CN103745442A - Non-local wavelet coefficient contraction-based image denoising method - Google Patents

Abstract

The invention discloses a non-local wavelet coefficient contraction-based image denoising method, which mainly solves the problem that image details are lost when denoising is performed by adopting a traditional image denoising method. The non-local wavelet coefficient contraction-based image denoising method comprises the following implementation steps: (1) establishing noise image-contained similarity groups, performing two-dimension wavelet transformation on similarity blocks in the similarity groups, and calculating non-local means of wavelet coefficients of the similarity groups; (2) contracting the wavelet coefficients by using a double-L1 norm model, then, performing wavelet inverse transformation to obtain estimated values of the similarity blocks, and performing integration on the estimated values to obtain primary estimation images; (3) performing residual cover on the primary estimation image, and executing the step (1) and the step (2) to obtain base estimation images; (4) establishing similarity groups of the base estimation images, and further obtaining the noise image-contained similarity groups; (5) performing Wiener collaborative filtering on the noise image-contained similarity groups to obtain denoised images. According to the non-local wavelet coefficient contraction-based image denoising method disclosed by the invention, while noise is smoothened, edge textures of images can be kept better. The non-local wavelet coefficient contraction-based image denoising method can be used for denoising processing of natural images.

Description

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

Technical field

The invention belongs to technical field of image processing, the image de-noising method specifically shrinking based on non local wavelet coefficient, can be used for the denoising to natural image.

Background technology

Image is the important sources of people's obtaining information, but image usually can be subject to the interference of various noises in generation and transmitting procedure, and this not only has influence on the visual effect of image, has also hindered the carrying out of the follow-up works such as feature extraction, target identification.Therefore, image denoising is the vital part of image processing field.

The object of image denoising recovers high-quality image clearly exactly from noisy image, keeps as much as possible the inherent feature information of image in the time of denoising.At present, a large amount of denoising methods are suggested, and wherein regularization method has obtained research widely, and the method is incorporated into variational formulation by observed image and priori, and it is vital emphasizing to find suitable prior image model.Traditional regularization method such as secondary Tikhonov method, the TV method hypothesis due to its piecewise constant, can be crossed smoothed image in denoising, therefore, is replaced very soon by the regularization method based on sparse property.The method has been utilized the sparse property in the part of image, with the linear combination of the some atoms in dictionary, carrys out presentation video piece, and each image block is to carry out separately rarefaction representation, do not consider and other image blocks between correlativity.

2005, the people such as Buades proposed non-local image de-noising method, and the method has broken through the thought of traditional part filter, made full use of the non local structural similarity of image, had obtained significant denoising effect.Subsequently, a lot of denoising methods based on non local thought have been there are, as methods such as BM3D, CSR, BM3D method is by the two dimensional image piece of the structural similarity formation three-dimensional array that flocks together, by to these three-dimensional array associating filtering, the estimated value of polymerization image block, has further improved denoising effect.But the method, owing to carrying out interblock one-dimensional transform to similar group, is weakened the part details of image, causes fringe region to fog.CSR method combines dictionary learning and documents structured Cluster, makes the sparse coding noise of image enough little, thereby improves denoising effect, but that the method implements is more consuming time, and the denoising effect of part edge is still undesirable.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, propose a kind of implementation method of the image denoising shrinking based on non local wavelet coefficient, to realize the taking into account of edge and smooth region in natural image denoising, improve image denoising effect.

For achieving the above object, the present invention includes following steps:

(1) in the noisy image of input, with step-length 3, get reference image block, according to Euclidean distance formula, calculate the distance d (Z of all image blocks in this reference block and its neighborhood _i, Z _i,j), the N of selected distance minimum ₂individual image block forms similar group of this reference block: S _i={ Z _i,j: min (d (Z _i, Z _i,j)), j=1...N ₂, i represents similar group of sequence number }, wherein, Z _ifor reference image block, Z _i,jfor Z _iimage block in neighborhood, N ₂for similar number in similar group;

(2) to similar in similar group, carry out two-dimensional wavelet transformation, obtain the wavelet coefficient of similar:

