CN105069762A - Image denoising method based on Shearlet transform and non-linear diffusion - Google Patents
Image denoising method based on Shearlet transform and non-linear diffusion Download PDFInfo
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Abstract
The invention discloses an image denoising method based on Shearlet transform and non-linear diffusion. The method includes the steps: firstly, inputting a noised image to an image processor; secondly, carrying out multiple dimensioned Shearlet transform for the noised image by the image processor, obtaining a low-frequency Shearlet transform coefficient and a high-frequency Shearlet transform coefficient, and recording the high-frequency Shearlet transform coefficient as an initial noised Shearlet coefficient; thirdly, continuously using, by the image processor, local Wiener filtering for [lambda] times to perform diffusion denoising for the initial noised Shearlet coefficient; fourthly, conducting signal reconstruction by the image processor, and obtaining a reconstructed image; fifthly, removing false details after the image processor performs non-linear diffusion for the reconstructed image; and sixthly, outputting a denoised image. The steps of the method are simple, and signals and noise can be distinguished quite effectively. Moreover, the detail features of the image are protected while noise is removed, and the image exhibits excellent performance.
Description
Technical field
The invention belongs to technical field of image processing, be specifically related to a kind of based on Shearlet conversion and the image de-noising method of nonlinear diffusion.
Background technology
The life of image and people is closely related, but image can be subject to the interference of various noise in the process of production and transfer, therefore carries out denoising to image, and the master, the objective effect that improve image just seem particularly important.In prior art about the method for image denoising and relative merits as follows:
On 02 05th, 2010, the people such as University of Electronic Science and Technology Liu Jinhua disclosed a kind of method for de-noising dual-tree complex wavelet image based on partial differential equation in the Chinese patent of 201010107623.0; On October 27th, 2014, Liu Jinhua is again disclose a kind of image de-noising method based on dual-tree complex wavelet transform in the Chinese patent of 201410584194.4 at application number, the patent application disclose a kind of image de-noising method based on dual-tree complex wavelet transform and partial differential equation of improvement, the method implements the non-thread diffusion form based on partial differential equation in wavelet field, noise can be removed very well, but dual-tree complex wavelet still lacks enough set directions, which has limited performance room for improvement.
On July 23rd, 2014, Xian Electronics Science and Technology University Wang Gui is graceful waits people to disclose a kind of contour wave domain Wiener Filtering denoising method based on two-dimentional Otsu in the Chinese patent of 201210061837.8, first the method carries out profile Wave Decomposition to noisy image, again two-dimentional Otsu segmentation is carried out to each high-frequency sub-band decomposited, obtain significant coefficient and insignificant coefficient; Calculate the oval window of high-frequency sub-band respectively, according to the signal variance of oval window estimation high-frequency sub-band, respectively Wiener filtering is carried out to significant coefficient and insignificant coefficient; The inverse transformation of profile ripple is carried out to the high-frequency sub-band after denoising, obtains denoising image FI; Non-local mean filtering is carried out to FI, obtains denoising and export.This patent shows, its performance is better than following three kinds of existing methods: one is the two Wiener filtering denoising method of a kind of wavelet field based on self-adapting window being better than proposing in article that X.Li delivered in " IEEEInternationalConferenceonMechatronicsandAutomation (IEEE mechano-electronic robotization international conference) " 114-118 page in 2010 " ImagedenoisingviadoublyWienerfilteringwithadaptivedirect ionalwindowsandmeanshiftalgorithminwaveletdomain (based on adaptive direction window and and the two Wiener Filtering denoising of wavelet field of mean shift algorithm) ", two is a kind of contour wave domain Wiener filtering denoising methods based on self-adapting window being better than proposing in article " Contourlet-basedimagedenoisingalgorithmusingadaptivewind ows (the contour wave domain image denoising with adaptive windows) " that Z.F.Zhou etc. delivered in " IEEEConferenceonIndustrialElectronicsandApplications (IEEE industrial electronic and application meeting) " 3654-3657 page in 2009, three is be better than Q.Zhao etc. in 2010 in " JournalofComputationalInformationSystems, (computing information Systems Journal) " article " the Imagedenoisingbasedonimprovednon-localmeansandnonsubsamp ledcontourlettransformWienerfiltering that delivers of the 6th volume the 2nd phase 601-610 page, (based on the non-local mean of improvement and the Wiener Filtering denoising of non-down sampling contourlet transform) " the middle a kind of non-down sampling contourlet territory Wiener filtering denoising method based on non-local mean proposed.
