CN101807292A - Image denoising method - Google Patents

Abstract

The invention provides an image denoising method, which comprises the following steps: designing a functional E (u); obtaining a corresponding Euler equation according to the functional E (u); deducing and solving a discrete mathematical model according to the Euler equation, wherein the discrete mathematical model is used for smoothening an image and strengthening detained information; inputting an image u0; carrying out iterative denoising for the input image u0 through the discrete mathematical model, thereby obtaining a denoised image u (i, j); removing spots on the denoised image u (i, j); and outputting an image which spots are removed. The image denoising method provided by the invention overcomes the 'block effect' introduced in the denoising method based on the second-order partial differential equation, and not only denoise the image, but also increases the contrast, thereby maintaining the detailed information of the texture and making the visual effect of the image more vivid and natural.

Description

A kind of image de-noising method

Technical field

The present invention relates to technical field of computer vision, particularly relate to a kind of image de-noising method of OO variation partial differential.

Background technology

Image denoising and enhancing are important research contents of Digital Image Processing, and the most popular at present Flame Image Process theory mainly comprises following three major types method: stochastic modeling (stochastic modelling), wavelet theory (wavelets theory) and Partial Differential Equation method (Partial-differential-equation/PDE).

Wherein, PDE occurs from eighties of last century the end of the eighties, because it has good mathematical theory and does support, significant progress is arranged in the nineties.It belongs to the important component part in the mathematical analysis, and is closely connected with physical world.What use the PDE method the earliest is heat-conduction equation in the isotropic medium, if gray level image is regarded as a temperature field in the isotropic medium, so the heat transfer process in this temperature field just corresponding Gauss's smoothing process of image, this corresponding relation makes PDE erect bridge between physics and Flame Image Process, and is widely used in other fields such as computer vision.

Since the later stage nineties in last century, people begin to utilize variational method and partial differential equation to carry out image repair, i.e. the part of losing in the blank map picture, or remove barrier in the image, such as noise etc., make image seem truer.Image repair in the variation partial differential equation field has two major sects, a kind of is some character of utilizing the structural images edge, suppose as simplicity or curvature are little etc., constructing corresponding functional then describes, be converted into PDE by variational method again and find the solution, this method is called OO variation partial differential method; Another kind is a diffusion process of directly considering certain character in the image, directly provides the PDE model and develops and find the solution, and this method is called processor-oriented variation partial differential method.These two class methods all are successful.

The method of utilizing processor-oriented PDE model to carry out image denoising and enhancing is of a great variety, here at different emphasis, roughly reduces three kinds of sorting techniques:

The design that focuses on PDE model coefficient of diffusion of first kind of sorting technique, big according to place, image border gradient, but not the little characteristics of edge's gradient make designed coefficient of diffusion slow in edge's rate of propagation, but not edge's rate of propagation are fast.Also the someone proposes to adopt measures such as gaussian filtering, second order local derviation and local variance in coefficient of diffusion, is used for details or reduction noise visibilitys such as preserving edge spike, thereby improves picture quality.

The design that focuses on PDE model dispersal direction of second kind of sorting technique, the denoising model that has is only carried out along the tangential direction at image texture edge, and not along carrying out perpendicular to the direction of edge tangent line, the denoising model that has can be carried out with the both direction vertical with tangent line simultaneously along the edge tangent line, the dispersal direction of the denoising model that has can determine that concrete deflection calculates by the integrated information of all pixels in the window by windowing.

The PDE model that focuses on of the third sorting technique is derived according to the partial differential equation of second order of image, or the quadravalence partial differential equation is derived.

And OO classical variation partial differential method is the regularization denoising model, and this method mainly is to find the solution the approximate of given noise image under the image smoothness constraint, and Tikhonov regularization method and TV method all are the classics of these class methods.

At present, overwhelming majority Variational PDE model all is based on partial differential equation of second order, and belong to the anisotropy diffusion process, although these class methods are proved to be able to keep doing between the two good balance at noise remove and edge, but image appears to have significantly " blocking effect ", this influence can make image visually lack the nature sense, can not reflect the true colours of image really, can cause the boundary that belongs to different masses in the identical smooth region of original image to show pseudo-edge simultaneously.

