CN101847256B - Image denoising method based on adaptive shear wave - Google Patents

Abstract

The invention discloses a threshold denoising method based on adaptive shear wave, mainly aiming to solve the problems of the existing threshold denoising method of shear wave that the direction of shear wave is not flexible and the adaptivity is poor. The method comprises the following steps: decomposing the Laplacian pyramid of down 2 sample of an image to obtain a detail image and an approximate image, constructing adaptive shear wave, using adaptive shear wave to perform direction dividing to the approximate image and obtain the direction coefficient matrix of each detail layer, performing hard threshold denoising to each coefficient matrix; then reconstructing each layer for each denoised coefficient matrix to obtain the reconstructed detail image; finally combining the detail image with the original approximate image, performing Laplacian pyramid reconstruction of down 2 sample, and finally obtaining the denoised image. The threshold denoising method of the invention is an extension for the existing shear wave; and by using the method, all the properties of the original shear wave can be completely maintained and image analysis can obtain more ideal effect.

Description

Image de-noising method based on adaptive shear wave

Technical field

The invention belongs to image processing field, relate to the denoising method of image, can be used for, hard-threshold, and the image denoising of non-local mean based on total variation.

Background technology

The shearing wave conversion is that a kind of " really " that K.Guo in 2005 and D.Labate propose tieed up the graphical representation method, and this method can well be caught the geometry of image.It is flexibly a kind of that shearing wave provides, multiple dimensioned, local, the analytical approach of directivity.

The shearing wave analysis is a kind of novel multi-scale geometric analysis instrument of inheriting the advantage of curve ripple and square wave, and through the convergent-divergent to basis function, radiation conversion such as shearing and translation generate the shearing wave function with different characteristic, for comprising C ²The high dimensional signal of singular curve or curve has optimal properties.For 2D signal; It not only can detect all singular points; Direction that can also adaptive tracking singular curve, along with the variation of scale parameter, the singularity characteristic of described function accurately; Realization is described the singularity in the high dimensional signal with classical multiscale analysis, has also set up the mathematical theory basis for square wave simultaneously.

For two-dimentional sectionally smooth signal, shearing wave can reach the rarefaction representation of theoretical property to it, because shearing wave still is a very new multi-scale geometric analysis instrument; Present application also is not very extensive; But it has the more unexistent outstanding characteristics of other multiple dimensioned Combination tool, as: (1) is defined in the Ka Tesen territory, can obtain various directions through shear transformation; Therefore he is unrestricted to the direction of shearing manipulation, can be on more direction analysis image; (2) inverse transformation only needs the inverse transformation of the simple synthetic rather than anisotropic filter of shearing wave wave filter, has simply fast discretize way of realization etc.These characteristics are accomplished something it in the image place, like image noise reduction, and compression, aspects such as enhancing and watermark.

Denoising method based on shearing wave has the total variation denoising, non-local mean denoising, the denoising of the laplacian pyramid method of laplacian pyramid and non-lower sampling.

Shearing wave decomposes noisy image with the laplacian pyramid decomposition based on the hard-threshold denoising method of laplacian decomposition, obtains image and approximate image, and detail pictures is combined shearing wave, obtains the detail coefficients of all directions.Then noisy detail coefficients is carried out hard-threshold and handle, the mould value is changed to zero less than the coefficient of threshold value, the coefficient of mould value greater than threshold value kept, because the more non-edge of general pairing coefficient module value, edge is big, so threshold denoising can effectively be removed noise.But, cause the application specific aim and the adaptivity of threshold denoising poor, thereby cause the Y-PSNR PSNR of denoising result can not reach more desirable index because original shearing wave shape can not change.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned prior art, propose a kind of image de-noising method, improve image denoising result's Y-PSNR PSNR, make it can reach more desirable index based on adaptive shear wave.