The effect that " although the contour wave domain Wiener Filtering denoising method based on two-dimentional Otsu " achieves, the method but needs to classify to wavelet coefficient, after implementing Wiener filtering denoising, also needs to carry out non-local mean filtering, implements complicated.
In order to overcome the above problems, the people such as Xian Electronics Science and Technology University seedling Qi Guang at application number be disclose in the Chinese patent of 201210364581.8 a kind of based on Shearlet conversion and the image de-noising method of Wiener filtering, first the method carries out symmetric extension to input source image, then shear transformation is used, then WAVELET PACKET DECOMPOSITION is used, traditional Wiener filtering is used to coefficient of dissociation, reconstructed image is obtained with the coefficient after process, finally carry out symmetry transformation and image co-registration, obtain final denoising image, this process employs Shearlet conversion there is multidirectional and Wiener filtering can according to advantages such as the Local Deviation adjustment wave filter outputs of image, overcome wavelet transformation in prior art and can not express the shortcoming of the anisotropy information of image very well, and the problem that the denoising effect using single threshold value to carry out same treatment to coefficient on different directions and cause is undesirable, thus image detail information can be analyzed more accurately in the high frequency coefficient on the different directions of image, but there is false details in the synthetic image due to Wiener filtering, have impact on the lifting of denoising performance.
Summary of the invention
Technical matters to be solved by this invention is for above-mentioned deficiency of the prior art; there is provided a kind of based on Shearlet conversion and the image de-noising method of nonlinear diffusion; its method step is simple; it is convenient to realize, and very effectively signal and noise difference can be come, and protect the minutia of image while removing noise; function admirable; practical, result of use is good, is convenient to promote the use of.
For solving the problems of the technologies described above, the technical solution used in the present invention is: a kind of based on Shearlet conversion and the image de-noising method of nonlinear diffusion, it is characterized in that the method comprises the following steps:
Step one, by noisy image input picture processor;
Step 2, image processor carry out multiple dimensioned Shearlet conversion to noisy image, obtain low frequency Shearlet coefficient and high frequency Shearlet coefficient, and high frequency Shearlet coefficient is designated as initial noisy Shearlet coefficient;
Step 3, image processor use λ local Wiener filtering to carry out diffusion filtering process to initial noisy Shearlet coefficient continuously; Wherein, λ is natural number and the value of λ is 2 ~ 15;
Step 4, image processor adopt Shearlet inverse transformation to carry out signal reconstruction to low frequency Shearlet coefficient and the initial noisy Shearlet coefficient after the process of step 3 diffusion filtering, obtain reconstructed image;
Step 5, image processor carry out the nonlinear diffusion aftertreatment based on partial differential equation to reconstructed image, remove the false details of reconstructed image;
Image after step 6, output denoising.
The above-mentioned image de-noising method based on Shearlet conversion and nonlinear diffusion, it is characterized in that: in step 2, image processor carries out five layers of multiple dimensioned Shearlet conversion to noisy image, ground floor and second layer two-stage high-frequency sub-band respectively have 16 directions, third layer and the 4th layer of two-stage high-frequency sub-band respectively have 8 directions, and layer 5 is low frequency sub-band.
The above-mentioned image de-noising method based on Shearlet conversion and nonlinear diffusion, it is characterized in that: in step 3, image processor uses λ local Wiener filtering to the detailed process that initial noisy Shearlet coefficient carries out diffusion filtering process to be continuously: using the input signal of initial noisy Shearlet coefficient as first time Wiener filtering, using the input signal of the output signal of current Wiener filtering as Wiener filtering next time; The high frequency Shearlet coefficient that the r time Wiener filtering is recovered at subband position (x, y) place to obtain is designated as z
r(x, y) and z
r(x, y)=W
r(x, y) z
r-1(x, y), wherein, the value of r is the natural number of 1 ~ λ, z
r-1(x, y) high frequency Shearlet coefficient for recovering at subband position (x, y) place to obtain by the r-1 time Wiener filtering, z
0(x, y) is the initial noisy coefficient at subband position (x, y) place, W
r(x, y) be the r time Wiener filtering and
n
r(x, y) is the noise contribution that will remove at subband position (x, y) place,
for n
rthe variance of (x, y) and getting
η is noise variance adjustment parameter and η is real number,
for initial noise variance in subband and
estimated to obtain by Monte-Carlo method; s
r(x, y) is the signal content that will recover at subband position (x, y) place,
for s
rthe variance of (x, y) and
according to formula
Estimation obtains,
for z
r-1the variance of (x, y), δ is s
rthe adjustment parameter of the variance of (x, y), and δ is nonnegative real number, R is constant and is positive integer, l1 and l2 is integer variable and value is-R ~ R, z
r-1(x-l1, y-l2) high frequency Shearlet coefficient for recovering at subband position (x-l1, y-l2) place to obtain by the r-1 time Wiener filtering, z
0(x-l1, y-l2) is the initial noisy coefficient at subband position (x-l1, y-l2) place.