This " blocking effect " GORO DAIMON partial differential equation to a great extent has in essence contact.(u (x, y), x, y ∈ Ω, Ω are image area) is smooth, and the second order local derviation of image intensity function is 0 so to have only the strength function of image.If image area is infinitely great, so this PDE model constantly diffusion also finally stops in a smooth image area.Yet image area all is limited, and often uses symmetrical boundary condition to be used to avoid the border distortion, and this constraint can make the both sides on border that equal intensity level is arranged.Because image gradient is 0 at these boundaries, so image can be along smooth image direction diffusion, to satisfy the boundary condition of 0 gradient.In order to keep the edge, remove noise simultaneously, this class PDE model is usually designed in the smooth region rate of propagation fast, and slow in edge's rate of propagation.Therefore through after certain diffusion time, image looks like by the flat site of varying strength value and forms, and perhaps the border of these flat sites is the edge, but also might be the core in the zone of big level and smooth inclination, generation " blocking effect ".

Summary of the invention

For overcoming above-mentioned defective, the purpose of this invention is to provide a kind of OO image de-noising method, this method can be used to remove the image " blocking effect " that noise causes, makes image seem more natural.

For achieving the above object, the invention provides a kind of image de-noising method, described method comprises the steps:

A1: design functional E (u);

A2:, obtain corresponding Eulerian equation according to described functional E (u);

A3: derive and find the solution the discrete mathematics model according to described Eulerian equation, described discrete mathematics model is used for smoothed image and strengthens detailed information;

A4: input picture u ₀

A5: described discrete mathematics model is to described input picture u ₀Carry out the iteration denoising, obtain after the denoising image u (i, j);

A6: (i j) carries out spot and removes to the image u after the described denoising; And

A7: the image after the output spot is removed.

Image de-noising method according to an embodiment of the invention, because it comprises the regular terms of quadravalence partial differential image smoothing and the data of contrast enhancing rely on two parts, thereby introduce the quadravalence partial differential and handle image, thereby overcome the existing second order partial differential method of utilizing and removed the image " blocking effect " that noise causes, make image seem more natural, when removing picture noise, strengthened the detailed information of image simultaneously.

Description of drawings

Above-mentioned and/or additional aspect of the present invention and advantage are from obviously and easily understanding becoming the description of embodiment below in conjunction with accompanying drawing, wherein:

Fig. 1 has shown the FB(flow block) according to image de-noising method of the present invention;

Fig. 2 has shown the original test pattern according to image de-noising method of the present invention;

Fig. 3 has shown according to the image after the interpolation Gaussian noise of image de-noising method of the present invention;

Fig. 4 has shown the denoising result according to image de-noising method of the present invention;

Fig. 5 has shown the P-M method denoising result according to image de-noising method of the present invention; And

Fig. 6 has shown the TV method denoising result according to image de-noising method of the present invention.

Embodiment

Describe embodiments of the invention below in detail, the example of described embodiment is shown in the drawings, and wherein identical from start to finish or similar label is represented identical or similar elements or the element with identical or similar functions.Below by the embodiment that is described with reference to the drawings is exemplary, only is used to explain the present invention, and can not be interpreted as limitation of the present invention.

Illustrate below with reference to accompanying drawings according to image de-noising method of the present invention.As shown in Figure 1, this method can comprise the steps:

A1: design functional E (u).

In the present embodiment, at a width of cloth digital picture, (x y) is illustrated in the Ω of image support territory u, and coordinate position is (x, the grey scale pixel value of y) locating.

Presentation video u (x, gradient fields y) also are the contrast field:

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

Reflected near the situation of change any point in the image, gradient magnitude has been represented the speed that changes, the direction indication of gradient the direction that changes, $|\▿u|=\sqrt{u_x^2+u_y^2}$ Be image gradient mould, u _xAnd u _yBe respectively the single order local derviation of image in x and y direction.

Image degree of comparing is stretched, can make detailed information more clear, contrast stretched image gradient fields W is expressed as:

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

Wherein, k is the gradient fields enlargement factor, and after stretching through gradient fields, original gradient fields direction does not change, but size increases.

