CN103745442B - The image de-noising method shunk based on non local wavelet coefficient - Google Patents

Abstract

The present invention proposes a kind of image de-noising method shunk based on non local wavelet coefficient, the problem mainly solving to lose image detail during conventional images denoising method denoising.Implementation step is: (1) builds similar group of noisy image, and similar block in similar group is made two-dimensional wavelet transformation, calculates the non-local mean of similar group of wavelet coefficient；(2) use double L1 Norm Model Shrinkage Wavelet coefficient, then carry out inverse wavelet transform, obtain similar block estimated value, and it is integrated, once estimated image；(3) to once estimating that image carries out residual error covering, and perform step (1) (2), obtain basis and estimate image；(4) build basis and estimate similar group of image, and then obtain similar group of noisy image；(5) similar group to noisy image carries out the collaborative filtering of wiener, obtains denoising image.The present invention while smooth noise, can preferably keep the Edge texture of image, can be used for the denoising to natural image.

Description

The image de-noising method shunk based on non local wavelet coefficient

Technical field

The invention belongs to technical field of image processing, the image denoising side specifically shunk based on non local wavelet coefficient Method, can be used for the denoising to natural image.

Background technology

Image is the important sources that people obtain information, but image usually can be by various noises in generation and transmitting procedure Interference, this not only has influence on the visual effect of image, also counteracts that entering of the follow-up work such as feature extraction, target recognition OK.Therefore, image denoising is the vital part of image processing field.

The purpose of image denoising recovers high-quality image clearly, while denoising as much as possible exactly from noisy image Keep the inherent feature information of image.At present, substantial amounts of denoising method has been suggested, and wherein regularization method obtains Studying widely, observed image and priori are incorporated into variational formulation by the method, emphasize to find suitable image Prior model it is critical that.Traditional regularization method, such as secondary Tikhonov method, TV method is due to its point Section constant it is assumed that understood smoothed image while denoising, therefore, quickly by based on openness regularization method institute Replace.The local that this process employs image is openness, represents image block with the linear combination of the some atoms in dictionary, Each image block is individually to carry out rarefaction representation, does not consider the dependency between other image blocks.

2005, Buades et al. proposed non-local image de-noising method, and the method breaches tradition part filter Thought, makes full use of the non local structural similarity of image, it is thus achieved that significantly denoising effect.Subsequently, occur in that a lot Denoising method based on non local thought, such as methods such as BM3D, CSR, BM3D method is by two dimensional image similar for structure Block flocks together formation three-dimensional array, by these three-dimensional array Federated filter, the estimated value of cohesive image block, entering One step improves denoising effect.But the method is owing to carrying out one-dimensional transform between block to similar group so that the part details of image Weakened, cause marginal area to fog.Dictionary learning and documents structured Cluster are combined by CSR method, make the dilute of image Dredge coding noise sufficiently small, thus improve denoising effect, but the method to implement ratio relatively time-consuming, and part edge Denoising effect is the most undesirable.

Summary of the invention

Present invention aims to the deficiency of above-mentioned prior art, propose a kind of to shrink based on non local wavelet coefficient The implementation method of image denoising, to realize taking into account edge and smooth region in natural image denoising, improves image denoising Effect.

For achieving the above object, the present invention comprises the steps:

(1) take reference image block with step-length 3 inputting in noisy image, according to Euclidean distance formula calculate this reference block and its Distance d (the Z of all image blocks in neighborhood_i,Z_i,j), the N that selected distance is minimum₂Individual image block constitutes the similar of this reference block Group: S_i={ Z_i,j:min(d(Z_i,Z_i,j)), j=1...N₂, i represents similar group of sequence number }, wherein, Z_iFor reference image block, Z_i,j For Z_iImage block in neighborhood, N₂For similar block number in similar group；

(2) similar block in similar group is carried out two-dimensional wavelet transformation, obtains the wavelet coefficient of similar block:

α_i,j=Τ_2D(Z_i,j),Z_i,j∈S_i

Wherein, Τ_2DRepresent two-dimensional wavelet transformation, α_i,jFor the wavelet coefficient of jth similar block in similar group of i-th；