The above-mentioned image de-noising method based on Shearlet conversion and nonlinear diffusion, is characterized in that: the value of η is the real number of 1 ~ 1.5.
The above-mentioned image de-noising method based on Shearlet conversion and nonlinear diffusion, it is characterized in that: the nonlinear diffusion aftertreatment that in step 5, image processor carries out based on partial differential equation to reconstructed image, the detailed process removing the false details of reconstructed image is: suppose that reconstructed image is I, to I partial differential equation
carry out nonlinear diffusion aftertreatment, wherein, div is divergence operator, and t is the moment that partial differential diffusion is evolved, and along with going deep into of diffusion, the value of t increases; I
t(i, j) is the grey scale pixel value at moment t position (i, j) place,
for I
tthe gradient of (i, j), c
t(i, j) for index spread function and
by partial differential equation
discretely to turn to:
Wherein,
for position in the north of (i, j), south, east, west four direction grey scale pixel value, K is Grads threshold and the value of K is 1 ~ 10, I
k(i, j) is the grey scale pixel value after the secondary diffusion filtering of the kth of position at (i, j) place, I
k-1(i, j) is the grey scale pixel value of position after kth-1 diffusion filtering at (i, j) place, I
0(i, j), for position is at the grey scale pixel value of the reconstructed image I at (i, j) place, k is number of iterations and the value of k is positive integer between 1 to 7.
The present invention compared with prior art has the following advantages:
1, method step of the present invention is simple, and it is convenient to realize.
2, compared to existing technology, the present invention can come signal and noise difference very effectively, and protects the minutia of image while removing noise, thus obtains the optimal recovery of original image.
3, the Shearlet that the present invention selects has enough set directions, can well catch the geometric properties of image; In denoising process, not only implement the diffusion atrophy of Wiener filtering based on amendment at Shearlet transform domain, also image is after reconstitution implemented the nonlinear diffusion based on partial differential equation, in order to remove the false details that reconstructed image generates, function admirable.
4, of the present invention practical, result of use is good, is convenient to promote the use of.
In sum, method step of the present invention is simple, and it is convenient to realize, and very effectively signal and noise difference can be come, and protect the minutia of image while removing noise, function admirable, practical, result of use is good, is convenient to promote the use of.
Below by drawings and Examples, technical scheme of the present invention is described in further detail.
Accompanying drawing explanation
Fig. 1 is method flow block diagram of the present invention.
Fig. 2 A is original Barbara image.
Fig. 2 B is noisy Barbara image.
Fig. 2 C is the denoising Barbara image after adopting the process of WWF method.
Fig. 2 D is the denoising Barbara image after adopting the process of GWF method.
Fig. 2 E is the denoising Barbara image after adopting the process of LBS method.
Fig. 2 F is the denoising Barbara image after adopting the process of ProbShrink method.
Fig. 2 G is the denoising Barbara image after adopting the process of UWTSURE-LET method.
Fig. 2 H is the denoising Barbara image after adopting the inventive method process.