In the present embodiment, $k=1+\mathrm{\λ}{e}^{(-|\▿u\left|\right)}$ , the maximum amplification of contrast has been reflected in λ＞0.

Take all factors into consideration the maintenance of image smoothing and the amplification of useful information.Under the approaching condition of image gradient field and goal gradient field W, make the regular terms minimum of image smoothing item, promptly seek and strengthen image u, make functional E (u) minimum:

$E\left(u\right)=\mathrm{\α}{\∫}_{\mathrm{\Ω}}\frac{1}{2}{\left(\right|{\▿}^{2}u\left|\right)}^2\mathrm{dxdy}+\mathrm{\β}{\∫}_{\mathrm{\Ω}}\frac{1}{2}{\left(\right|\▿u-W^{*}\left|\right)}^2\mathrm{dxdy}$

Above-mentioned functional E (u) comprises two part regular terms and data rely on item.Wherein,

Be regular terms, the bound term that the expression output image is level and smooth, For output image u to input noise image u ₀Data rely on.This data rely on item and require image and input picture after the denoising should have similarity on the content, and positive parameter alpha and β have represented that this functional regular terms and data rely on the proportion of item.

Wherein, $W^{*}=k\▿u_0=(k\frac{\∂u_0}{\∂x},k\frac{\∂u_0}{\∂y}),$ u ₀Be the initial observation image.

The expression Laplace operator: ${\▿}^2(\·)=u_{\mathrm{xx}}+u_{\mathrm{yy}}$

u _XxAnd u _YyBe respectively the second order local derviation of image in x and y direction.

A2:, obtain corresponding Eulerian equation according to functional E (u).

Obtain the corresponding Eulerian equation of functional E (u), and described Eulerian equation derivation mathematical model.

The present invention is directed to functional E (u), corresponding Eulerian equation is

$\frac{\∂f}{\∂u}-\frac{\∂}{\∂x}\left(\frac{\∂f}{\∂u_x}\right)-\frac{\∂}{\∂y}\left(\frac{\∂f}{\∂u_y}\right)+\frac{\∂}{\∂\mathrm{xx}}\left(\frac{\∂f}{\∂u_{\mathrm{xx}}}\right)+\frac{\∂}{\∂\mathrm{yy}}\left(\frac{\∂f}{\∂u_{\mathrm{yy}}}\right)=0$

Wherein

$f=\frac{1}{2}\mathrm{\α}{\left(\right|{\▿}^{2}u\left|\right)}^2+\frac{1}{2}\mathrm{\β}{\left(\right|\▿u-W^{*}\left|\right)}^2$

$=\frac{1}{2}\mathrm{\α}{\left(\right|u_{\mathrm{xx}}+u_{\mathrm{yy}}\left|\right)}^2+\frac{1}{2}\mathrm{\β}({(u_x-(1+\mathrm{\λ}{e}^{(-|\▿u\left|\right)})u_{0x})}^2+{(u_y-(1+\mathrm{\λ}{e}^{(-|\▿u\left|\right)})u_{0y})}^2),$

u _0xAnd u _0yBe respectively initial observation image u ₀(x, single order local derviation y) is promptly along the gradient of x direction and y direction.

Can obtain according to above-mentioned Eulerian equation:

$\frac{\∂f}{\∂u}=0$

$\frac{\∂f}{\∂u_x}=(u_x-(1+\mathrm{\λ}{e}^{(-|\▿u\left|\right)})u_{0x})(1+\mathrm{\λ}{e}^{(-|\▿u\left|\right)}{u}_x{u}_{0x}/|\▿u\left|\right)$

$\frac{\∂f}{\∂u_y}=(u_y-(1+\mathrm{\λ}{e}^{(-|\▿u\left|\right|)})u_{0y})(1+\mathrm{\λ}{e}^{(-|\▿u\left|\right)}{u}_y{u}_{0y}/|\▿u\left|\right)$

$\frac{\∂f}{\∂u_{\mathrm{xx}}}=\frac{\∂f}{\∂u_{\mathrm{yy}}}=\left|{\▿}^{2}u\right|\mathrm{sign}\left({\▿}^{2}u\right)=\left|{\▿}^{2}u\right|\frac{{\▿}^2}{\left|{\▿}^{2}u\right|}={\▿}^{2}u$

