CN109472756A - Image de-noising method based on shearing wave conversion and with directionality local Wiener filtering - Google Patents
Image de-noising method based on shearing wave conversion and with directionality local Wiener filtering Download PDFInfo
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Abstract
The invention belongs to technical field of image processing, it is related to the image de-noising method based on shearing wave conversion and with directionality local Wiener filtering, noisy image is read first, multiple dimensioned two-dimensional discrete shearing Wave Decomposition is carried out to the noisy image and obtains K+1 sub-band images, include a low-frequency image and K high frequency imaging, then Directional Decomposition is carried out to sub-band images using shearing wave filter group, obtains high frequency imaging coefficient of frequency and low-frequency image coefficient of frequency；High frequency imaging coefficient of frequency is filtered using the local Wiener filtering algorithm with directional window, the shearing wave coefficient after being denoised；Low-frequency image coefficient of frequency is filtered using quick two-sided filter, the shearing wave coefficient after being denoised；Shearing wave inversion process is carried out to whole shearing wave coefficients, the clean image after being denoised.The method of the present invention can be applied to the denoising of the optics gray level image containing white Gaussian noise, to obtain image that have high s/n ratio, clearer.
Description
Technical field
The invention belongs to technical field of image processing, are related to a kind of based on shearing wave conversion and with the filter of directionality part wiener
The image de-noising method of wave can be applied to the optics gray level image denoising containing white Gaussian noise, have high s/n ratio to obtain
, clearer image.
Background technique
In image preprocessing field, in order to remove the white Gaussian noise contained in original image, to obtain high quality, height
The clear image of signal-to-noise ratio, and the method for favourable conditions and use image denoising is provided for post processing of image.Currently, most of figures
As the method for denoising concentrates on the denoising method based on wavelet transformation.
Patented technology " a kind of dual-tree complex wavelet image denoising side based on partial differential equation that University of Electronic Science and Technology possesses
It is disclosed in method " (publication number: CN101777179A, grant date: on February 15th, 2012, applying date: on February 05th, 2010)
A kind of method for de-noising dual-tree complex wavelet image based on partial differential equation.This method carries out double trees to the noisy image of input first
Complex wavelet transform decomposes, and carries out isotropic diffusion to two low frequency subband images after decomposition；It redesigns improved adaptive
Model is answered, the dual-tree complex wavelet transform mould and gradient-norm of high frequency detail sub-band images in each direction are calculated, it is multiple small using double trees
The weighted average of wave conversion mould and gradient-norm improves P-M model to design a kind of adaptive diffusion coefficient function；Then right
Improved adaptive model sliding-model control, and anisotropy parameter is carried out to 6 high-frequency sub-band images；It is multiple finally to carry out double trees
Wavelet inverse transformation, the image after output denoising.Although this method has the preferable ability for distinguishing noise and signal, still
Have the drawback that: dual-tree complex wavelet lacks translation invariance, and the image after the denoising caused is distorted, main to show
For ringing effect and puppet Gibbs effect.In addition, making an uproar on different scale when the method does not account for wavelet decomposition in denoising
Sound is different to the annoyance level of image, therefore cannot reach denoising effect well.
" Tian Pei, Li Qingzhou, Ma Ping, Niu Yuguang, ' a kind of image denoising based on wavelet transformation is new in document by Tian Pei et al.
It proposes in method ' [J], Chinese graphics image journal, 13 (3), 395-399 (2008) " based on wavelet transformation and Wiener filtering
Image de-noising method.This method carries out wavelet transformation to image first；Then according to the wavelet coefficient of Gaussian noise and image
Wavelet coefficient between existing different characteristics, on different scale different directions wavelet coefficient carry out Wiener filtering；Finally
Inverse wavelet transform is carried out to filtered wavelet coefficient, the image after being denoised.Although the method can be improved the peak of image
It is worth signal-to-noise ratio (PSNR), and more image detail informations can be retained.But still have the drawback that: wavelet transformation cannot
Anisotropic detailed information in enough images of expression well, therefore cannot remove and contain in anisotropic image well
Noise.