α _i,j＝Τ _2D(Z _i,j),Z _i,j∈S _i

Wherein, Τ _2Drepresent two-dimensional wavelet transformation, α _i,jit is the wavelet coefficient of j similar in i similar group;

(3), according to non-local mean formula, calculate the non-local mean μ of each similar group of wavelet coefficient _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 similar corresponding weights, h is 12 σ _n, σ _npoor for noise criteria, W represents normalization operation;

(4) use two L ₁the contracting function of Norm Model, calculates the wavelet coefficient estimated value of similar

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

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 contraction coefficient, and b is the non-local mean for the treatment of that contraction coefficient is corresponding, τ ₁and τ ₂be two different collapse threshold,

c ₁, c ₂be the constant of two different numerical value, c ₁value is 0.1, c ₂value is 0.9, σ _nfor noise criteria poor, σ _iby α _iestimate the standard deviation obtaining, α _i={ α _{i, 1}... α _i,j, δ _iby α _i-μ _iestimate the standard deviation obtaining;

(5) to wavelet coefficient estimated value carry out inverse wavelet transform, obtain similar estimated value, integrate all estimated values, obtain estimated image Y one time:

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

Wherein, X is noisy image, and x is the pixel in X,

represent 2-d wavelet inverse transformation, χ _jit is image block

fundamental function,

time, χ _jvalue is 1, otherwise is 0;

(6) obtain estimated image Y is carried out to residual error and refill, in residual error, refill repeating step on figure (1)-(5), obtain basic estimated image Y'; Work as σ _nduring > 50, basic estimated image Y' is carried out once to identical residual error again and refill operation.

(7) to the basic estimated image Y' obtaining, with step-length N _schoose reference block, according to Euclidean distance formula, build its similar group

and record in similar group the coordinate information of similar:

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

Wherein, with

respectively reference block and the candidate blocks in basic estimated image,

represent

l ₂norm squared, N ₁' * N ₁' be tile size, τ judges two threshold values whether image block is similar, σ _n≤ 40 o'clock, τ value was 400, σ _nduring > 40, τ value is 3500;

(8) according to similar coordinate information, from noisy image, extract corresponding image block, form similar group

to basic estimated image similar group

with similar group of noisy image

all carry out three-dimension varying, obtain conversion coefficient separately, according to similar group

conversion coefficient calculate dimension and receive contraction coefficient W _i, then according to similar group

conversion coefficient and dimension receive contraction coefficient W _i, obtain similar group in similar 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 _3Dthe three-dimension varying that expression is comprised of two-dimensional dct transform and interblock one-dimensional wavelet transform,

represent three-dimensional inverse transformation, expression is to similar group

conversion coefficient take absolute value square, W _ifor similar group

corresponding dimension is received contraction coefficient;

(9) to similar group that obtains

in similar estimated value weighted mean, obtain denoising image Y'':

Wherein, ω _iit is similar group

corresponding weights,

represent W _il ₂norm squared.

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

1. the present invention is owing to carrying out in wavelet field, and implementation procedure 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 _i,japproach the non-local mean μ of similar group of wavelet coefficient _i, contraction phase, like piece wavelet coefficient, obtains similar estimated value accurately effectively.

3. the present invention is owing to having used two L ₁norm Model contracting function, can access basic estimated image accurately, and then obtains noisy image similarity group accurately

receive contraction coefficient W with dimension _ithereby, accurately calculate pixel estimated value, in the time of can smooth noise, keep and edge and the grain details of Recovery image.

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention;

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

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

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

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

Embodiment

With reference to accompanying drawing 1, the present invention is based on the image de-noising method that non local wavelet coefficient shrinks, comprise the steps:

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

1.1) in without the test pattern of making an uproar, adding standard deviation is σ _nnoise, obtain noisy image X:

X=U+σ _n*randn(N)，

Wherein, U is that N is the sum of all pixels in U without making an uproar test pattern, and randn () is for producing the function of random number in matlab language;

1.2) in noisy image X, with step-length 3, get reference block Z _i, according to range formula, calculate this reference block and its big or small distance d (Z for 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,jl ₂norm squared, N ₁* N ₁for tile size, N ₁value is that 8, w value is that 39, exp represents exponent arithmetic, and h is 12 σ _n, σ _npoor for noise criteria, W represents normalization operation;

1.3) get the minimum N of distance ₂individual 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...N ₂, i represents similar group of sequence number },

Wherein, min represents to get N ₂individual minimum value, N ₂for similar number in similar group, σ _n≤ 30 o'clock, N ₂value is 16; σ _nduring > 30, N ₂value is 20.