$\frac{\∂}{\∂\mathrm{xx}}\left(\frac{\∂f}{\∂u_{\mathrm{xx}}}\right)+\frac{\∂}{\∂\mathrm{yy}}\left(\frac{\∂f}{\∂u_{\mathrm{yy}}}\right)={\▿}^2\left({\▿}^{2}u\right),$

And then utilize the gradient descent method can obtain mathematical model:

$\frac{\∂u}{\∂t}=-(\mathrm{\β}(-\frac{\∂}{\∂x}\left(\frac{\∂f}{\∂u_x}\right)-\frac{\∂}{\∂y}\left(\frac{\∂f}{\∂u_y}\right))+\mathrm{\α}(\frac{\∂}{\∂\mathrm{xx}}\left(\frac{\∂f}{\∂u_{\mathrm{xx}}}\right)-\frac{\∂}{\∂\mathrm{yy}}\left(\frac{\∂f}{\∂u_{\mathrm{yy}}}\right)\left)\right)$

$=\mathrm{\β}(\frac{\∂}{\∂x}\left(\frac{\∂f}{\∂u_x}\right)+\frac{\∂}{\∂y}\left(\frac{\∂f}{\∂u_y}\right))-{\mathrm{\α}\▿}^2\left({\▿}^{2}u\right)$

Wherein, t express time.

A3: derive and find the solution the discrete mathematics model according to Eulerian equation, the discrete mathematics model is used for smoothed image and strengthens detailed information.

According to the mathematical model that obtains in the steps A 2

$\frac{\∂u}{\∂t}=-(\mathrm{\β}(-\frac{\∂}{\∂x}\left(\frac{\∂f}{\∂u_x}\right)-\frac{\∂}{\∂y}\left(\frac{\∂f}{\∂u_y}\right))+\mathrm{\α}(\frac{\∂}{\∂\mathrm{xx}}\left(\frac{\∂f}{\∂u_{\mathrm{xx}}}\right)-\frac{\∂}{\∂\mathrm{yy}}\left(\frac{\∂f}{\∂u_{\mathrm{yy}}}\right)\left)\right)$

$=\mathrm{\β}(\frac{\∂}{\∂x}\left(\frac{\∂f}{\∂u_x}\right)+\frac{\∂}{\∂y}\left(\frac{\∂f}{\∂u_y}\right))-{\mathrm{\α}\▿}^2\left({\▿}^{2}u\right),$

Utilize the gradient descent method to derive the discrete mathematics model:

$\frac{\∂u}{\∂t}=\frac{u^{n+1}-u^n}{\mathrm{\Δt}}=\mathrm{\β}(\frac{\∂}{\∂x_{-}}\left(\frac{\∂f}{\∂u_{x+}^n}\right)+\frac{\∂}{\∂y_{-}}\left(\frac{\∂f}{\∂u_{y+}^n}\right))-\mathrm{\α}{\▿}^2\left({\▿}^2{u}^n\right)$

$u^{n+1}=u^n+\mathrm{\Δt}(\mathrm{\β}(\frac{\∂}{\∂x_{-}}\left(\frac{\∂f}{\∂u_{x+}^n}\right)+\frac{\∂}{\∂y_{-}}\left(\frac{\∂f}{\∂u_{y+}^n}\right))-\mathrm{\α}{\▿}^2\left({\▿}^2{u}^n\right))$

Wherein, Δ t represents the iteration interval time parameter, and n represents the iterations parameter.In order to prevent image translation, when x and y direction were asked local derviation, forward direction and backward difference hocketed to image ,+number and-forward direction and the backward difference that adopt of expression number respectively.

A4. input picture u ₀

Import the original denoising image u that treats ₀

A5. the discrete mathematics model is to input picture u ₀Carry out the iteration denoising, obtain after the denoising image u (i, j).

According to the above-mentioned discrete mathematics model that obtains, it is level and smooth that the input noise image is carried out Gauss, the iteration denoising, and spot is removed, and then obtains the image after the denoising.

Obtain Gauss's discrete mathematics model in steps A 3 after, in order to obtain better result, carry out utilizing the gaussian filtering smooth noise before the enhancing of iteration denoising and contrast again, promptly carry out convolution operation G*u with Gaussian filter and original image, G is the smoothing kernel function.

