CN102890820A - Image denoising method based on shearlet transformation and Wiener filtering - Google Patents

Abstract

The invention discloses an image denoising method based on shearlet transformation and Wiener filtering. The method comprises the following steps of: (1) source image input; (2) symmetric extension; (3) shear transformation; (4) wavelet packet decomposition; (5) Wiener filtering; (6) inverse wavelet packet transformation; (7) inverse shear transformation; (8) inverse symmetry transformation; (9) image fusion; and (10) denoised image output. By the image denoising method, the defect that the anisotropic information of an image cannot be expressed very well by the wavelet transformation in the prior art is overcome; the problem that a denoising effect is non-ideal because coefficients are subjected to the same processing in different directions by using a single threshold is solved; the advantages that the shearlet transformation has multi-directionality, the output of a filter can be adjusted by the Wiener filtering according to the regional variance of the image and the like are utilized; and therefore, detailed information of the image can be analyzed more accurately in high-frequency coefficients in different directions of the image. Finally, a high-quality denoised image is obtained.

Description

Image de-noising method based on shearlet conversion and Wiener filtering

Technical field

The invention belongs to technical field of image processing, further relate in the image preprocessing technical field image de-noising method based on shearlet conversion and Wiener filtering.Can be applicable to contain the optics gray level image denoising of white Gaussian noise, to obtain to have the more clearly image of high s/n ratio.The present invention is applied to can effectively reduce in graphical analysis, the image pre-service noise in the image, especially for the image that contains Gaussian noise, can obtain better denoising effect, more can satisfy people's visual psychology and the requirement of practical application.

Background technology

In the image preprocessing technical field, in order to remove the white Gaussian noise that contains in the original image, obtaining the picture rich in detail of high-quality, high s/n ratio, and for providing advantage, post processing of image adopts the method for image denoising.At present image de-noising method mainly adopts based on the Threshold Denoising Method of wavelet transformation with based on the methods such as Wiener filtering denoising of wavelet transformation and realizes image denoising.

The patented technology that University of Electronic Science and Technology has " a kind of method for de-noising dual-tree complex wavelet image based on partial differential equation " (publication number: CN101777179A, authorize day: on 02 15th, 2012, applying date: on 02 05th, 2010) in a kind of method for de-noising dual-tree complex wavelet image based on partial differential equation is disclosed.The method is at first carried out the dual-tree complex wavelet transform decomposition to the noisy image of input, and two low frequency sub-band images after decomposing are carried out isotropic diffusion; The adaptive model of design improvement again, calculate dual-tree complex wavelet transform mould and the gradient-norm of high frequency detail subbands image on each direction, utilize two weighted means of setting WAVELET TRANSFORM MODULUS and gradient-norm to design a kind of adaptive coefficient of diffusion function and improve the P-M model; Then improved adaptive model discretize is processed, and six high-frequency sub-band images are carried out the anisotropy diffusion; Carry out at last the dual-tree complex wavelet inverse transformation, the image after the output denoising.Although the method has the ability of distinguishing preferably noise and signal, still the shortcoming of existence is, dual-tree complex wavelet transform lacks translation invariance, and distortion appears in image after the denoising that causes obtaining, and main manifestations is ringing effect and pseudo-Gibbs effect.The method does not consider that when denoising therefore noise can not reach good denoising effect to the difference of image disruption degree on the different scale of wavelet decomposition in addition.

The people such as Tian Pei have proposed the image de-noising method based on wavelet transformation and Wiener filtering in document " Tian Pei, Li Qingzhou, Ma Ping; Niu Yuguang, ' a kind of image denoising new method based on wavelet transformation ' [J], Chinese graphics image journal; 13 (3), 395-399 (2008) ".The method is at first carried out wavelet transformation to image; Then the different characteristics that exists between the wavelet coefficient according to the wavelet coefficient of Gaussian noise and image is carried out Wiener filtering to the wavelet coefficient on the different scale different directions; At last filtered wavelet coefficient is carried out inverse wavelet transform, obtain image after the denoising.Make an uproar than (PSNR) although the method can improve the peak value of image, and can keep more image detail information.But the shortcoming that still exists is that wavelet transformation can not well be expressed the anisotropic detailed information in the image, therefore can not remove well the noise that contains in the anisotropic image.