In order to solve problem above, Xian Electronics Science and Technology University Miao Qi is wide et al. application No. is 201210364581.8
" a kind of image de-noising method based on Shearlet transformation and Wiener filtering " is disclosed in Chinese patent, this method is first to defeated
Enter source images and carry out symmetric extension, then use shear transformation, then use WAVELET PACKET DECOMPOSITION, tradition dimension is used to decomposition coefficient
Nanofiltration wave, with treated, coefficient obtains reconstructed image, finally carries out symmetry transformation and image co-registration, obtains finally denoising image
This process employs Shearlet transformation there is multidirectional and Wiener filtering can be adjusted according to the Local Deviation of image to filter
The advantages that device exports, overcomes the shortcomings that wavelet transformation cannot express the anisotropy information of image very well in the prior art, with
And coefficient on different directions is carried out using single threshold value to denoise the undesirable problem of effect caused by same treatment, so as to
It is enough that image detail information is more accurately analyzed in the high frequency coefficient on the different directions of image, but due to the life of Wiener filtering
There is false details at image, affects the promotion of denoising performance.
Summary of the invention
It is a kind of based on shearing wave conversion and with directionality the purpose of the present invention is in view of the above shortcomings of the prior art, proposing
The image de-noising method of local Wiener filtering, this method is easy to operate, and it is convenient to realize, can be highly desirable signal and noise
It being distinguished, and protects the minutia of image while removing noise, function admirable is practical, and using effect is good,
Convenient for promoting the use of.
The purpose of the present invention is achieved through the following technical solutions: locally tieing up based on shearing wave conversion and with directionality
The image de-noising method of nanofiltration wave, the image de-noising method include the following steps: step 1: reading noisy image, contain first to this
Image of making an uproar carries out multiple dimensioned two-dimensional discrete and shears Wave Decomposition, which carries out multiple dimensioned two-dimensional discrete shearing Wave Decomposition and obtain
K+1 sub-band images, the sub-band images include a low-frequency image and K high frequency imaging, then using shearing wave filter
Group carries out Directional Decomposition to the sub-band images, respectively obtains high frequency imaging coefficient of frequency and low-frequency image coefficient of frequency；Step
2: high frequency imaging coefficient of frequency obtained in the step 1 being carried out using the local Wiener filtering algorithm with directional window
Filtering processing, the shearing wave coefficient after being denoised；Step 3: using quick two-sided filter to low obtained in the step 1
Frequency picture frequency coefficient is filtered, the shearing wave coefficient after being denoised；Step 4: to the shearing wave in the step 2
Shearing wave coefficient in coefficient and the step 3 carries out shearing wave inversion process, the clean image after being denoised.
Further, more rulers are carried out to the noisy image using non-lower sampling pyramid filter group in the step 1
It spends two-dimensional discrete and shears Wave Decomposition.
Further, more rulers are carried out to the noisy image using non-lower sampling pyramid filter group in the step 1
It spends two-dimensional discrete and shears Wave Decomposition, Directional Decomposition then is carried out to the sub-band images using shearing wave filter group and realizes direction
Localization.
Further, multiple dimensioned shearing wave conversion, the shearing wave transformation for mula are carried out to noisy image in the step 1
For
Wherein, a is scale parameter, and s is shear parameters, and t is translation parameters,Indicate parabolic linear content
Matrix,Indicate shearing matrix.
Further, the method being filtered in the step 2 to high frequency imaging coefficient of frequency includes two parts: first
First all coefficient in transform domain in a directionality window centered on every bit high frequency imaging signal averagely obtain the high frequency
The variance of picture signalI.e.
In formula, (0, x) ≡ max (x), W and #W respectively represent the number of directionality window and directionality window midpoint,It is noisy image by the transformed high frequency imaging coefficient of frequency of shearing wave；Directionality window W's is defined as:
Wherein, r, a > 0 controls the size of Directional Windows
And shape, θ ∈ [- π, π] determine the direction of Directional Windows；
Then, the coefficient in transform domain of original image is determined by the local Wiener filtering to noisy image coefficient in transform domain,
I.e.