Technical scheme of the present invention comprises the steps:

1. the image de-noising method based on adaptive shear wave comprises the steps:

(1) descend the laplacian pyramid of 2 samplings to decompose for noisy image, obtain detail pictures D1 and D2, and approximate image A;

(2) structure adaptive shear wave:

2a) at existing shearing wave basis function

Basic enterprising line function divide, it is divided into [0.86 ,-0.06], (0.06,0.14), [0.14,0.94] three intervals are used function f respectively to the function in these three intervals ₂, f ₁, f ₃Expression, and given qualification is interval;

2b) set a parameter a, be defined as auto-adaptive parameter, and make that its span is (0; + ∞), with [0.86 ,-0.06] of above-mentioned division; (0.06,0.14), [0.14; 0.94] three intervals, structure adaptive shear wave basis function

$s{\widehat{\mathrm{\&psi;}}}_2\left(\mathrm{\&xi;}\right)=\left\{\begin{array}{cc}{\widehat{\mathrm{\&psi;}}}_2\left(\frac{4+a}{5}(\mathrm{\&xi;}-\frac{7}{10}\&times;\frac{(a-1)}{4+a}\right)& \frac{5\mathrm{<figure-callout\; id="4"\; label="a"\; filenames="HSA00000149406300021.png"\; state="\{\{state\}\}">a</figure-callout>}}{4+a}\&times;0.14\&le;\mathrm{\&xi;}\&le;1-\frac{5a}{4+a}\&times;0.06\\ 1& -0.06\&times;\frac{5\mathrm{<figure-callout\; id="4"\; label="a"\; filenames="HSA00000149406300021.png"\; state="\{\{state\}\}">a</figure-callout>}}{4+a}<\mathrm{\&xi;}<0.14\&times;\frac{5\mathrm{<figure-callout\; id="4"\; label="a"\; filenames="HSA00000149406300021.png"\; state="\{\{state\}\}">a</figure-callout>}}{4+a}\\ {\widehat{\mathrm{\&psi;}}}_2\left(\frac{4+a}{5}(\mathrm{\&xi;}+\frac{3}{10}\&times;\frac{(a-1)}{4+a}\right)& -(1-\frac{5a}{4+a}\&times;0.14)\&le;\mathrm{\&xi;}\&le;-\frac{5a}{4+a}\&times;0.06\end{array}\right.$

Wherein ξ is an argument of function,

be existing shearing wave basis function;

This basis function

satisfies following formula:

$\underset{l^{\&prime;}=-2^j+1}{\overset{2^j-1}{\mathrm{\&Sigma;}}}s{\widehat{\mathrm{\&psi;}}}_2{\left|(2^{(j-1)}\mathrm{\&xi;}-l^{\&prime;})\right|}^2=1$

Wherein j is a scale parameter, and its conversion has determined the basis function yardstick, and l ' is a translation parameters, and it is big more, and the more past positive axis of basis function moves;

2c) according to the basis function of adaptive shear wave; Make up adaptive shear wave

d=0; 1, j=1,2; 3 ..; M=-j ,-(j-1) ... j-1, j; The structure formula is following:

$\left.\begin{array}{c}{W}_{j,m}^{\left(0\right)}\left(\mathrm{\&xi;}\right)=s{\widehat{\mathrm{\&psi;}}}_2(j\frac{{\mathrm{\&xi;}}_2}{{\mathrm{\&xi;}}_1}-m){\mathrm{\&chi;}}_{D_0}\\ W_{j,m}^{\left(1\right)}\left(\mathrm{\&xi;}\right)=s{\widehat{\mathrm{\&psi;}}}_2(j\frac{{\mathrm{\&xi;}}_1}{{\mathrm{\&xi;}}_2}-m){\mathrm{\&chi;}}_{D_1}\end{array}\right\}$

Be defined as: ${\mathrm{\&chi;}}_{D_d}({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)=\left\{\begin{array}{cc}1& ({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)\&Element;D_d\\ 0& ({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)\&NotElement;D_d\end{array}\right.,$

D _dBe defined as:

Wherein

representes two-dimentional set of real numbers

2d) right again

Press:

Again be planned to W _{J, l},

L=1 wherein, 2 ... 4j; N=2,3 ... .2j;

L=[2j+1], [2j+1] expression to 2j+1 get round up whole;

J is the integer more than or equal to 1; M gets-and j is to the integer of j,

2e) according to the adaptive shear wave W that constructs _{J, l},, and it is inserted the auto-adaptive parameter a value of setting

(3) utilize adaptive shear wave after the auto-adaptive parameter a value, detail pictures D1 and D2 are carried out denoising, obtain the detail pictures rD1 and the rD2 of reconstruct;

(4) the detail pictures rD1 that pairing approximation image A and reconstruct obtain, reconstruct is carried out in the rD2 utilization laplacian pyramid restructing algorithm of 2 samplings down, obtains reconstructed image.