In sum, although obtaining preferably effect aspect the image denoising based on the image de-noising method of wavelet transformation.But wavelet transformation can not well be expressed the anisotropy information of image, such as the marginal information in the digital image and line feature information, so after the denoising that the denoising method of utilizing based on wavelet transformation obtains in the image, the inevitable blooming that occurs to a certain degree on the edge in the image and the details position.

Summary of the invention

The objective of the invention is the shortcoming of the undesirable and image fault of the image denoising effect that causes based on the image de-noising method of wavelet transformation for prior art, proposed the image de-noising method based on shearlet conversion and Wiener filtering.In the present invention the decomposition principle based on the shearlet conversion of image have been comprised symmetric extension, three parts of shear transformation and WAVELET PACKET DECOMPOSITION.The present invention takes full advantage of shearlet transfer pair image and decomposes the advantage that the coefficient of dissociation that obtains can better show the detailed information of image, utilize simultaneously Wiener filtering can better remove the characteristics of white Gaussian noise, shearlet conversion and Wiener filtering are combined to carry out image denoising.Image can suppress noise effectively after the denoising that finally obtains, and can keep again the more detailed information of image.

The concrete steps that the present invention realizes are as follows:

(1) input source image

In computing machine, use matlab software and read the source images that is stored in the hard disc of computer space.

(2) symmetric extension

2a) source images is carried out horizontal symmetrical expansion, a certain in two vertical edges boundary lines of image as axis of symmetry, with the another side of image mapped to axis of symmetry, obtains the horizontal extension image by the horizontal extension formula;

2b) source images is carried out vertical symmetry expansion, a certain in two horizontal sides boundary lines of image as axis of symmetry, with the another side of image mapped to axis of symmetry, obtains the extends perpendicular image by the extends perpendicular formula.

(3) shear transformation

Image after the expansion that obtains in the step (2) is carried out shear transformation by the shear transformation formula, and deposit the image behind the shear transformation in calculator memory.

(4) WAVELET PACKET DECOMPOSITION

Utilize the discrete wavelet packet disassembling tool respectively image behind the shear transformation to be carried out the multiple dimensioned decomposition of wavelet packet, low frequency coefficient and high frequency coefficient after obtaining decomposing deposit calculator memory in.

(5) Wiener filtering

5a) all high frequency coefficients in the read step (4);

5b) utilize the S filter instrument to step 5a) in the high frequency coefficient that reads carry out Wiener filtering and process, obtain filtered high frequency coefficient, deposit filtered high frequency coefficient in calculator memory.

(6) contrary wavelet package transforms

Utilize contrary wavelet package transforms instrument to step 5b) in the low frequency coefficient of the correspondence that obtains in the filtered high frequency coefficient that obtains and the step (4) carry out contrary wavelet package transforms, obtain the image behind the contrary wavelet package transforms, and deposit calculator memory in.

(7) contrary shear transformation

Image behind the contrary wavelet package transforms that obtains in the step (6) is carried out contrary shear transformation by contrary shear transformation formula, and image deposits calculator memory in behind the contrary shear transformation that will obtain.

(8) contrary symmetric extension

The image that obtains in the step (7) is carried out the contrary symmetric extension of level and vertical against symmetric extension by the contrary symmetric extension formula of level and vertical contrary symmetric extension formula respectively, obtain against expanding rear image.

(9) image co-registration

Image after the contrary expansion of step (8) is carried out image co-registration by the data average formula, obtain the image after the denoising.

(10) result images after the output denoising.

Compared with prior art, the present invention has the following advantages:

First, the present invention exploded view as the time, use shearlet transfer pair image and carry out multiple dimensioned decomposition, because the shearlet conversion has a multidirectional, thereby can obtain high-frequency information and the low-frequency information of Noise image in a plurality of directions, in order to effectively catch image detail.Overcome the shortcoming of the anisotropy information that wavelet transformation in the prior art can not fine expression image, so that use the detailed information of the Noise image that the method among the present invention obtains to be analyzed more accurately.

The second, the present invention has used the method for Wiener filtering when the high frequency coefficient after the noisy picture breakdown being carried out the filtering processing.Because Wiener filtering can be adjusted according to the Local Deviation of image the output of wave filter, carry out region adaptivity filtering with the high frequency coefficient to the Noise image and process.Overcome that Threshold Denoising Method of the prior art carries out identical processing to the coefficient on the different scale different directions and the undesirable problem of denoising effect that causes, white Gaussian noise can better be suppressed in the high frequency coefficient of the Noise image that the method among the present invention obtains so that use.