(3) according to non-local mean formula, the non-local mean μ of each similar group of wavelet coefficient is calculated_i:

${\mathrm{\μ}}_i=\underset{j\∈S_i}{\mathrm{\Σ}}{\mathrm{\ω}}_{i,j}{\mathrm{\α}}_{i,j},j=1...N_2$

ω_i,j=exp (-d (Z_i,Z_i,j))/h)/W

Wherein, ω_i,jFor the weights that similar block is corresponding, h is 12 σ_n, σ_nPoor for noise criteria, W represents that normalization operates；

(4) double L is used₁The contracting function of Norm Model, calculates the wavelet coefficient estimated value of similar block

${\widehat{\mathrm{\&alpha;}}}_{i,j}=\left\{\begin{array}{cc}{S}_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,{\mathrm{\&mu;}}_i}\left({\mathrm{\&alpha;}}_{i,j}\right)& {\mathrm{\&mu;}}_i\&GreaterEqual;0\\ -S_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,-{\mathrm{\&mu;}}_i}\left({\mathrm{\&alpha;}}_{i,j}\right)& {\mathrm{\&mu;}}_i<0\end{array}\right.$

Wherein,For contracting function, it is defined as:

$S_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,b}\left(t\right)=\left\{\begin{array}{cc}t+{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2& t<-{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\\ 0& -{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\&le;t\&le;{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\\ t-{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2& {\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\&le;t\&le;{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2+b\\ b& {\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2+b\&le;t\&le;{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2+b\\ t-{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2& t>{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2+b\end{array}\right.$

Wherein, t is for treating constriction coefficient, and b is to treat the non-local mean that constriction coefficient is corresponding, τ₁And τ₂It is two different receipts Contracting threshold value,c₁, c₂It is the constant of two different numerical value, c₁Value is 0.1, c₂ Value is 0.9, σ_nPoor for noise criteria, σ_iIt is by α_iEstimate the standard deviation obtained, α_i={ α_i,1...α_i,j, δ_iBy α_i-μ_i Estimate the standard deviation obtained；

(5) to wavelet coefficient estimated valueCarry out inverse wavelet transform, obtain similar block estimated value, integrate all estimated values, Once estimated image Y:

${\hat{Y}}_{i,j}=T_{2D}^{-1}\left({\widehat{\mathrm{\&alpha;}}}_{i,j}\right)$

Wherein, X is noisy image, and x is the pixel in X,Represent 2-d wavelet inverse transformation, χ_jIt it is image block Characteristic function,Time, χ_jValue is 1, is otherwise 0；

(6) the once estimation image Y obtained is carried out residual error to refill, refill repetition step (1)-(5) on figure in residual error, obtain Image Y' is estimated on basis；Work as σ_nDuring ＞ 50, basis is estimated, and image Y' performs the most identical residual error again and refills operation.

(7) image Y' is estimated, with step-length N in the basis obtained_sChoose reference block, build its phase according to Euclidean distance formula Like groupAnd record the coordinate information of similar block in similar group:

$S_i^1=\{{\hat{Y}}_{i,j}^{\text{'}}:\frac{{\left|\right|{\hat{Y}}_i^{\text{'}}-{\hat{Y}}_{i,j}^{\text{'}}\left|\right|}_2^2}{{\left(N_1^{\text{'}}\right)}^2}<\mathrm{\&tau;}\}$

Wherein,WithIt is that the reference block in image and candidate blocks are estimated in basis respectively,Represent's L₂Norm squared, N₁'×N₁' it is tile size, τ is to judge the threshold value that two image blocks are the most similar, σ_nWhen≤40, τ value is 400, σ_nDuring ＞ 40, τ value is 3500；

(8) according to similar block coordinate information, from noisy image, extract corresponding image block, constitute similar groupTo base Plinth estimates similar group of imageSimilar with noisy image groupAll carry out three-dimension varying, obtain respective conversion coefficient, According to similar groupConversion coefficient calculate wiener constriction coefficient W_i, further according to similar groupConversion coefficient and wiener shrink Coefficient W_i, obtain similar groupMiddle similar block estimated value:

$W_i=\frac{{\left|T_{3D}\left(S_i^1\right)\right|}^2}{{\left|T_{3D}\left(S_i^1\right)\right|}^2+{{\mathrm{\&sigma;}}_n}^2}$

${\hat{Y}}_{S_i^2}^{\text{'}}=T_{3D}^{-1}\left(W_i{T}_{3D}\left(S_i^2\right)\right)$

Wherein, Τ_3DRepresent the three-dimension varying being made up of one-dimensional wavelet transform between two-dimensional dct transform and block,Represent three Dimension inverse transformation,Represent similar groupConversion coefficient take absolute value square, W_iFor similar groupCorresponding dimension Receive constriction coefficient；

(9) to similar group obtainedMiddle similar block estimated value weighted average, obtains denoising image Y'':

Wherein, ω_iIt it is similar groupCorresponding weights,Represent W_iL₂Norm squared.

The present invention compared with prior art has the advantage that

1. due to the fact that and carry out in wavelet field, it is achieved process is simple, speed is fast.

2. the present invention takes full advantage of the non local similarity of image, makes the wavelet coefficient α of similar block_i,jLittle close to similar group The non-local mean μ of wave system number_i, it is possible to effectively shrink similar block wavelet coefficient, obtain similar block estimated value accurately.

3. due to the fact that and employ double L₁Norm Model contracting function, it is possible to obtain basis accurately and estimate image, and then Obtain the most noisy image similarity groupWith wiener constriction coefficient W_i, thus accurately calculate pixel estimated value, it is possible to Keep and recover edge and the grain details of image while smooth noise.

Accompanying drawing explanation

Fig. 1 is the flowchart of the present invention；

Fig. 2 is the three width test images that the present invention tests use；

Fig. 3 is with existing three kinds of methods and the present invention denoising result to House image；

Fig. 4 is with existing three kinds of methods and and the present invention denoising result to Cameraman image；

Fig. 5 is with existing three kinds of methods and the present invention denoising result to Barbara image.

Detailed description of the invention

Referring to the drawings 1, the image de-noising method that the present invention shrinks based on non local wavelet coefficient, comprise the steps:

Step 1, builds its similar group to noisy image X.

1.1) adding standard deviation in without test image of making an uproar is σ_nNoise, obtain noisy image X:

X=U+σ_n* randn (N),

Wherein, U is for without making an uproar test figure, and N is the sum of all pixels in U, and randn () is to produce at random in matlab language The function of number；

1.2) in noisy image X, reference block Z is taken with step-length 3_i, calculating this reference block according to range formula with its size is Distance d (the Z of candidate blocks in w × w neighborhood_i,Z_i,j) and corresponding weights ω_i,j:

$d(Z_i,Z_{i,j})=\frac{{\left|\right|Z_i-Z_{i,j}\left|\right|}_2^2}{{\left(N_1\right)}^2}$

ω_i,j=exp (-d (Z_i,Z_i,j))/h)/W,

Wherein, Z_iFor reference block, Z_i,jFor Z_iImage block in neighborhood,Represent Z_i-Z_i,jL₂Norm is put down Side, N₁×N₁For tile size, N₁Value is 8, and w value is 39, and exp represents exponent arithmetic, and h is 12 σ_n, σ_n Poor for noise criteria, W represents that normalization operates；

1.3) N that distance is minimum is taken₂Individual image block, forms reference block Z_iSimilar group of S_i:

S_i={ Z_i,j:min(d(Z_i,Z_i,j)), j=1...N₂, i represents similar group of sequence number },

Wherein, min represents and takes N₂Individual minima, N₂For similar block number in similar group, σ_nWhen≤30, N₂Value is 16；σ_nDuring ＞ 30, N₂Value is 20.