Step 2, in similar group similar carry out wavelet transformation, obtain the wavelet coefficient α of similar _i,j:

α _i,j＝Τ2D(Z _i,j),Z _i,j∈S _i，

Wherein, Τ _2Drepresent two-dimentional bior1.5 wavelet transformation, and be three layers of decomposition, α _i,jit is the wavelet coefficient of j similar in i similar group.

Step 3, according to weights ω _i,jwith similar wavelet coefficient α _i,j, utilize non-local mean formula to calculate the non-local mean μ of each similar group 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, is used two L ₁the contracting function of Norm Model is to similar wavelet coefficient α _i,jshrink.

4.1) by similar wavelet coefficient α _i,jform the wavelet coefficient set α of similar group _i, α _i={ α _{i, 1}... α _i,j, use α _ievery row deduct non-local mean μ _iobtain newly gathering α _i-μ _i, α _i-μ _i={ (α _{i, 1}-μ _i) ... (α _i,j-μ _i);

4.2) calculate wavelet coefficient set α _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 τ ₁, according to new set α _i-μ _istandard deviation δ _icalculate the second collapse threshold τ ₂:

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

Wherein, σ _nfor noise criteria poor, c ₁, c ₂be the constant of two different numerical value, c ₁value is 0.1, c ₂value is 0.9;

4.4) the two L of definition ₁the contracting function of Norm Model for:

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

Wherein, t is for treating contraction coefficient, and b is the non-local mean for the treatment of that contraction coefficient is corresponding;

4.5) according to two collapse threshold τ ₁, τ ₂non-local mean μ with similar group of wavelet coefficient _i, utilize contracting function

contraction phase is like piece wavelet coefficient α _i,j, obtain similar 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 wavelet coefficient estimated value

obtain estimated image Y one time.

5.1) to similar wavelet coefficient estimated value

carry out inverse wavelet transform, obtain similar 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) integrate all similar estimated values obtain estimated image Y one time:

Wherein, X is noisy image, and x is the pixel in X, χ _jit is image block

fundamental function,

time, χ _jvalue is 1, otherwise is 0.

Step 6, carries out residual error to an estimated image Y and refills, and 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 error

execution step 1-5, obtains basic estimated image Y'.

7.1) calculate residual error and refill image

noise 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 poor figure

variance,

7.2) according to residual error, refill image noise criteria poor

residual error is refilled to image

execution step 1-5, obtains basic estimated image Y';

7.3) work as σ _nduring > 50, basic estimated image Y' is carried out to step 6, step 7.1 again) and step 7.2); Otherwise, directly perform step 8.

Step 8, to the basic estimated image Y' obtaining, with step-length N _schoose reference block, according to range formula, build its 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,

with

respectively reference block and the candidate blocks in basic estimated image,

represent l ₂norm squared, N ₁' * N ₁' be tile size, τ judges two threshold values whether image block is similar, σ _n≤ 40 o'clock, N _svalue is 3, N ₁' value is that 8, τ value is 400; σ _nduring > 40, N _svalue is 6, N ₁' value is that 11, τ value is 3500.

Step 9, according to similar group

in the positional information of similar, from noisy image X, extract corresponding image block, and with the image block extracting, form similar group of noisy image X

Step 10, to noisy image X similar group

carry out the collaborative filtering of Wei Na, obtain similar group

in similar estimated value

10.1) similar group to basic estimated image Y'

carry out three-dimension varying, according to its conversion coefficient, calculate dimension and receive contraction 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 _3Dthe three-dimension varying that expression is comprised of two-dimensional dct transform and interblock one dimension haar wavelet transformation, expression is to similar group

conversion coefficient take absolute value square;

10.2) similar group to noisy image X

carry out three-dimension varying, according to its conversion coefficient and dimension, receive contraction coefficient Wi and calculate similar group

in the estimated value of similar

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

Wherein, W _ifor dimension is received contraction coefficient, represent three-dimensional inverse transformation.