Description of drawings

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

Fig. 2 is that the present invention is used for carried out the analogous diagram of denoising by the noisy image of noise slight pollution;

Fig. 3 is that the present invention is used for carried out the analogous diagram of denoising by the noisy image of noise severe contamination.

Embodiment

With reference to Fig. 1, the specific embodiment of the invention is as follows:

Step 1, the input source image

In computing machine, use matlab software and read the source images that is stored in the hard disc of computer space.

Step 2, symmetric extension

For fear of the boundary effect that may occur in the denoising process through the image behind the shear transformation, the present invention is to carrying out symmetric extension in horizontal and vertical directions respectively to source images first.

2a) source images is carried out horizontal symmetrical expansion, a certain in two vertical edges boundary lines of image as axis of symmetry, with the another side of image mapped to axis of symmetry, obtains the horizontal extension image by the horizontal extension formula;

Wherein, f (i, j) be source images at the gray-scale value of coordinate (i, j) position, n is the columns of the pixel of source images, f _h(i, j) is that the horizontal extension image is at the gray-scale value of coordinate (i, j) position;

2b) source images is carried out vertical symmetry expansion, a certain in two horizontal sides boundary lines of image as axis of symmetry, with the another side of image mapped to axis of symmetry, obtains the extends perpendicular image by the extends perpendicular formula;

Wherein, f (i, j) be source images at the gray-scale value of coordinate (i, j) position, m is the line number of the pixel of source images, f (i, j) is that the horizontal extension image is at the gray-scale value of coordinate (i, j) position.

Step 3, shear transformation

Carry out shear transformation to expanding rear image by the shear transformation formula, and deposit the image behind the shear transformation in calculator memory;

If

If

Wherein, x ', y ' are coordinate corresponding to image pixel behind the shear transformation, and x, y are coordinate corresponding to image pixel behind the symmetric extension, k ∈ [2 ^(ndir), 2 ^(ndir)], k ∈ Z, ndir are direction parameter, ndir=0,1 or 2, s shear matrix, f ' (x ', y ') be behind the shear transformation image coordinate (x ', y ') grey scale pixel value of position, f (x, y) is the gray-scale value of transform expansion image in coordinate (x, y) position.

Step 4, WAVELET PACKET DECOMPOSITION

Utilize the discrete wavelet packet disassembling tool respectively image behind the shear transformation to be carried out three layers of multiple dimensioned decomposition of wavelet packet, low frequency coefficient and high frequency coefficient after obtaining decomposing deposit calculator memory in;

4a) with the low-pass filter in the image input WAVELET PACKET DECOMPOSITION instrument behind the shear transformation, obtain one deck low frequency coefficient I of WAVELET PACKET DECOMPOSITION through filtering _L1

4b) with the Hi-pass filter in the image input WAVELET PACKET DECOMPOSITION instrument behind the shear transformation, obtain one deck high frequency coefficient I of WAVELET PACKET DECOMPOSITION through filtering _H1

One deck low frequency coefficient I that 4c) WAVELET PACKET DECOMPOSITION is obtained _L1Input the low-pass filter in the WAVELET PACKET DECOMPOSITION instrument, obtain two layers of low frequency coefficient I of WAVELET PACKET DECOMPOSITION through filtering _L2

One deck low frequency coefficient I that 4d) WAVELET PACKET DECOMPOSITION is obtained _L1Input the Hi-pass filter in the WAVELET PACKET DECOMPOSITION instrument, obtain the two floor heights frequency coefficient I of WAVELET PACKET DECOMPOSITION through filtering _H2

Two layers of low frequency coefficient I that 4e) WAVELET PACKET DECOMPOSITION obtained _L2Input the low-pass filter in the WAVELET PACKET DECOMPOSITION instrument, obtain three layers of low frequency coefficient I of WAVELET PACKET DECOMPOSITION through filtering _L3

Two layers of low frequency coefficient I that 4f) WAVELET PACKET DECOMPOSITION obtained _L2Input the Hi-pass filter in the WAVELET PACKET DECOMPOSITION instrument, obtain the three floor heights frequency coefficient I of WAVELET PACKET DECOMPOSITION through filtering _H3

Step 5, Wiener filtering

5a) read WAVELET PACKET DECOMPOSITION and obtain all high frequency coefficients;

5b) utilize the S filter instrument that the high frequency coefficient that reads is carried out Wiener filtering and process, obtain filtered high frequency coefficient, the window size of S filter selects 5 * 5, then deposits filtered high frequency coefficient in calculator memory.