Step 2, carries out wavelet transformation to similar block in similar group, obtains the wavelet coefficient α of similar block_i,j:

α_i,j=Τ 2D (Z_i,j),Z_i,j∈S_i,

Wherein, Τ_2DRepresent two dimension bior1.5 wavelet transformation, and be three layers of decomposition, α_i,jFor jth in similar group of i-th The wavelet coefficient of similar block.

Step 3, according to weights ω_i,jWith similar block wavelet coefficient α_i,j, utilize non-local mean formula to calculate each similar group The non-local mean μ of wavelet coefficient_i:

${\mathrm{\&mu;}}_i=\underset{j\&Element;S_i}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_{i,j}{\mathrm{\&alpha;}}_{i,j},j=1...N_2.$

Step 4, uses double L₁The contracting function of Norm Model is to similar block wavelet coefficient α_i,jShrink.

4.1) by similar block wavelet coefficient α_i,jForm the wavelet coefficient set α of similar group_i, α_i={ α_i,1...α_i,j, use α_i's Each column deducts non-local mean μ_iObtain new set α_i-μ_i, α_i-μ_i={ (α_i,1-μ_i)...(α_i,j-μ_i)}；

4.2) wavelet coefficient set α is calculated_iStandard deviation sigma_iWith new set α_i-μ_iStandard deviation δ_i:

${\mathrm{\&sigma;}}_i=\sqrt{\frac{1}{N_2}\mathrm{\&Sigma;}{\left({\mathrm{\&alpha;}}_i\right)}^2},{\mathrm{\&delta;}}_i=\sqrt{\frac{1}{N_2}\mathrm{\&Sigma;}{({\mathrm{\&alpha;}}_i-{\mathrm{\&mu;}}_i)}^2},$

4.3) according to wavelet coefficient set α_iStandard deviation sigma_iCalculate the first collapse threshold τ₁, according to new set α_i-μ_iMark Quasi-difference δ_iCalculate the second collapse threshold τ₂:

${\mathrm{\&tau;}}_1=\frac{c_1\sqrt{2}{{\mathrm{\&sigma;}}_n}^2}{{\mathrm{\&sigma;}}_i},{\mathrm{\&tau;}}_2=\frac{c_2\sqrt{2}{{\mathrm{\&sigma;}}_n}^2}{{\mathrm{\&delta;}}_i},$

Wherein, σ_nPoor for noise criteria, c₁, c₂It is the constant of two different numerical value, c₁Value is 0.1, c₂Value is 0.9；

4.4) the double L of definition₁The contracting function of Norm ModelFor:

$S_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,b}\left(t\right)=\left\{\begin{array}{cc}t+{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2& t<-{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\\ 0& -{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\&le;t\&le;{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\\ t-{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2& {\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\&le;t\&le;{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2+b\\ b& {\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2+b\&le;t\&le;{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2+b\\ t-{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2& t>{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2+b\end{array}\right.,$

Wherein, t is for treating constriction coefficient, and b is to treat the non-local mean that constriction coefficient is corresponding；

4.5) according to two collapse threshold τ₁、τ₂Non-local mean μ with similar group of wavelet coefficient_i, utilize contracting functionShrink similar block wavelet coefficient α_i,j, obtain similar block wavelet coefficient estimated value

${\widehat{\mathrm{\&alpha;}}}_{i,j}=\left\{\begin{array}{cc}{S}_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,{\mathrm{\&mu;}}_i}\left({\mathrm{\&alpha;}}_{i,j}\right)& {\mathrm{\&mu;}}_i\&GreaterEqual;0\\ -S_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,-{\mathrm{\&mu;}}_i}\left({\mathrm{\&alpha;}}_{i,j}\right)& {\mathrm{\&mu;}}_i<0\end{array}\right..$

Step 5, according to similar block wavelet coefficient estimated valueOnce estimated image Y.

5.1) to similar block wavelet coefficient estimated valueCarry out inverse wavelet transform, obtain similar block estimated value

${\hat{Y}}_{i,j}=T_{2D}^{-1}\left({\widehat{\mathrm{\&alpha;}}}_{i,j}\right),$

Wherein,Represent 2-d wavelet inverse transformation；

5.2) all similar block estimated values are integratedOnce estimated image Y:

Wherein, X is noisy image, and x is the pixel in X, χ_jIt it is image blockCharacteristic function,Time, χ_jValue is 1, is otherwise 0.

