{\&sigma;}}_x=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{(x_i-{\mathrm{\&mu;}}_x)}^2},$ ${\mathrm{\&sigma;}}_y=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{(x_i-{\mathrm{\&mu;}}_y)}^2},$ ${\mathrm{\&sigma;}}_{\mathrm{xy}}=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i(x_i-{\mathrm{\&mu;}}_x)(y_i-{\mathrm{\&mu;}}_y),}$ C ₁＝(K ₁×L) ²，C ₂＝(K ₂×L) ²；

Wherein, x _i, y _i(i=1 2...N) is respectively the element of x and y, and N is the dimension of x and y, ω _iBe the weighting coefficient of i element and satisfy

K ₁=0.01, K ₂=0.03, L=255.

9. image de-noising method according to claim 1 is characterized in that, with chambolle projecting method solving model (2), the solution formula that obtains is in the described step (3)

$v^n=u^n-\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\mathrm{div}p,$

Wherein, $p^0=0,p^{k+1}=\frac{p^k+\mathrm{\&tau;}\&dtri;({\mathrm{div}p}^k-\frac{\mathrm{\&mu;}}{\mathrm{\&lambda;}}{u}^n)}{1+\mathrm{\&tau;}|\&dtri;({\mathrm{div}p}^k-\frac{\mathrm{\&mu;}}{\mathrm{\&lambda;}}{u}^n)|},$ τ represents the iteration interval time parameter.

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