Step 6, contrary wavelet package transforms

Utilize contrary wavelet package transforms instrument to step 5b) in the low frequency coefficient of the correspondence that obtains in the filtered high frequency coefficient that obtains and the step 4 carry out contrary wavelet package transforms, obtain the image f " (x " behind the contrary wavelet package transforms, y "), and deposit calculator memory in.

Step 7, contrary shear transformation

Image behind the contrary wavelet package transforms that obtains in the step (6) is carried out contrary shear transformation by contrary shear transformation formula, and image deposits calculator memory in behind the contrary shear transformation that will obtain;

If

If

Wherein, x _i", y _i" be coordinate corresponding to image pixel behind the contrary shear transformation, subscript i represents the inverse transformation of shear transformation, x ", y " be coordinate corresponding to image pixel, k ∈ [2 ^(ndir), 2 ^(ndir)], k ∈ Z, superscript ndir are direction parameter, ndir=0,1 or 2, s ' be the contrary matrix of shearing, f " (x ", y ") be the front image of contrary shear transformation (x ", the gray-scale value of y ") position, f _i" (x _i", y _i") be behind the contrary shear transformation image at (x _i", y _iThe gray-scale value of ") position.

Step 8, contrary symmetric extension

The image that obtains in the step (7) is carried out the contrary symmetric extension of level and vertical against symmetric extension by the contrary symmetric extension formula of level and vertical contrary symmetric extension formula respectively, obtain against expanding rear image;

The contrary symmetric extension formula of level is as follows:

$f(i,j)=\frac{f(i,j)+f(i,2n-j)}{2},(1\≤i\≤m,1\≤j\≤n)$

Wherein, f (i, j) be image pixel behind the contrary symmetric extension of level at the locational gray-scale value of coordinate (i, j), m and n are respectively line number and the columns of source images.

Vertical contrary symmetric extension formula is as follows:

$f(i,j)=\frac{f(i,j)+f(2m-i,j)}{2},(1\≤i\≤m,1\≤j\≤n)$

Wherein, f (i, j) be image pixel behind the vertical contrary symmetric extension at the locational gray-scale value of coordinate (i, j), m and n are respectively line number and the columns of source images.

Step 9, image co-registration

Image after the contrary expansion of step (8) is carried out image co-registration by the data average formula, obtain the image after the denoising;

$F(i,j)=\frac{\underset{p=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}{f}_p(i,j)}{\mathrm{num}}$

Wherein, F (i, j) is the gray-scale value of image after the denoising in coordinate (i, j) position, and num is the number of the image after the contrary expansion, f _p(i, j) is that p contrary expanded images is at the gray-scale value of coordinate (i, j) position.

Step 10, the result images after the output denoising.

Effect of the present invention can further specify by following emulation.

Emulation 1, among the present invention by the emulation of the noisy image denoising of noise slight pollution.

Emulation 1 simulated conditions is to carry out under MATLAB7.0 software.

With reference to Fig. 2, to Lena image commonly used, size is 512 * 512 pixels, and 256 grades of gray level images carry out emulation experiment.Fig. 2 (a) is original clearly Lena image; Fig. 2 (b) is that containing noise criteria poor is 50 Lena image; Fig. 2 (c) is based on the denoising result of the inventive method; Fig. 2 (d) is based on the result of the Wiener filtering denoising of Contourlet conversion; Fig. 2 (e) is based on the result of the Wiener filtering denoising of wavelet transformation.

Can find out from Fig. 2 (e), after the denoising that obtains based on the Wiener filtering denoising method (WTWN) of wavelet transformation missing image the Partial Feature of image, and image is smooth-out after the denoising, causes image fault.Can clearly find out from Fig. 2 (d),, descend to some extent on the subjective quality assessment of image although image can keep the marginal information of image preferably after the denoising that obtains based on the Wiener filtering denoising method (CTWN) of Contourlet conversion.And can find out clearly that from Fig. 2 (c) denoising method (STWN) that the present invention proposes can obtain preferably denoising effect, and not only effectively suppressed noise, improve signal noise ratio (snr) of image; And the detailed information that has well kept image.The following evaluating of denoising image calculation that respectively top three kinds of methods is obtained: Y-PSNR (PSNR), final data is as shown in table 1.