Step 6, to once estimating that image Y carries out residual error and refills, obtains residual error and refills image

$\stackrel{\&OverBar;}{Y}=Y+\mathrm{\&delta;}(X-Y),$

Wherein, δ is that residual error refills parameter, and value is 0.02.

Step 7, refills image to residual errorPerform step 1-5, obtain basis and estimate image Y'.

7.1) calculate residual error and refill imageNoise criteria poor

${\widehat{\mathrm{\&sigma;}}}_n=\mathrm{\&lambda;}\sqrt{{{\mathrm{\&sigma;}}_n}^2-{{\mathrm{\&delta;}}_n}^2},$

Wherein, λ is constant, and value is 0.23,For difference figureVariance,

7.2) image is refilled according to residual errorNoise criteria poorResidual error is refilled imagePerform step 1-5, obtain base Plinth estimates image Y'；

7.3) σ is worked as_nDuring ＞ 50, basis is estimated that image Y' performs step 6, a step 7.1 again) and step 7.2)；No Then, step 8 is directly performed.

Step 8, estimates image Y', with step-length N to the basis obtained_sChoose reference block, build its phase according to range formula Like group

$S_i^1=\{{\hat{Y}}_{i,j}^{\text{'}}:\frac{{\left|\right|{\hat{Y}}_i^{\text{'}}-{\hat{Y}}_{i,j}^{\text{'}}\left|\right|}_2^2}{{\left(N_1^{\text{'}}\right)}^2}<\mathrm{\&tau;}\},$

Wherein,WithIt is that the reference block in image and candidate blocks are estimated in basis respectively,Represent's L₂Norm squared, N₁'×N₁' it is tile size, τ is to judge the threshold value that two image blocks are the most similar, σ_nWhen≤40, N_sValue is 3, N₁' value is 8, τ value is 400；σ_nDuring ＞ 40, N_sValue is 6, N₁' value is 11, τ takes Value is 3500.

Step 9, according to similar groupThe positional information of middle similar block, extracts corresponding image block from noisy image X, And similar group of noisy image X is formed with the image block extracted

Step 10, similar group to noisy image XCarry out the collaborative filtering of wiener, obtain similar groupMiddle similar block is estimated Evaluation

10.1) basis is estimated image Y' similar groupCarry out three-dimension varying, calculate wiener according to its conversion coefficient and shrink Coefficient W_i:

$W_i=\frac{{\left|T_{3D}\left(S_i^1\right)\right|}^2}{{\left|T_{3D}\left(S_i^1\right)\right|}^2+{{\mathrm{\&sigma;}}_n}^2},$

Wherein, Τ_3DRepresent the three-dimension varying being made up of haar wavelet transformation one-dimensional between two-dimensional dct transform and block, Represent similar groupConversion coefficient take absolute value square；

10.2) similar group to noisy image XCarry out three-dimension varying, according to its conversion coefficient and wiener constriction coefficient Wi Calculate similar groupThe estimated value of middle similar block

${\hat{Y}}_{S_i^2}^{\text{'}}=T_{3D}^{-1}\left(W_i{T}_{3D}\left(S_i^2\right)\right),$

Wherein, W_iFor wiener constriction coefficient,Represent three-dimensional inverse transformation.

Step 11, to similar groupMiddle similar block estimated value weighted average, obtains denoising image Y'':

$Y^{\text{'}}=\{{\hat{y}}^{\text{'}}\left(x\right)=\frac{\underset{i\&Element;X}{\mathrm{\&Sigma;}}\underset{j\&Element;S_i^2}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_i{\hat{Y}}_{i,j}^{\text{'}}\left(x\right)}{\underset{i\&Element;X}{\mathrm{\&Sigma;}}\underset{j\&Element;S_i^2}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_i{\mathrm{\&chi;}}_j\left(x\right)},\&ForAll;x\&Element;X\},$

Wherein, ω_iIt it is similar groupCorresponding weights,Represent W_iL₂Norm squared.