The gaussian kernel function of choosing in the embodiment of the invention is:

$G\left(x\right)=\exp (-\frac{{\left|\right|x\left|\right|}^2}{2{\mathrm{\σ}}^2}),(x=-2,-\mathrm{1,0,1,2};\mathrm{\σ}=0.5)$

Generating window size is the mask of 5*5.

Image according to the discrete mathematics model that obtains in the steps A 3 and Gauss after level and smooth carries out the iteration denoising.

Image to Gauss after level and smooth calculates each rank local derviation respectively.Each rank local derviation comprises:

${\▿}^2\left(u\right)=u(i-1,j)+u(i,j-1)+u(i+1,j)+u(i,j+1)-4u(i,j);$

u _x+(i，j)＝u(i+1，j)-u(i，j)；

u _x-(i，j)＝u(i，j)-u(i-1，j)；

u _0x+(i，j)＝u ₀(i+1，j)-u ₀(i，j)；

u _y+(i，j)＝u(i，j+1)-u(i，j)；

u _y-(i，j)＝u(i，j)-u(i，j-1)；

u _0y+(i，j)＝u ₀(i，j+1)-u ₀(i，j)；

$|\▿u|=\sqrt{u_{x+}^2+{\left(\left(\frac{\mathrm{sign}\left(u_{y+}\right)+\mathrm{sign}\left(u_{y-}\right)}{2}\right)\min \left(\right|u_{y+}|,|u_{y-}\left|\right)\right)}^2};$

Wherein sign () is a sign function.

$\frac{\∂}{\∂x_{-}}\left(\frac{\∂f}{\∂u_{x+}}\right)=\frac{\∂f}{\∂u_{x+}}(i,j)-\frac{\∂f}{\∂u_{x+}}(i-1,j);$

$\frac{\∂}{\∂y_{-}}\left(\frac{\∂f}{\∂u_{y+}}\right)=\frac{\∂f}{\∂u_{y+}}(i,j)-\frac{\∂f}{\∂u_{y+}}(i,j-1);$

(i, j) presentation video x=i, the position coordinates of y=j, 2≤i≤M-1,2≤j≤N-1, M and N are the line number and the columns of image pixel.

For sharp point: u _P(1, j)=u _P(2, j);

u _P(M，j)＝u _P(M-1，j)；

u _P(i，1)＝u _P(i，2)；

u _P(i，N)＝u _P(i，N-1)，

Wherein P represents x+, x-, y+, y-, 0x+ and 0y+.

After finishing above-mentioned each rank local derviation calculating, level and smooth excessively for preventing image, can print and show simultaneously, need be to each rank local derviation u of image _X+(i, j), u _Y+(i, j), u _X-(i, j), u _Y-(i, j), u _0x+(i, j), u _0y+(i j) takes amplitude limiting processing.

In the present embodiment, at gray level image indication range (0-255), adopt following method to carry out amplitude limit:

u ^*(i，j)＝min(255，u _P(i，j))

u ^**(i，j)＝max(0，u ^*(i，j))

Wherein, u ^*(i, j) result behind the expression amplitude limit.

According to above-mentioned local derviation computation process, obtain after the denoising image u (i, j).

A6: (i j) carries out spot and removes to the image u after the denoising.

Since partial differential equation easily make image u after the denoising (i j) leaves black or white dot, therefore, need (i j) carries out spot and removes to the image u after the denoising that obtains among the above-mentioned steps A5.Adopt following method to carry out spot and remove, comprising:

$u(i,j)=\left\{\begin{array}{cc}m& \mathrm{if}{|u(i,j)-m|}^2>{\mathrm{l\σ}}^2\\ u(i,j)& \mathrm{otherwise}\end{array}\right.$

Wherein, $m=\frac{u(i,j-1)+u(i,j+1)+u(i-1,j)+u(i+1,j)}{4},$

${\mathrm{\σ}}^2=\frac{u^2(i,j-1)+u^2(i,j+1)+u^2(i-1,j)+u^2(i+1,j)}{4}-m^2,$

L is an adjustable parameter.