PSNR value after table 1CTWN, STWN and the inventive method denoising

σ	noisy	WTWN	CTWN	STWN
					10	28.1179	34.7788	33.9715	35.167
20	22.1020	30.8331	30.6299	31.8370
					30	18.5790	28.3909	28.9229	30.108
40	16.0851	26.5236	27.8225	28.964
					50	14.1275	25.0222	26.8859	28.004
60	12.5705	23.6963	26.2903	27.356

Can find out that from the objective evaluation measured value of table 1 the present invention is better than existing other all algorithms, Y-PSNR is the highest, shows that the present invention can obtain better denoising effect, and image is more clear after the denoising, has higher PSRN.

Emulation 2, among the present invention by the emulation of the noisy image denoising of noise severe contamination.

Emulation 2 simulated conditions are to carry out under MATLAB7.0 software.

With reference to Fig. 3, to Lena image commonly used, size is 512 * 512 pixels, and 256 grades of gray level images carry out emulation experiment.Fig. 3 (a) is original clearly Lena image; Fig. 3 (b) is that containing noise criteria poor is 100 Lena image; Fig. 3 (c) is based on the denoising result of the inventive method; Fig. 3 (d) is based on the result of hard-threshold (STTD) denoising of shearlet conversion.

From passable the finding out of Fig. 3 (d), based on the hard-threshold denoising method (STTD) of shearlet conversion although denoising after image can keep preferably the local features such as image border, ring, pseudo-Gibbs vision distortion phenomenon appear.And can find out that from Fig. 3 (c) denoising method (STWN) that the present invention proposes not only can suppress noise effectively, and better stayed the detailed information of image.The following evaluating of denoising image calculation that respectively top two kinds of methods is obtained: Y-PSNR (PSNR), final data is as shown in table 2.

PSNR value after table 2STTD and the inventive method denoising

σ	noisy	STTD	STWN
				40	16.1080	28.7026	28.9138
50	14.1409	27.5368	28.0370
				60	12.5616	26.6703	27.3638
70	11.2193	25.8510	26.7635
				80	10.0596	25.2345	26.3891
90	9.0459	24.6395	25.9372
				100	8.1363	24.1178	25.5594
150	4.6131	21.9662	24.2220
				200	2.1085	20.2769	23.2871
250	0.1905	19.1194	22.6823

Can find out from the objective evaluation measured value of table 2, the present invention is better than the hard-threshold denoising method based on the shearlet conversion, the PSNR of image and edge hold facility have more advantage than the hard-threshold denoising based on the shearlet conversion after denoising, and can find out that this advantage is more and more obvious along with image contains the poor increase of noise criteria.By the PSNR value of two kinds of distinct methods acquisitions in the difference comparison sheet 2 and the denoising effect figure of two kinds of distinct methods among Fig. 3, we can draw the present invention can obtain better denoising effect, obtains higher PSRN, better keeps the information of image.

Claims (10)

1. image de-noising method based on shearlet conversion and Wiener filtering, concrete operation step is as follows:

(1) input source image

In computing machine, use matlab software and read the source images that is stored in the hard disc of computer space;

(2) symmetric extension

2a) source images is carried out horizontal symmetrical expansion, a certain in two vertical edges boundary lines of image as axis of symmetry, with the another side of image mapped to axis of symmetry, obtains the horizontal extension image by the horizontal extension formula;

2b) source images is carried out vertical symmetry expansion, a certain in two horizontal sides boundary lines of image as axis of symmetry, with the another side of image mapped to axis of symmetry, obtains the extends perpendicular image by the extends perpendicular formula;

(3) shear transformation

Image after the expansion that obtains in the step (2) is carried out shear transformation by the shear transformation formula, and deposit the image behind the shear transformation in calculator memory;

(4) WAVELET PACKET DECOMPOSITION

Utilize the discrete wavelet packet disassembling tool respectively image behind the shear transformation to be carried out the multiple dimensioned decomposition of wavelet packet, low frequency coefficient and high frequency coefficient after obtaining decomposing deposit calculator memory in;

(5) Wiener filtering

5a) all high frequency coefficients in the read step (4);

5b) utilize the S filter instrument to step 5a) in the high frequency coefficient that reads carry out Wiener filtering and process, obtain filtered high frequency coefficient, deposit filtered high frequency coefficient in calculator memory;