Effect of the present invention can be further characterized by by following experiment:

One. experiment condition

Experiment condition: in experiment, uses six width test images to test, and various denoising methods are all to use matlab language Speech programming realization, and all use randn (' seed', 0) to add noise.

Wherein as in figure 2 it is shown, wherein, Fig. 2 (a) is the House image of 256 × 256 sizes to three width test images, Fig. 2 (b) Being that Fig. 2 (a) figure with the addition of the noisy image that noise criteria difference is 100 noises, Fig. 2 (c) is 256 × 256 sizes Cameraman image, Fig. 2 (d) is that Fig. 2 (c) figure with the addition of the noisy image that noise criteria difference is 75 noises, Fig. 2 (e) Being the Barbara image of 512 × 512 sizes, Fig. 2 (f) is that Fig. 2 (e) figure with the addition of noise criteria difference is that 50 noises contain Make an uproar image.

Two. experiment content and interpretation of result:

2.1) under these experimental conditions, BM3D method, CSR method, LSSC method and the present invention is used to enter respectively Row experiment carries out denoising emulation experiment to Fig. 2.

Experiment 1, uses BM3D method, CSR method, LSSC method and the present invention to enter the House image of Fig. 2 (a) Row denoising, as it is shown on figure 3, wherein, Fig. 3 (a) is the denoising image that BM3D method obtains to result, and Fig. 3 (b) is CSR The denoising image that method obtains, Fig. 3 (c) is the denoising image that LSSC method obtains, and Fig. 3 (d) is the denoising that the present invention obtains Image；

Experiment 2, uses BM3D method, CSR method, LSSC method and the present invention Cameraman to Fig. 2 (c) Image carries out denoising, and as shown in Figure 4, wherein, Fig. 4 (a) is the denoising image that BM3D method obtains to result, Fig. 4 (b) Being the denoising image that obtains of CSR method, Fig. 4 (c) is the denoising image that LSSC method obtains, and Fig. 4 (d) is that the present invention obtains The denoising image arrived；

Experiment 3, uses BM3D method, CSR method, LSSC method and the present invention Barbara image to Fig. 2 (e) Carrying out denoising, as it is shown in figure 5, wherein, Fig. 5 (a) is the denoising image that BM3D method obtains to result, and Fig. 5 (b) is CSR The denoising image that method obtains, Fig. 5 (c) is the denoising image that LSSC method obtains, and Fig. 5 (d) is the denoising that the present invention obtains Image.

From Fig. 3, Fig. 4 and Fig. 5 it can be seen that existing BM3D method can preferably remove noise, but can make The edge blurry of image and can not keep the seriality at edge, creates obvious Gibbs' effect in denoising image；Compare BM3D method, the denoising effect of existing CSR method makes moderate progress, and can preferably recover Edge texture region, corresponding Denoising image in Gibbs' effect reduced, but part edge still can be made while denoising to obscure, and homogeneity range Territory is the most smooth；Existing LSSC method has a strongest noise inhibiting ability to the smooth region of image, but meeting " mistake Smooth " edge and texture region, even cannot recover part edge region；Compare above-mentioned existing three kinds of denoising methods, The present invention is when smooth noise, it is possible to preferably retains image detail information, and introduces less glitch, is especially making an uproar When sound intensity is bigger, denoising effect can significantly improve.

2.2) the Y-PSNR PSNR after six width test image denoisings is calculated, with PSNR as the quantitative assessment of denoising Index, its computational methods are:

$\mathrm{PSNR}=101g\left[\frac{u_{\max }^2}{\frac{1}{\left|N\right|}\underset{i\&Element;N}{\mathrm{\&Sigma;}}{[\hat{v}\left(i\right)-u\left(i\right)]}^2}\right]$

Wherein, u (i) is that original nothing is made an uproar figure,For the result figure after denoising, u_max=max{u (i), i ∈ N}, N table Diagram is as size.