Embodiment
As shown in Figure 1, of the present invention based on Shearlet conversion and the image de-noising method of nonlinear diffusion, it is characterized in that the method comprises the following steps:
Step one, by noisy image input picture processor;
Step 2, image processor carry out multiple dimensioned Shearlet conversion to noisy image, obtain low frequency Shearlet coefficient and high frequency Shearlet coefficient, and high frequency Shearlet coefficient is designated as initial noisy Shearlet coefficient;
Step 3, image processor use λ local Wiener filtering to carry out diffusion filtering process to initial noisy Shearlet coefficient continuously; Wherein, λ is natural number and the value of λ is 2 ~ 15;
Step 4, image processor adopt Shearlet inverse transformation to carry out signal reconstruction to low frequency Shearlet coefficient and the initial noisy Shearlet coefficient after the process of step 3 diffusion filtering, obtain reconstructed image;
Step 5, image processor carry out the nonlinear diffusion aftertreatment based on partial differential equation to reconstructed image, remove the false details of reconstructed image;
Image after step 6, output denoising.
In the present embodiment, in step 2, image processor carries out five layers of multiple dimensioned Shearlet conversion to noisy image, ground floor and second layer two-stage high-frequency sub-band respectively have 16 directions, and third layer and the 4th layer of two-stage high-frequency sub-band respectively have 8 directions, and layer 5 is low frequency sub-band.
During concrete enforcement, the Shearlet adopted is transformed to G.R.Easley, D.Labate, the discrete non-lower sampling Shearlet proposed in the article " Sparsedirectionalimagerepresentationsusingthediscreteshe arlettransform (the image orientation rarefaction representation converted based on discrete Shearlet) " that W.Q.Lim delivered in " AppliedandComputationalHarmonicAnalysis (application and calculate frequency analysis) " the 25th volume the 1st phase 25th ~ 46 pages in 2008 converts, the window function selected is " Meyer ", this discrete Shearlet conversion has translation invariance and good directivity, the geometric properties of the more effective seizure image of energy.
In the present embodiment, in step 3, image processor uses λ local Wiener filtering to the detailed process that initial noisy Shearlet coefficient carries out diffusion filtering process to be continuously: using the input signal of initial noisy Shearlet coefficient as first time Wiener filtering, using the input signal of the output signal of current Wiener filtering as Wiener filtering next time; The high frequency Shearlet coefficient that the r time Wiener filtering is recovered at subband position (x, y) place to obtain is designated as z
r(x, y) and z
r(x, y)=W
r(x, y) z
r-1(x, y), wherein, the value of r is the natural number of 1 ~ λ, z
r-1(x, y) high frequency Shearlet coefficient for recovering at subband position (x, y) place to obtain by the r-1 time Wiener filtering, z
0(x, y) is the initial noisy coefficient at subband position (x, y) place, W
r(x, y) be the r time Wiener filtering and
n
r(x, y) is the noise contribution that will remove at subband position (x, y) place,
for n
rthe variance of (x, y) and getting
η is noise variance adjustment parameter and η is real number,
for initial noise variance in subband and
estimated to obtain by Monte-Carlo method; s
r(x, y) is the signal content that will recover at subband position (x, y) place,
for s
rthe variance of (x, y) and
according to formula
Estimation obtains,
for z
r-1the variance of (x, y), δ is s
rthe adjustment parameter of the variance of (x, y), and δ is nonnegative real number, R is constant and is positive integer, l1 and l2 is integer variable and value is-R ~ R, z
r-1(x-l1, y-l2) high frequency Shearlet coefficient for recovering at subband position (x-l1, y-l2) place to obtain by the r-1 time Wiener filtering, z
0(x-l1, y-l2) is the initial noisy coefficient at subband position (x-l1, y-l2) place.
When image processor in step 2 carries out five layers of multiple dimensioned Shearlet conversion to noisy image, processing in ground floor high-frequency sub-band in Shearlet coefficient to the 4th layer of high-frequency sub-band during Shearlet coefficient in step 3, the value of R is followed successively by 7,2,2,2.
In the present embodiment, the value of λ is the value of 10, η is the real number of 1 ~ 1.5.Preferably, the value of η is 1.2, namely
namely in the present invention, the noise variance of each Wiener filtering is initial noise variance in subband
1.2/10ths times, the signal variance of each Wiener filtering is estimated by current input signal, and gets δ=0, and namely the present invention is in traditional Wiener filtering
method of estimation revise, after amendment, variance yields is less than
signal detail can not be removed again in diffusion filtering process.