(6) contrary wavelet package transforms

Utilize contrary wavelet package transforms instrument to step 5b) in the low frequency coefficient of the correspondence that obtains in the filtered high frequency coefficient that obtains and the step (4) carry out contrary wavelet package transforms, obtain the image behind the contrary wavelet package transforms, and deposit calculator memory in;

(7) contrary shear transformation

Image behind the contrary wavelet package transforms that obtains in the step (6) is carried out contrary shear transformation by contrary shear transformation formula, and image deposits calculator memory in behind the contrary shear transformation that will obtain;

(8) contrary symmetric extension

The image that obtains in the step (7) is carried out the contrary symmetric extension of level and vertical against symmetric extension by the contrary symmetric extension formula of level and vertical contrary symmetric extension formula respectively, obtain against expanding rear image;

(9) image co-registration

Image after the contrary expansion of step (8) is carried out image co-registration by the data average formula, obtain the image after the denoising;

(10) result images after the output denoising.

2. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1, it is characterized in that: the horizontal symmetrical extends equation step 2a) is as follows:

Wherein, f (i, j) be source images at the gray-scale value of coordinate (i, j) position, n is the columns of the pixel of source images, f _h(i, j) is that the horizontal extension image is at the gray-scale value of coordinate (i, j) position.

3. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1, it is characterized in that: the vertical symmetry extends equation step 2b) is as follows:

Wherein, f (i, j) be source images at the gray-scale value of coordinate (i, j) position, m is the line number of the pixel of source images, f _v(i, j) is that the horizontal extension image is at the gray-scale value of coordinate (i, j) position.

4. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1, it is characterized in that: the shear transformation formula described in the step (3) is as follows:

If

If

Wherein, x ', y ' are coordinate corresponding to image pixel behind the shear transformation, and x, y are coordinate corresponding to image pixel behind the symmetric extension, k ∈ [2 ^(ndir), 2 ^(ndir)], k ∈ Z, ndir are direction parameter, ndir=0,1 or 2, s shear matrix, f ' (x ', y ') be behind the shear transformation image coordinate (x ', y ') grey scale pixel value of position, f (x, y) is the gray-scale value of transform expansion image in coordinate (x, y) position.

5. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1 is characterized in that: the three layers of WAVELET PACKET DECOMPOSITION of WAVELET PACKET DECOMPOSITION employing described in the step (4).

6. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1 is characterized in that: the window size of S filter selection 5 * 5 in the high frequency coefficient Wiener filtering step 5b).

7. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1, it is characterized in that: the contrary shear transformation formula described in the step (7) is as follows:

If

If

Wherein, x _i", y _i" be coordinate corresponding to image pixel behind the contrary shear transformation, subscript i represents the inverse transformation of shear transformation, x ", y " be coordinate corresponding to image pixel, k ∈ [2 ^(ndir), 2 ^(ndir)], k ∈ Z, superscript ndir are direction parameter, ndir=0,1 or 2, s ' be the contrary matrix of shearing, f " (x ", y ") be the front image of contrary shear transformation (x ", the gray-scale value of y ") position, f _i" (x _i", y _i") be behind the contrary shear transformation image at (x _i", y _iThe gray-scale value of ") position.

8. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1 is characterized in that: the contrary symmetric extension formula of the level described in the step (8) is as follows:

$f(i,j)=\frac{f(i,j)+f(i,2n-j)}{2},(1\≤i\≤m,1\≤j\≤n)$

Wherein, f (i, j) be image pixel behind the contrary symmetric extension of level at the locational gray-scale value of coordinate (i, j), m and n are respectively line number and the columns of source images.

9. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1, it is characterized in that: the vertical title extends equation described in the step (8) is as follows:

$f(i,j)=\frac{f(i,j)+f(2m-i,j)}{2},(1\≤i\≤m,1\≤j\≤n)$

Wherein, f (i, j) be image pixel behind the vertical contrary symmetric extension at the locational gray-scale value of coordinate (i, j), m and n are respectively line number and the columns of source images.

10. the image de-noising method based on shearlet conversion and Wiener filtering according to claim 1, it is characterized in that: the data average formula described in the step (9) is as follows:

$F(i,j)=\frac{\underset{p=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}{f}_p(i,j)}{\mathrm{num}}$

Wherein, F (i, j) is the gray-scale value of image after the denoising in coordinate (i, j) position, and num is the number of the image after the contrary expansion, f _p(i, j) is that p contrary expanded images is at the gray-scale value of coordinate (i, j) position.

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