The present invention and original compared with techniques have following advantage:

1) the present invention is because the adaptive shear wave basis function of being constructed is the basis function that has shearing wave now to be carried out auto-adaptive parameter handle; In the time of when auto-adaptive parameter gets 1; The adaptive shear wave basis function is exactly existing shearing wave basis function; Thereby can utilize this adaptive shear wave to combine existing laplacian pyramid algorithm, image is carried out threshold denoising based on following 2 samplings.

2) the present invention is because according to different frequency bands; The self-adaptation adaptive shear wave is chosen different parameters, go to obtain the directional information of each frequency band, and obtain more sparse matrix of coefficients with the shape of the best; Thereby overcome in the prior art unicity of the frequency band all directions being chosen shearing wave; The frequency domain direction characteristic that can help threshold denoising with the research image of prior art more, and the various algorithms in the analysis of ability combining image are for the graphical analysis application provides bigger help;

3) simulation result shows; The adaptive shear wave that the present invention constructed can satisfy the sparse character that existing shearing wave produces matrix of coefficients; And can be as a kind of adequate condition of qualified shearing wave, in the application of threshold denoising, also embodied the result that can compare favourably with prior art; When by getting different value in the table two auto-adaptive parameter a, the Y-PSNR index of the effect of denoising obviously is superior to prior art;

4) the present invention overcome the shape of original shearing wave inflexible with direction distribute dumb, thereby can be applicable to threshold denoising.

Description of drawings

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

Fig. 2 is the signature to each ingredient of existing shearing wave basis function figure;

Fig. 3 works as a=1, and it is infinite that a is tending towards, and a is tending towards at 0 o'clock, the basis function image of resulting adaptive shear wave;

Fig. 4 is all directions zoning plan to adaptive shear wave of the present invention;

Fig. 5 is result's contrast of carrying out local denoising with existing shearing wave and adaptive shear wave of the present invention.

Embodiment

With reference to Fig. 1, concrete performing step of the present invention is following:

Step 1 descends the laplacian pyramid of 2 samplings to decompose for noisy image, decomposes twice, obtains detail pictures outermost layer D2, inferior outer detail pictures D1 and approximate image A.

Step 2, the structure adaptive shear wave

1, it is following to construct existing shearing wave basis function constitution step at frequency domain:

1a) structure lump function h ₁, this h ₁Satisfying can be little to infinite rank in (2,2) interval interior 0, and at (2,2) interior 0≤h ₁≤1, at [1,1] interior h ₁=1, the h of structure ₁Expression formula is following:

$h_1\left(\mathrm{\&xi;}\right)=e^{-\frac{28{(\mathrm{\&xi;}-1)}^{14}}{2^{14}}}---(1-1)$

Wherein ξ is an argument of function

1b) structure auxiliary function h ₂This h ₂Expression formula is following:

$h_2\left(\mathrm{\&xi;}\right)=\sqrt{1-e^{\frac{1}{(\mathrm{\&xi;}-1)}}}---(1-2)$

1c) on preceding two step bases, obtain the left side and prop up function h, this h expression formula is following:

h(ξ)＝h ₁(ξ)h ₂(ξ) (1-3)

1d) constructed fuction the right function g, this function g expression formula is following:

$g\left(\mathrm{\&xi;}\right)=\sqrt{1-\frac{(1-e^{-\frac{1}{\mathrm{\&xi;}-2}})}{e^{{\left(\frac{28{(\mathrm{\&xi;}-2)}^{14}}{2^{14}}\right)}^2}}}---(1-4)$

Function h is propped up on the left side that 1e) utilizes the front to obtain and function g is propped up on the right, and its expression formula of structure shearing wave basis function

is following:

${\widehat{\mathrm{\&psi;}}}_2\left(\mathrm{\&xi;}\right)=\left\{\begin{array}{cc}h(2\mathrm{\&xi;}+1)& -1\&le;\mathrm{\&xi;}<0\\ g\left(2\mathrm{\&xi;}\right)& 0\&le;\mathrm{\&xi;}<-1\\ 0& \end{array}\right.---(1-5)$

2. on the basis of basis function

, make up the adaptive shear wave basis function:

2a) with reference to Fig. 2, at the shearing wave basis function The basis on, it is carried out function divides, it is divided into three parts [0.86 ,-0.06], (0.06,0.14), [0.14,0.94] is used three function f respectively to the function in these three intervals ₂, f ₁, f ₃Represent;

2b) given auto-adaptive parameter a, and make its span for (0 ,+∞); With [0.86 ,-0.06] of above-mentioned division, (0.06; 0.14); [0.14,0.94] three intervals, structure adaptive shear wave basis function

$s{\widehat{\mathrm{\&psi;}}}_2\left(\mathrm{\&xi;}\right)=\left\{\begin{array}{cc}{\widehat{\mathrm{\&psi;}}}_2\left(\frac{4+a}{5}(\mathrm{\&xi;}-\frac{7}{10}\&times;\frac{(a-1)}{4+a}\right)& \frac{5a}{4+a}\&times;0.14\&le;\mathrm{\&xi;}\&le;1-\frac{5a}{4+a}\&times;0.06\\ 1& -0.06\&times;\frac{5a}{4+a}<\mathrm{\&xi;}<0.14\&times;\frac{5a}{4+a}\\ {\widehat{\mathrm{\&psi;}}}_2\left(\frac{4+a}{5}(\mathrm{\&xi;}+\frac{3}{10}\&times;\frac{(a-1)}{4+a}\right)& -(1-\frac{5a}{4+a}\&times;0.14)\&le;\mathrm{\&xi;}\&le;-\frac{5a}{4+a}\&times;0.06\end{array}\right.---\left(2\right)$

The shape of being somebody's turn to do will satisfy following requirement:

When a → ∞; Its function image very near one high be 1; Be [0.3 between the Support; 0.7] rectangular window; With reference to Fig. 3 (a); When a=1; Whole function

is exactly that original

is with reference to Fig. 3 (b); When a → 0; The supporting zone of center section shortens to zero with unlimited, and the function supporting zone on both sides will expand to maximum, the flat in the middle of such functional image will be similar to and not have; With reference to Fig. 3 (c),

satisfies following formula:

$\underset{l^{\&prime;}=-2^j+1}{\overset{2^j-1}{\mathrm{\&Sigma;}}}s{\widehat{\mathrm{\&psi;}}}_2{\left|(2^{(j-1)}\mathrm{\&xi;}-l^{\&prime;})\right|}^2=1---\left(3\right)$

2c) according to the basis function of adaptive shear wave; Make up adaptive shear wave d=0; 1, j=1,2; 3 ..; M=-j ,-(j-1) ... j-1, j; The structure formula is following:

$\left.\begin{array}{c}{W}_{j,m}^{\left(0\right)}\left(\mathrm{\&xi;}\right)=s{\widehat{\mathrm{\&psi;}}}_2(j\frac{{\mathrm{\&xi;}}_2}{{\mathrm{\&xi;}}_1}-m){\mathrm{\&chi;}}_{D_0}\\ W_{j,m}^{\left(1\right)}\left(\mathrm{\&xi;}\right)=s{\widehat{\mathrm{\&psi;}}}_2(j\frac{{\mathrm{\&xi;}}_1}{{\mathrm{\&xi;}}_2}-m){\mathrm{\&chi;}}_{D_1}\end{array}\right\}$

Be defined as: ${\mathrm{\&chi;}}_{D_d}({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)=\left\{\begin{array}{cc}1& ({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)\&Element;D_d\\ 0& ({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)\&NotElement;D_d\end{array}\right.,$

D _dBe defined as:

D _dRegion representation with reference to Fig. 4

Wherein

representes two-dimentional set of real numbers

2d) to adaptive shear wave

Again planning obtains W _{J, l}(l=1,2 ... .4j) planning of planning is regular as follows again:

$W_{j,1}=W_{j,-j}^{\left(0\right)}+W_{j,-j}^{\left(1\right)},$ $W_{j,4j}=W_{j,j}^{\left(0\right)}+W_{j,j}^{\left(1\right)},$ $W_{j,n}=W_{j,n-L}^{\left(0\right)},$ $W_{j,n+2j-1}=W_{j,n-L}^{\left(1\right)}$

N=2 wherein, 2 ... .2j, l=1,2 ... 4j; L=[2j+1], [2j+1] expression rounds 2j+1

2e) according to the adaptive shear wave W that constructs _{J, l},, and it is inserted the auto-adaptive parameter a value of setting

Step 3, utilize the adaptive shear wave after the auto-adaptive parameter a value, detail pictures D1 and D2 are carried out threshold denoising, obtain the detail pictures rD1 and the rD2 of reconstruct.

(3a) to D1, D2 carries out DFT DFT respectively, obtains the frequency spectrum DFT (D1) of the details behind the DFT, DFT (D2);

(3b) with DFT (D1) with the four directions to shearing wave W _{J, l}(j=1) carry out dot product, in like manner use DFT (D2) with from all directions to W _{J, l}(j=2) carry out dot product, obtain four matrix of coefficients f respectively _{1, l}(l=1,2,3,4) and eight matrix of coefficients f _{2, l}(l=1,2,3.......8);

(3c) to the top matrix of coefficients f that obtains _{J, l}Carry out the hard-threshold denoising, make threshold value

Wherein,

Be coefficient of correspondence matrix f _{J, l}Variance,

Be coefficient of correspondence matrix f _{J, l}The Noise Estimation variance, noise variance

Estimate that with DSMC DSMC obtains

Wherein E () expression asks expectation, δ to represent that noise criteria is poor; The selection of threshold rule is: for matrix of coefficients f _{J, l}The absolute value of element is more than or equal to τ _{J, l}The reservation initial value, for matrix of coefficients f _{J, l}The absolute value of element is less than τ _{J, l}Zero setting, so just removed matrix of coefficients f _{J, l}The noise at contained most of non-edge;

(3d) matrix of coefficients after the denoising is carried out discrete Fourier transformation DFT, obtain DFT (f _{J, l}), making F _{J, l}=W _{I, l}* DFT (f _{J, l}) adaptive shear wave of answering; Again to F _{J, l}Inverse discrete Fourier transform IDFT; Then with the IDFT (F of eight directions of j=2 _{2, l}) addition, obtain outermost details reconstructed image rD1, with the IDFT (F of the four direction of j=1 _{1, l}), obtain time outer field details reconstructed image rD2.

Step 4, the detail pictures rD1 that reconstruct is obtained, rD2 in conjunction with approximate image A, descends the laplacian pyramid reconstruct method of 2 samplings, obtains the image after reconstructed image and the denoising.

Effect of the present invention can further specify through following emulation:

1, simulated conditions

With one 256 * 256 natural image lena_256.bmp, three 512 * 512 natural image lena512.bmp, barbara512.bmp, flower.bmp move under matalab7.01.

2, emulation content

A. be that 256 * 256 natural image lena_256.bmp is decomposed into three layers with the laplacian pyramid method: two-layer detail pictures D1, D2, one deck approximate image A to the described size of front simulated conditions; Take from adaptation parameter a=0.1 respectively, 0.2,0,5,1,2,5,10 adaptive shear wave decomposes, and obtains the matrix of coefficients f of each layer _{J, l}, count each matrix of coefficients f _{J, l}Histogrammic maximal value of coefficient and steepness, statistics such as table 1.

Table 1 auto-adaptive parameter is got the coefficient histogram maximal value and the steepness of different value

In the table 1; A is an auto-adaptive parameter, and it presses the value of table one respectively, and the two big indexs of the coefficient histogram that comes out being weighed the sparse degree of matrix of coefficients come out respectively; Wherein 4-1 representes the matrix of coefficients of a direction in the outermost layer four direction; 8-1 representes time the matrix of coefficients of first direction of outer eight directions, 4-2 in like manner ... ... ..8-8.