In the present embodiment, the nonlinear diffusion aftertreatment that in step 5, image processor carries out based on partial differential equation to reconstructed image, the detailed process removing the false details of reconstructed image is: suppose that reconstructed image is I, to I partial differential equation
carry out nonlinear diffusion aftertreatment, wherein, div is divergence operator, and t is the moment that partial differential diffusion is evolved, and along with going deep into of diffusion, the value of t increases; I
t(i, j) is the grey scale pixel value at moment t position (i, j) place,
for I
tthe gradient of (i, j), c
t(i, j) for index spread function and
by partial differential equation
discretely to turn to:
Wherein,
for position in the north of (i, j), south, east, west four direction grey scale pixel value, K is Grads threshold and the value of K is 1 ~ 10, be preferably 6, I
k(i, j) is the grey scale pixel value after the secondary diffusion filtering of the kth of position at (i, j) place, I
k-1(i, j) is the grey scale pixel value of position after kth-1 diffusion filtering at (i, j) place, I
0(i, j), for position is at the grey scale pixel value of the reconstructed image I at (i, j) place, k is number of iterations and the value of k is positive integer between 1 to 7.
In the present embodiment, described image processor is computing machine.
In order to verify the technique effect that the present invention can produce, the emulation demonstration below employing MATLAB7.0 software has carried out; In simulation process, the noise that test pattern adds be average be zero and with various criterion difference σ white Gaussian noise.
Emulation 1
Size is adopted to be that Lena and the Barbara image of 512 × 512 pixels is as test pattern, SD represents the inventive method, emulation 1 gives the good Wavelet domain image denoising algorithm of the inventive method with the classics to occur in the world and the comparing result of local Wiener Filtering denoise algorithm, the Y-PSNR (PSNR) that different denoising method exports more as shown in table 1:
In table 1, " Wavelet Domain Wiener Filtering " image de-noising method of the classics proposed in the WWF article " Lowcomplexityimagedenoisingbasedonstatisticalmodelingofw aveletcoefficients (the low complex degree image denoising based on wavelet coefficient statistical model) " that to be M.K.Mihcak etc. delivered in " IEEESignalProcessingLetters (IEEE signal transacting bulletin) " the 6th volume the 12nd phase 300-303 page in 1999; GWF " Wiener filtering based on gradient field " image de-noising method that to be X.Zhang etc. proposed in the article " Gradient-basedWienerfilterforimagedenoising (denoising of gradient field Wiener Filtering) " delivered of volume the 3rd phase 934-344 page in " ComputersandElectricalEngineering (computing machine and electrical engineering) " the 39th in 2013; LBS is article " Bivariateshrinkagewithlocalvarianceestimation (the bivariate atrophy with local variance estimation) " middle " the bivariate atrophy based on local variance estimation " image de-noising method proposed that L.Sendur equals to deliver in " IEEESignalProcessingLetters (IEEE signal transacting bulletin) " the 9th volume the 12nd phase 438-441 page for 2002; The image de-noising method of " probability comprising important information based on wavelet coefficient carries out atrophy " that propose in the ProbShrink article that to be A.Pizurica etc. delivered in " IEEETransactionsonImageProcessing (IEEE image procossing transactions) " the 15th volume the 3rd phase 654-665 page in 2006 " Estimatingtheprobabilityofthepresenceofasignalofinterest inmultiresolutionsingle-andmultibandimagedenoising (probability estimate that in multiresolution single-band and multiband image denoising, signal of interest exists) "; The image de-noising method of " smooth without inclined evaluation of risk and threshold value linear expansion based on this " that propose in the UWTSURE-LET article " TheSURE-LETapproachtoimagedenoising (image denoising based on SURE-LET method) " that to be T.Blu etc. delivered in " IEEETransactionsonImageProcessing (IEEE image procossing transactions) " the 16th volume o. 11th 2778-2786 page in 2007.
The comparison of the Y-PSNR PSNR that the different denoising method of table 1 exports
Can find out from table 1, the present invention is better than other image de-noising methods above-mentioned, and Y-PSNR (PSNR) is the highest.
The visual effect that Fig. 2 A ~ 2H gives the Barbara image procossing of several method for standard deviation sigma=25 compares.Wherein, Fig. 2 A is original Barbara image, Fig. 2 B is noisy Barbara image, Fig. 2 C is the denoising Barbara image after using the process of WWF method, Fig. 2 D is the denoising Barbara image after using the process of GWF method, Fig. 2 E is the denoising Barbara image after using the process of LBS method, Fig. 2 F is the denoising Barbara image after using the process of ProbShrink method, Fig. 2 G be with the process of UWTSURE-LET method after denoising Barbara image, Fig. 2 H be with method process of the present invention after denoising Barbara image.