In noise criteria difference σ_nWhen being 25,35,50,75,100, to six width test image denoisings respectively, after calculating denoising PSNR value, as shown in table 1.

In table 1, each cell lists existing three kinds of denoising methods six width test images corresponding with the present invention PSNR value, the upper left side of the most each cell is the PSNR value of BM3D method, and upper right side is the PSNR of CSR method Value, lower left is the PSNR value of LSSC method, and lower right is the PSNR value of the present invention.

Table 1 denoising result contrasts

As it can be seen from table 1 the present invention all increases relative to the PSNR evaluation index of existing three kinds of denoising methods. The present invention can preferably keep edge and the grain details of image while smooth noise.

Claims (2)

1. the image de-noising method shunk based on non local wavelet coefficient, comprises the steps:

(1) in inputting noisy image, take reference image block with step-length 3, calculate this reference picture according to Euclidean distance formula Block and the distance d (Z of all image blocks in its neighborhood_i,Z_i,j), the N that selected distance is minimum₂Individual image block constitutes this with reference to figure As block similar group: S_i={ Z_i,j:min(d(Z_i,Z_i,j)), j=1...N₂, wherein i represents similar group of sequence number }, wherein, Z_iFor Reference image block, Z_i,jFor Z_iImage block in neighborhood, N₂For similar block number in similar group；

(2) similar block in similar group is carried out two-dimensional wavelet transformation, obtains the wavelet coefficient of similar block:

α_i,j=Τ_2D(Z_i,j),Z_i,j∈S_i

Wherein, Τ_2DRepresent two-dimensional wavelet transformation, α_i,jFor the wavelet coefficient of jth similar block in similar group of i-th；

(3) according to non-local mean formula, the non-local mean μ of each similar group of wavelet coefficient is calculated_i:

${\mathrm{\&mu;}}_i=\underset{j\&Element;S_i}{\&Sigma;}{\mathrm{\&omega;}}_{i,j}{\mathrm{\&alpha;}}_{i,j},j=\mathrm{1...}{N}_2$

ω_i,j=exp (-d (Z_i,Z_i,j))/h/W

Wherein, ω_i,jFor the weights that similar block is corresponding, h is 12 σ_n, σ_nPoor for noise criteria, W represents that normalization operates；

(4) double L is used₁The contracting function of Norm Model, calculates the wavelet coefficient estimated value of similar block

${\widehat{\mathrm{\&alpha;}}}_{i,j}=\left\{\begin{array}{cc}{S}_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,{\mathrm{\&mu;}}_i}\left({\mathrm{\&alpha;}}_{i,j}\right)& {\mathrm{\&mu;}}_i\&GreaterEqual;0\\ -S_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,-{\mathrm{\&mu;}}_i}\left({\mathrm{\&alpha;}}_{i,j}\right)& {\mathrm{\&mu;}}_i<0\end{array}\right.$

Wherein,For contracting function, it is defined as:

$S_{{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,{\mathrm{\&mu;}}_i}\left({\mathrm{\&alpha;}}_{i,j}\right)=\left\{\begin{array}{cc}{\mathrm{\&alpha;}}_{i,j}+{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2& {\mathrm{\&alpha;}}_{i,j}<-{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\\ 0& -{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\&le;{\mathrm{\&alpha;}}_{i,j}\&le;{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\\ {\mathrm{\&alpha;}}_{i,j}-{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2& {\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2\&le;{\mathrm{\&alpha;}}_{i,j}\&le;{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2+{\mathrm{\&mu;}}_i\\ {\mathrm{\&mu;}}_i& {\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2+{\mathrm{\&mu;}}_i\&le;{\mathrm{\&alpha;}}_{i,j}\&le;{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2+{\mathrm{\&mu;}}_i\\ {\mathrm{\&alpha;}}_{i,j}-{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_2& {\mathrm{\&alpha;}}_{i,j}>{\mathrm{\&tau;}}_1+{\mathrm{\&tau;}}_2+{\mathrm{\&mu;}}_i\end{array}\right.$