B. be 512 * 512 natural image lena512.bmp to described three width of cloth sizes of simulated conditions, barbara512.bmp, flower.bmp add that standard deviation δ is respectively 15; 20; 25,30 white Gaussian noise, given auto-adaptive parameter a=1 earlier; Then respectively they are carried out the laplacian pyramid decomposition based on following 2 samplings of adaptive shear wave, obtain noisy matrix of coefficients f _{J, l}Again noisy matrix of coefficients is carried out threshold value The hard-threshold denoising; Carry out each levels of detail reconstruct and the laplacian pyramid reconstruct of 2 samplings down again, obtain reconstructed image; In to reconstructed image, minus element all is changed to 0, the element greater than 255 all is changed to 255, and the integer that again other element is rounded up obtains the image after the denoising; Constantly adjust auto-adaptive parameter at last; Obtain better denoising result; As shown in table 2 and Fig. 5, wherein (5a) is the topography of original image, (5b) for the lena512.bmp image being added the topography that standard deviation is 20 white Gaussian noise; The denoising result of (5c) fitting certainly for existing shearing wave (5d) is the partial result of adaptive shear wave.

The comparison diagram of the Y-PSNR (PSNR) of the various conversion threshold denoisings of table 2

3, analysis of simulation result

Can observe out from table 1, the common law that these values showed of emulation experiment A is exactly: the high peak that the coefficient histogram is appeared, long streaking.The value of auto-adaptive parameter is remaining high this sparse advantage of matrix of coefficients, has also just proved the rationality that adaptive shear wave exists.

Can find out that from table 2 emulation experiment B, just can obtain no less than the denoising result with existing shearing wave as long as parameter a gets rational value for pictures different.Can observe out with (5d) contrast from (5c), adaptive shear wave than existing shearing wave denoising to the details of image keep with noise smoothly better.

Claims (2)

1. the image de-noising method based on adaptive shear wave comprises the steps:

(1) descend the laplacian pyramid of 2 samplings to decompose for noisy image, obtain detail pictures D1 and D2, and approximate image A;

(2) structure adaptive shear wave:

2a) at existing shearing wave basis function

Basic enterprising line function divide, it is divided into [0.86 ,-0.06], (0.06,0.14), [0.14,0.94] three intervals are used function f respectively to the function in these three intervals ₂, f ₁, f ₃Expression, and given qualification is interval;

2b) set a parameter a, be defined as auto-adaptive parameter, and make that its span is (0; + ∞), with [0.86 ,-0.06] of above-mentioned division; (0.06,0.14), [0.14; 0.94] three intervals, structure adaptive shear wave basis function

$s{\widehat{\mathrm{\&psi;}}}_2\left(\mathrm{\&xi;}\right)=\left\{\begin{array}{cc}{\widehat{\mathrm{\&psi;}}}_2\left(\frac{4+a}{5}(\mathrm{\&xi;}-\frac{7}{10}\&times;\frac{(a-1)}{4+a}\right)& \frac{5a}{4+a}\&times;0.14\&le;\mathrm{\&xi;}\&le;1-\frac{5a}{4+a}\&times;0.06\\ 1& -0.06\&times;\frac{5a}{4+a}<\mathrm{\&xi;}<0.14\&times;\frac{5a}{4+a}\\ {\widehat{\mathrm{\&psi;}}}_2\left(\frac{4+a}{5}(\mathrm{\&xi;}+\frac{3}{10}\&times;\frac{(a-1)}{4+a}\right)& -(1-\frac{5a}{4+a}\&times;0.14)\&le;\mathrm{\&xi;}\&le;-\frac{5a}{4+a}\&times;0.06\end{array}\right.$

Wherein ξ is an argument of function,

be existing shearing wave basis function;

This basis function

satisfies following formula:

$\underset{l^{\&prime;}=-2^j+1}{\overset{2^j-1}{\mathrm{\&Sigma;}}}s{\widehat{\mathrm{\&psi;}}}_2{\left|(2^{(j-1)}\mathrm{\&xi;}-l^{\&prime;})\right|}^2=1$

Wherein j is a scale parameter, and its conversion has determined the basis function yardstick, and l ' is a translation parameters, and it is big more, and the more past positive axis of basis function moves;

2c) according to the basis function of adaptive shear wave; Make up adaptive shear wave

d=0; 1, j=1,2; 3 ..; M=-j ,-(j-1) ... j-1, j; The structure formula is following:

$\left.\begin{array}{c}{W}_{j,m}^{\left(0\right)}\left(\mathrm{\&xi;}\right)=s{\widehat{\mathrm{\&psi;}}}_2(j\frac{{\mathrm{\&xi;}}_2}{{\mathrm{\&xi;}}_1}-m){\mathrm{\&chi;}}_{D_0}\\ W_{j,m}^{\left(1\right)}\left(\mathrm{\&xi;}\right)=s{\widehat{\mathrm{\&psi;}}}_2(j\frac{{\mathrm{\&xi;}}_1}{{\mathrm{\&xi;}}_2}-m){\mathrm{\&chi;}}_{D_1}\end{array}\right\}$

Be defined as: ${\mathrm{\&chi;}}_{D_d}({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)=\left\{\begin{array}{cc}1& ({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)\&Element;D_d\\ 0& ({\mathrm{\&xi;}}_1,{\mathrm{\&xi;}}_2)\&NotElement;D_d\end{array}\right.,$

D _dBe defined as:

Wherein

representes two-dimentional set of real numbers

2d) right again

Press: $W_{j,1}=W_{j,-j}^{\left(0\right)}+W_{j,-j}^{\left(1\right)},W_{j,4j}=W_{j,j}^{\left(0\right)}+W_{j,j}^{\left(1\right)},W_{j,n}=W_{j,n-L}^{\left(0\right)},$ $W_{j,n+2j-1}=W_{j,n-L}^{\left(1\right)}$ Again be planned to W _{J, l},

L=1 wherein, 2 ... 4j; N=2,3 ... .2j;

L=[2j+1], [2j+1] expression to 2j+1 get round up whole;

J is the integer more than or equal to 1; M gets-and j is to the integer of j,

2e) according to the adaptive shear wave W that constructs _{J, l},, and it is inserted the auto-adaptive parameter a value of setting

(3) utilize adaptive shear wave after the auto-adaptive parameter a value, as follows detail pictures D1 and D2 carried out denoising, obtain the detail pictures rD1 and the rD2 of reconstruct:

3a) to detail pictures D1, D2 carries out DFT respectively, obtains detail pictures frequency spectrum DFT (D1) and DFT (D2) behind the DFT;

3b) with the adaptive shear wave W of DFT (D1) with four direction _{J, l}, j=1 carries out dot product, carries out contrary DFT IDFT again, obtains four matrix of coefficients f respectively _{1, l}, l=1,2,3,4, in like manner DFT (D2) with from all directions to W _{J, l}, j=2 carries out dot product, carries out inverse discrete Fourier transform again, obtains eight matrix of coefficients f _{2, l}, l=1,2,3.......8;

3c) to the top matrix of coefficients f that obtains _{J, l}Carry out hard-threshold τ _{J, l}Choose, selection of threshold is used threshold value

Wherein,

Be coefficient of correspondence matrix f _{J, l}Variance,

Be coefficient of correspondence matrix f _{J, l}The Noise Estimation variance, the Noise Estimation variance

Use Monte Carlo method

estimates; Wherein E () expression asks expectation, δ to represent that noise criteria is poor;

3d) with the threshold tau of choosing _{J, l}To matrix of coefficients f _{J, l}Carry out denoising;

3e) to the matrix of coefficients f behind the threshold denoising _{J, l}Carry out each layer reconstruct, obtain the detail pictures rD1 and the rD2 of reconstruct;

(4) the detail pictures rD1 that pairing approximation image A and reconstruct obtain, reconstruct is carried out in the rD2 utilization laplacian pyramid restructing algorithm of 2 samplings down, obtains reconstructed image.

2. method according to claim 1, wherein step 3d) threshold tau chosen of described usefulness _{J, l}To matrix of coefficients f _{J, l}Carrying out denoising, is to use f _{J, l}The absolute value of element and the threshold tau of choosing _{J, l}Compare, if matrix of coefficients f _{J, l}The absolute value of element is more than or equal to τ _{J, l}, then this element is retained, if matrix of coefficients f _{J, l}The absolute value of element is less than τ _{J, l}, then with this element zero setting, to remove matrix of coefficients f _{J, l}Contained noise.

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