As can be seen from Fig. 2 A ~ 2H, in the denoising Barbara image after the process of WWF method, there is obvious false details; In denoising Barbara image after the process of GWF method, there is a lot of noise; Although the denoising Barbara image after LBS method, ProbShrink method and the process of UWTSURE-LET method has surmounted the denoising Barbara image after WWF method and the process of GWF method in visual effect, but compared with the denoising Barbara image after method process of the present invention, still there is more false details.The present invention better can preserve the feature of image while removing noise, and visual effect is best.
As can be seen from above-mentioned contrast, the present invention is better than Wavelet domain image denoising method and the local Wiener Filtering of existing some other classics in the world in subjective and objective effect.
Emulation 2
Size is adopted to be that Lena and the Barbara image of 512 × 512 pixels is as test pattern, SD represents the inventive method, emulation 2 gives the inventive method and the good comparing result spreading the image de-noising method of form based on wavelet field occurred in the world, and the comparison of the Y-PSNR (PSNR) that different denoising method exports is as shown in table 2 and table 3:
One " based on the nonlinear diffusion of partial differential equation in the wavelet field " image de-noising method proposed in the WMSAD article that to be J.zhong etc. delivered in " IEEETransactionsonCircuitsandSystemsI:RegularPapers (IEEE Circuits and Systems transactions Part I: regularly paper) " the 55th volume the 9th phase 2716-2725 page in 2008 " Wavelet-basedmultiscaleanisotropicgiffusionwithadaptives tatisticalanalysisforimagerestoration (the multiple dimensioned anisotropy parameter Postprocessing technique based on wavelet transformation and self-adaptation statistical study) "; SWCD is A.K.Mandava etc. in calendar year 2001 in " JournalofElectronicImaging (electronic imaging magazine) " the 20th one that proposes of the article " Imagedenoisingbasedonadaptivenonlineardiffusioninwavelet domain (denoising of wavelet field self-adaptation nonlinear diffusion image) " delivered of volume the 3rd phase 033016-1-033016-7 page image de-noising method that " utilizes the nonlinear diffusion of contextual information in stationary wavelet territory ".
The comparison of the output PSNR of table 2SD and WMSAD
The comparison of the output PSNR of table 3SD and SWCD
Can find out from table 2 and table 3, the present invention is better than the image de-noising method based on diffusion form in the first-class wavelet field in the existing world, and Y-PSNR (PSNR) is the highest.
Emulation 3
Size is adopted to be that Lena and the Barbara image of 512 × 512 pixels is as test pattern, SD represents the inventive method, emulation 3 gives the comparing result of the inventive method and technology 1 and technology 2, and the comparison of the Y-PSNR (PSNR) that different denoising method exports is as shown in table 4 and table 5:
The comparison of the output PSNR of table 4SD and technology 1
The comparison of the output PSNR of table 5SD and technology 2
Technology 1 is the application number mentioned in background technology is the image de-noising method based on Shearlet conversion and Wiener filtering disclosed in the Chinese patent of 201210364581.8, technology 2 to be the application numbers mentioned in background technology be 201210061837.8 Chinese patent disclosed in based on the contour wave domain Wiener Filtering denoising method of two-dimentional Otsu.
Can find out from table 4 and table 5, the present invention is better than the image de-noising method in technology 1 and technology 2, and Y-PSNR (PSNR) is the highest.
The above; it is only preferred embodiment of the present invention; not the present invention is imposed any restrictions, every above embodiment is done according to the technology of the present invention essence any simple modification, change and equivalent structure change, all still belong in the protection domain of technical solution of the present invention.