Step 11, to similar group

in similar estimated value weighted mean, obtain 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 is similar group

corresponding weights, represent W _il ₂norm squared.

Effect of the present invention can further confirm by following experiment:

One. experiment condition

Experiment condition: in experiment, use six width test patterns to test, various denoising methods are all to use matlab Programming with Pascal Language to realize, and all use randn (' seed', 0) to add noise.

Wherein three width test patterns as shown in Figure 2, wherein, Fig. 2 (a) is the House image of 256 * 256 sizes, Fig. 2 (b) is that to Fig. 2 (a) figure, having added noise criteria poor is the noisy image of 100 noises, Fig. 2 (c) is the Cameraman image of 256 * 256 sizes, Fig. 2 (d) is that to Fig. 2 (c) figure, having added noise criteria poor is the noisy image of 75 noises, Fig. 2 (e) is the Barbara image of 512 * 512 sizes, and Fig. 2 (f) is that to Fig. 2 (e) figure, having added noise criteria poor is the noisy image of 50 noises.

Two. experiment content and interpretation of result:

2.1), under above-mentioned experiment condition, use respectively BM3D method, CSR method, LSSC method and the present invention to test Fig. 2 is carried out to denoising emulation experiment.

Experiment 1, use BM3D method, CSR method, LSSC method and the present invention to carry out denoising to the House image of Fig. 2 (a), result as shown in Figure 3, wherein, Fig. 3 (a) is the denoising image that BM3D method obtains, Fig. 3 (b) is the denoising image that CSR method obtains, and Fig. 3 (c) is the denoising image that LSSC method obtains, and Fig. 3 (d) is the denoising image that the present invention obtains;

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

Experiment 3, use BM3D method, CSR method, LSSC method and the present invention to carry out denoising to the Barbara image of Fig. 2 (e), result as shown in Figure 5, wherein, Fig. 5 (a) is the denoising image that BM3D method obtains, Fig. 5 (b) is the denoising image that CSR method obtains, and Fig. 5 (c) is the denoising image that LSSC method obtains, and Fig. 5 (d) is the denoising image that the present invention obtains.

From Fig. 3, Fig. 4 and Fig. 5, can find out, existing BM3D method can be removed noise preferably, but can make the edge fog of image and continuity that can not keep the edge information, has produced obvious Gibbs' effect in denoising image; Compare BM3D method, the denoising effect of existing CSR method makes moderate progress, and can recover preferably Edge texture region, and in corresponding denoising image, Gibbs' effect reduces to some extent, but in denoising, still can make part edge fuzzy, and homogeneous area is level and smooth not; Existing LSSC method has very strong noise inhibiting ability to the smooth region of image, but meeting " excessively level and smooth " edge and texture region even cannot recover part edge region; Compare above-mentioned existing three kinds of denoising methods, the present invention, when smooth noise, can retain image detail information better, and introduces less glitch, and especially, when noise intensity is larger, denoising effect can significantly improve.

2.2) calculate the Y-PSNR PSNR after six width test pattern denoisings, the quantitative evaluation index with PSNR as denoising, its computing method 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 the original nothing figure that makes an uproar,

for the result figure after denoising, u _max=max{u (i), i ∈ N}, N presentation video size.

At the poor σ of noise criteria _nbe 25,35,50,75,100 o'clock, to the denoising respectively of six width test patterns, calculate the PSNR value after denoising, as shown in table 1.

In table 1, each cell has been listed the PSNR value of existing three kinds of denoising methods and six width test patterns corresponding to the present invention, wherein the upper left side of each cell is the PSNR value of BM3D method, upper right side is the PSNR value of CSR method, lower left is the PSNR value of LSSC method, and lower right is PSNR value of the present invention.

The contrast of table 1 denoising result

As can be seen from Table 1, the present invention all increases with respect to the PSNR evaluation index of existing three kinds of denoising methods.When the present invention can smooth noise, keep better edge and the grain details of image.