To steps A 6, finish an iteration denoising of this method by above-mentioned steps A1.Along with the increase of iterations n, image is more smooth-out.But iterations is too high, and image is too level and smooth, causes not fogging clear.Therefore, n is set at a with iterations, and when satisfying n=a, Image Smoothness and sharpness all meet the demands.

Therefore, repeating step A5 is to steps A 6, until iterations n=a, and execution in step A7: the image after the output spot is removed.

Fig. 2 shows the original image that the input noise image is a nuclear magnetic resonance cranial nerve image.This image transitions is a gray level image, and size is the 220*193 pixel.As shown in Figure 3, the input noise image is added 0.05 Gaussian noise, utilize the variation Partial Differential Equation method of present embodiment and conventional P-M method and TV method respectively image to be carried out denoising then respectively.

Fig. 4 shows OO variation partial differential equation denoising result.In the present embodiment, concrete parameter is set to Δ t=0.25, and iterations is that n is 3 times, and Gauss's smoothing kernel mask size is 5*5, σ=0.5, λ=5, l=1, α=0.025, α=0.025, β=0.01, peak-peak signal to noise ratio (S/N ratio) PSNR=21.6204, experimental result is as shown in Figure 4.

Fig. 5 is a P-M method denoising result.

The P-M method, concrete parameter is set to Δ t=1/7, and iterations n is 10 times, and the coefficient of diffusion parameter is 30, peak-peak signal to noise ratio (S/N ratio) PSNR=20.6550.

Fig. 6 is a TV method denoising result.

The TV method, concrete parameter is set to Δ t=0.25, and iterations n is 5 times, peak-peak signal to noise ratio (S/N ratio) PSNR=20.5713.

In conjunction with the image after Fig. 4, Fig. 5 and the denoising shown in Figure 6, adopt the image after P-M and the denoising of TV method, image shows too stiff and stiff, has blocking effect and pseudo-edge phenomenon, visual effect is bad, P-M method especially, the noise influence is seriously.

The embodiment of the invention utilizes OO variation Partial Differential Equation method to derive the denoising mathematical model, overcome " blocking effect " introduced based on the partial differential equation of second order denoising method, make image in denoising, increase contrast, the detailed information that has effectively kept texture, image visual effect is more true to nature, nature.

One of ordinary skill in the art will appreciate that and realize that all or part of step that the foregoing description method is carried is to finish by the relevant hardware of programmed instruction, described program can be stored in a kind of computer-readable recording medium, this program comprises one of step or its combination of method embodiment when carrying out.

In addition, each functional unit in each embodiment of the present invention can be integrated in the processing module, also can be that the independent physics in each unit exists, and also can be integrated in the module two or more unit.Above-mentioned integrated module both can adopt the form of hardware to realize, also can adopt the form of software function module to realize.If described integrated module realizes with the form of software function module and during as independently production marketing or use, also can be stored in the computer read/write memory medium.The above-mentioned storage medium of mentioning can be a ROM (read-only memory), disk or CD etc.

More than disclosed only be the preferred embodiments of the present invention, can not limit the scope of the present invention with this certainly.Be appreciated that the equivalent variations of doing according to the present invention's essence defined in the appended claims and scope, still belong to the scope that the present invention is contained.

Claims (10)

1. image de-noising method, described method comprises the steps:

A1: design functional E (u);

A2:, obtain corresponding Eulerian equation according to described functional E (u);

A3: derive and find the solution the discrete mathematics model according to described Eulerian equation, described discrete mathematics model is used for smoothed image and strengthens detailed information;

A4: input picture u ₀

A5: described discrete mathematics model is to described input picture u ₀Carry out the iteration denoising, obtain after the denoising image u (i, j);

A6: (i j) carries out spot and removes to the image u after the described denoising; And

A7: the image after the output spot is removed.