Wherein, α_i,jFor treating constriction coefficient, μ_iIt is to treat the non-local mean that constriction coefficient is corresponding, τ₁And τ₂It is two differences Collapse threshold,c₁, c₂It is the constant of two different numerical value, c₁Value is 0.1, c₂Value is 0.9, σ_nPoor for noise criteria, σ_iIt is by α_iEstimate the standard deviation obtained, α_i={ α_i,1...α_i,j, δ_iBe by α_i-μ_iEstimate the standard deviation obtained；

(5) to wavelet coefficient estimated valueCarry out inverse wavelet transform, obtain similar block estimated value, integrate all estimated values, Once estimated image Y:

${\hat{Y}}_{i,j}=T_{2D}^{-1}\left({\widehat{\mathrm{\&alpha;}}}_{i,j}\right)$

Wherein, X is noisy image, and x is the pixel in X,Represent 2-d wavelet inverse transformation, χ_jX () is figure As blockCharacteristic function,Time, χ_jX () value is 1, be otherwise 0；

(6) the once estimation image Y obtained is carried out residual error to refill, refill repetition step (1)-(5) on figure in residual error, obtain Image Y' is estimated on basis；Work as σ_n> 50 time, basis is estimated that image Y' performs the most identical residual error again and refills operation；

(7) image Y' is estimated, with step-length N in the basis obtained_sChoose reference image block, build according to Euclidean distance formula Its similar groupAnd record the coordinate information of similar block in similar group:

$S_i^1=\left\{{\hat{Y}}_{i,j}^{\&prime;}:\frac{\left|\right|{\hat{Y}}_i^{\&prime;}-{\hat{Y}}_{i,j}^{\&prime;}|{|}_2^2}{{\left(N_1^{\&prime;}\right)}^2}<\mathrm{\&tau;}\right\}$

Wherein,WithIt is that the reference image block in image and candidate blocks are estimated in basis respectively,Represent L₂Norm squared, N₁'×N₁' it is tile size, τ is to judge the threshold value that two image blocks are the most similar, σ_nWhen≤40, τ value is 400, σ_n> 40 time, τ value is 3500；

(8) according to similar block coordinate information, from noisy image, extract corresponding image block, constitute similar groupTo base Plinth estimates similar group of imageSimilar with noisy image groupAll carry out three-dimension varying, obtain respective conversion coefficient, According to similar groupConversion coefficient calculate wiener constriction coefficient W_i, further according to similar groupConversion coefficient and wiener shrink Coefficient W_i, obtain similar groupMiddle similar block estimated value:

$W_i=\frac{|T_{3D}\left(S_i^1\right){|}^2}{|T_{3D}\left(S_i^1\right){|}^2+{{\mathrm{\&sigma;}}_n}^2}$

${\hat{Y}}_{S_i^2}^{\&prime;\&prime;}=T_{3D}^{-1}\left(W_i{T}_{3D}\right(S_i^2\left)\right)$

Wherein, Τ_3DRepresent the three-dimension varying being made up of one-dimensional wavelet transform between two-dimensional dct transform and block,Represent three Dimension inverse transformation,Represent similar groupConversion coefficient take absolute value square, W_iFor similar groupWith subscript i Corresponding similar groupWiener constriction coefficient；

(9) to similar group obtainedMiddle similar block estimated value weighted average, obtains denoising image Y ":

Wherein, ω_iIt it is similar groupCorresponding weights,Represent W_iL₂Norm squared.

Denoising method the most according to claim 1, wherein described in step (1) according to Euclidean distance formula calculate reference Image block and the distance d (Z of all image blocks in its neighborhood_i,Z_i,j), its formula is as follows:

$d(Z_i,Z_{i,j})=\frac{\left|\right|Z_i-Z_{i,j}|{|}_2^2}{{\left(N_1\right)}^2}$

Wherein, Z_iFor reference image block, Z_i,jFor Z_iImage block in neighborhood,Represent Z_i-Z_i,jL₂Model Several squares, N₁×N₁For tile size.