Claims (2)

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

(1) in the noisy image of input, with step-length 3, get reference image block, according to Euclidean distance formula, calculate the distance d (Z of all image blocks in this reference block and its neighborhood _i, Z _i,j), the N of selected distance minimum ₂individual image block forms similar group of this reference block: S _i={ Z _i,j: min (d (Z _i, Z _{i, j)}), j=1...N ₂, i represents similar group of sequence number }, wherein, Z _ifor reference image block, Z _i,jfor Z _iimage block in neighborhood, N ₂for similar number in similar group;

(2) to similar in similar group, carry out two-dimensional wavelet transformation, obtain the wavelet coefficient of similar:

α _i,j＝Τ _2D(Z _i,j),Z _i,j∈S _i

Wherein, Τ _2Drepresent two-dimensional wavelet transformation, α _i,jit is the wavelet coefficient of j similar in i similar group;

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

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

ω _i,j＝exp(-d(Z _i,Z _i,j))/h)/W

Wherein, ω _i,jfor similar corresponding weights, h is 12 σ _n, σ _npoor for noise criteria, W represents normalization operation;

(4) use two L ₁the contracting function of Norm Model, calculates the wavelet coefficient estimated value of similar

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

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 contraction coefficient, and b is the non-local mean for the treatment of that contraction coefficient is corresponding, τ ₁and τ ₂be two different collapse threshold,

c ₁, c ₂be the constant of two different numerical value, c ₁value is 0.1, c ₂value is 0.9, σ _nfor noise criteria poor, σ _iby α _iestimate the standard deviation obtaining, α _i={ α _{i, 1}... α _i,j, δ _iby α _i-μ _iestimate the standard deviation obtaining;

(5) to wavelet coefficient estimated value

carry out inverse wavelet transform, obtain similar estimated value, integrate all estimated values, obtain estimated image Y one time:

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

Wherein, X is noisy image, and x is the pixel in X, represent 2-d wavelet inverse transformation, χ _jit is image block fundamental function,

time, χ _jvalue is 1, otherwise is 0;

(6) obtain estimated image Y is carried out to residual error and refill, in residual error, refill repeating step on figure (1)-(5), obtain basic estimated image Y'; Work as σ _nduring > 50, basic estimated image Y' is carried out once to identical residual error again and refill operation.

(7) to the basic estimated image Y' obtaining, with step-length N _schoose reference block, according to Euclidean distance formula, build its similar group

, and record in similar group the coordinate information of similar:

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

Wherein,

with

respectively reference block and the candidate blocks in basic estimated image,

represent

l ₂norm squared, N ₁' * N ₁' be tile size, τ judges two threshold values whether image block is similar, σ _n≤ 40 o'clock, τ value was 400, σ _nduring > 40, τ value is 3500;

(8) according to similar coordinate information, from noisy image, extract corresponding image block, form similar group

to basic estimated image similar group

with similar group of noisy image

all carry out three-dimension varying, obtain conversion coefficient separately, according to similar group conversion coefficient calculate dimension and receive contraction coefficient W _i, then according to similar group

conversion coefficient and dimension receive contraction coefficient W _i, obtain similar group

in similar 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 _3Dthe three-dimension varying that expression is comprised of two-dimensional dct transform and interblock one-dimensional wavelet transform,

represent three-dimensional inverse transformation,

expression is to similar group

conversion coefficient take absolute value square, W _ifor similar group

corresponding dimension is received contraction coefficient;

(9) to similar group that obtains

in similar estimated value weighted mean, obtain denoising image Y'':

Wherein, ω _iit is similar group

corresponding weights,

represent W _il ₂norm squared.

2. denoising method according to claim 1, wherein step (1) described according to the distance d (Z of all image blocks in Euclidean distance formula computing reference piece and its neighborhood _i, Z _i,j), its formula is as follows:

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

Wherein, Z _ifor reference image block, Z _i,jfor Z _iimage block in neighborhood,

represent Z _i-Z _i,jl ₂norm squared, N ₁* N ₁for tile size.

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