Claims (5)
1., based on Shearlet conversion and the image de-noising method of nonlinear diffusion, it is characterized in that, the method comprises the following steps:
Step one, by noisy image input picture processor;
Step 2, image processor carry out multiple dimensioned Shearlet conversion to noisy image, obtain low frequency Shearlet coefficient and high frequency Shearlet coefficient, and high frequency Shearlet coefficient is designated as initial noisy Shearlet coefficient;
Step 3, image processor use λ local Wiener filtering to carry out diffusion filtering process to initial noisy Shearlet coefficient continuously; Wherein, λ is natural number and the value of λ is 2 ~ 15;
Step 4, image processor adopt Shearlet inverse transformation to carry out signal reconstruction to low frequency Shearlet coefficient and the initial noisy Shearlet coefficient after the process of step 3 diffusion filtering, obtain reconstructed image;
Step 5, image processor carry out the nonlinear diffusion aftertreatment based on partial differential equation to reconstructed image, remove the false details of reconstructed image;
Image after step 6, output denoising.
2. according to according to claim 1 based on Shearlet conversion and the image de-noising method of nonlinear diffusion, it is characterized in that: in step 2, image processor carries out five layers of multiple dimensioned Shearlet conversion to noisy image, ground floor and second layer two-stage high-frequency sub-band respectively have 16 directions, third layer and the 4th layer of two-stage high-frequency sub-band respectively have 8 directions, and layer 5 is low frequency sub-band.
3. according to according to claim 1 based on Shearlet conversion and the image de-noising method of nonlinear diffusion, it is characterized in that: in step 3, image processor uses λ local Wiener filtering to the detailed process that initial noisy Shearlet coefficient carries out diffusion filtering process to be continuously: using the input signal of initial noisy Shearlet coefficient as first time Wiener filtering, using the input signal of the output signal of current Wiener filtering as Wiener filtering next time; The high frequency Shearlet coefficient that the r time Wiener filtering is recovered at subband position (x, y) place to obtain is designated as z
r(x, y) and z
r(x, y)=W
r(x, y) z
r-1(x, y), wherein, the value of r is the natural number of 1 ~ λ, z
r-1(x, y) high frequency Shearlet coefficient for recovering at subband position (x, y) place to obtain by the r-1 time Wiener filtering, z
0(x, y) is the initial noisy coefficient at subband position (x, y) place, W
r(x, y) be the r time Wiener filtering and
n
r(x, y) is the noise contribution that will remove at subband position (x, y) place,
for n
rthe variance of (x, y) and getting
η is noise variance adjustment parameter and η is real number,
for initial noise variance in subband and
estimated to obtain by Monte-Carlo method; s
r(x, y) is the signal content that will recover at subband position (x, y) place,
for s
rthe variance of (x, y) and
according to formula
Estimation obtains,
for z
r-1the variance of (x, y), δ is s
rthe adjustment parameter of the variance of (x, y), and δ is nonnegative real number, R is constant and is positive integer, l1 and l2 is integer variable and value is-R ~ R, z
r-1(x-l1, y-l2) high frequency Shearlet coefficient for recovering at subband position (x-l1, y-l2) place to obtain by the r-1 time Wiener filtering, z
0(x-l1, y-l2) is the initial noisy coefficient at subband position (x-l1, y-l2) place.
4. according to according to claim 3 based on Shearlet conversion and the image de-noising method of nonlinear diffusion, it is characterized in that: the value of η is the real number of 1 ~ 1.5.
5. according to according to claim 1 based on Shearlet conversion and the image de-noising method of nonlinear diffusion, it is characterized in that: the nonlinear diffusion aftertreatment that in step 5, image processor carries out based on partial differential equation to reconstructed image, the detailed process removing the false details of reconstructed image is: suppose that reconstructed image is I, to I partial differential equation
carry out nonlinear diffusion aftertreatment, wherein, div is divergence operator, and t is the moment that partial differential diffusion is evolved, and along with going deep into of diffusion, the value of t increases; I
t(i, j) is the grey scale pixel value at moment t position (i, j) place,
for I
tthe gradient of (i, j), c
t(i, j) for index spread function and
by partial differential equation
Discretely to turn to:
Wherein,
(u=1,2,3,4) for position in the north of (i, j), south, east, west four direction grey scale pixel value, K is Grads threshold and the value of K is 1 ~ 10, I
k(i, j) is the grey scale pixel value after the secondary diffusion filtering of the kth of position at (i, j) place, I
k-1(i, j) is the grey scale pixel value of position after kth-1 diffusion filtering at (i, j) place, I
0(i, j), for position is at the grey scale pixel value of the reconstructed image I at (i, j) place, k is number of iterations and the value of k is positive integer between 1 to 7.
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