2. image de-noising method as claimed in claim 1 is characterized in that, described functional E (u) is $E\left(u\right)=\mathrm{\α}{\∫}_{\mathrm{\Ω}}\frac{1}{2}{\left(\right|{\▿}^{2}u\left|\right)}^2\mathrm{dxdy}+\mathrm{\β}{\∫}_{\mathrm{\Ω}}\frac{1}{2}{\left(\right|\▿u-W^{*}\left|\right)}^2\mathrm{dxdy},$ Described functional E (u) comprises regular terms

In order to the bound term of level and smooth of expression output image, data rely on item

In order to represent that output image u is to initial observation image u ₀Contrast strengthen,

Wherein, positive parameter alpha and β are the proportion that described functional regular terms and data rely on item, and (x is in the Ω of image support territory y) to u, and coordinate position is (x, the grey scale pixel value of y) locating.

3. image de-noising method as claimed in claim 1 is characterized in that, the Eulerian equation that functional E (u) described in the described steps A 2 is corresponding is

$\frac{\∂f}{\∂u}-\frac{\∂}{\∂x}\left(\frac{\∂f}{\∂u_x}\right)-\frac{\∂}{\∂y}\left(\frac{\∂f}{\∂u_y}\right)+\frac{\∂}{\∂\mathrm{xx}}\left(\frac{\∂f}{\∂u_{\mathrm{xx}}}\right)+\frac{\∂}{\∂\mathrm{yy}}\left(\frac{\∂f}{\∂u_{\mathrm{yy}}}\right)=0.$

4. image de-noising method as claimed in claim 1 is characterized in that, deriving and find the solution the discrete mathematics model according to described Eulerian equation is

$u^{n+1}=u^n+\mathrm{\Δt}(\mathrm{\β}(\frac{\∂}{\∂x_{-}}\left(\frac{\∂f}{\∂u_{x+}^n}\right)+\frac{\∂}{{\∂y}_{-}}\left(\frac{\∂f}{\∂u_{y+}^n}\right))-{\mathrm{\α}\▿}^2\left({\▿}^2{u}^n\right)),$

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

5. as claim 1 or 4 described image de-noising methods, it is characterized in that, in steps A 3, utilize the gradient descent method described discrete mathematics model of deriving.

6. image de-noising method as claimed in claim 1 is characterized in that, described steps A 5 further comprises: before the iteration denoising, adopt Gauss's pre-filtering to carry out smooth noise to input picture.

7. image de-noising method as claimed in claim 6 is characterized in that, described Gauss's pre-filtering comprises adopts Gaussian filter and described input noise image to carry out convolution, and wherein, the gaussian kernel function in described Gauss's pre-filtering is

$k\left(x\right)=\exp (-\frac{{\left|\right|x\left|\right|}^2}{2{\mathrm{\σ}}^2})$ (x=-2 ,-1,0,1,2; σ=0.5), generating window size is the mask of 5*5.

8. image de-noising method as claimed in claim 1 is characterized in that, described steps A 5 further comprises: to the image after Gauss's pre-filtering,

Each rank local derviation u of computed image _X+(i, j), u _Y+(i, j), u _X-(i, j), u _Y-(i, j), u _0x+(i, j), u _0y+(i, j); And each rank local derviation u _X+(i, j), u _Y+(i, j), u _X-(i, j), u _Y-(i, j), u _0x+(i, j), u _0y+(i j) carries out amplitude limit.

9. image de-noising method as claimed in claim 8 is characterized in that, to each rank local derviation u _X+(i, j), u _Y+(i, j), u _X-(i, j), u _Y-(i, j), u _0x+(i, j), u _0y+(i, j) step of carrying out amplitude limit comprises that with described each rank local derviation amplitude limit be ((u ^*(i, j), (u ^*(i, j)), wherein

u ^*(i，j)＝min(255，u _p(i，j))，u ^**(i，j)＝max(0，u ^*(i，j))。

10. image de-noising method as claimed in claim 1 is characterized in that, described steps A 6 comprises that further utilizing following formula to carry out spot removes:

$u(i,j)=\left\{\begin{array}{cc}m& \mathrm{if}{|u(i,j)-m|}^2>l{\mathrm{\σ}}^2\\ u(i,j)& \mathrm{otherwise}\end{array}\right.,$ Wherein,

$m=\frac{u(i,j-1)+u(i,j+1)+u(i-1,j)+u(i+1,j)}{4}$

${\mathrm{\σ}}^2=\frac{u^2(i,j-1)+u^2(i,j+1)+u^2(i-1,j)+u^2(i+1,j)}{4}-m^2.$

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