Further, the frequency abstraction direction for being matched with shearing wave conversion is chosen in the direction of the directionality window.
Further, when being filtered in the step 3 to low-frequency image coefficient of frequency, it is assumed thatIt represents input low-frequency image I and increases the three-dimensional image matrix obtained after dimension,Three-dimensional weight matrix is represented, then the structure of quick two-sided filter are as follows:
In formula, (x, y) is the coordinate of the low-frequency image pixel of input,The linear convolution of matrix is represented, int erp is
Interpolating function, G are the spatial neighbor degree factor G after linearisationsWith gray scale similarity factor GrProduct；ssSpatial domain is represented to adopt
Sample rate, srRepresent pixel codomain sample rate.
Image de-noising method proposed by the present invention based on shearing wave conversion and with directionality local Wiener filtering, will have
Directionality local Wiener filtering and quick bilateral filtering combine, after making full use of shearing wave conversion to decompose noisy image
The advantages of detailed information of original image can preferably be shown, carries out noisy image using shearing wave conversion multiple dimensioned more
Directional Decomposition denoises each high frequency direction subband using having directive local Wiener filtering algorithm, utilization orientation
Property local Wiener filtering the characteristics of capable of preferably removing white Gaussian noise, shearing wave conversion is filtered with directionality part wiener
Wave is combined to carry out noisy image denoising.Although the noise of noisy image is largely focused on high frequency imaging, low frequency figure
As also containing a little noise, so being denoised to low-frequency image using quick bilateral filtering algorithm, after finally obtained denoising
Image not only can effectively inhibit noise, but also the more detailed information of image can be retained.
The present invention carries out multi-resolution decomposition to noisy image when decomposing noisy image, using shearing wave conversion, due to cutting
Wave conversion is cut with multidirectional, it is thus possible to the high-frequency information and low-frequency information of noisy image are obtained in a plurality of directions, with
Just image detail is effectively captured, lacking for image anisotropy information cannot be expressed very well by overcoming wavelet transformation in the prior art
Point.
For the present invention when the high frequency coefficient after decomposing to noisy image is filtered, invention applies with direction
The method of the local Wiener filtering of property.Local Wiener filtering is it is crucial that estimation to picture signal variance, the present invention use
The variance of picture signal is estimated with being averaged for all values in directive window function, and the direction of directionality window is chosen for
Frequency abstraction direction assigned in shearing wave conversion, for rectangular window, directionality window can more accurately estimate image
The variance of signal.
The present invention generates following beneficial effect compared with prior art.(1) the present invention overcomes the changes of small echo in the prior art
The shortcomings that changing the anisotropy information that cannot express image well, and paid no attention to using the single Wiener filtering denoising effect of tradition
The problem of thinking utilizes the good anisotropy of shearing wave conversion, multiresolution, multiple dimensioned, multi-direction characteristic and preferable office
The features such as portion's characteristic etc., use the local Wiener filtering algorithm with Directional Windows to denoise each high frequency direction subband, from
And the information of high frequency imaging coefficient of frequency in image all directions can be more accurately analyzed, obtain the denoising image of high quality.
(2) the method for the present invention is easy to operate, and it is convenient to realize, highly desirable signal and noise can be distinguished, and is removing
The minutia of image is protected while noise, function admirable is practical, and using effect is good, convenient for promoting the use of, especially
For the image containing Gaussian noise, preferably denoising effect can be obtained, the visual demand of people is more can satisfy and actually answers
Demand.
Detailed description of the invention
Fig. 1 is the present invention is based on shearing wave conversion and with the image de-noising method flow chart of directionality local Wiener filtering.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and examples.
As shown in Figure 1, the image de-noising method of the invention based on shearing wave conversion and with directionality local Wiener filtering,
Specific embodiment is as follows:
Firstly, reading the noisy image being stored in hard disc of computer space in computer terminal application MATLAB software, so
Multiple dimensioned two-dimensional discrete is carried out to the noisy image using non-lower sampling pyramid filter group afterwards and shears Wave Decomposition, noisy figure
As obtaining K+1 sub-band images by K grades of sampling pyramids, shearing wave filter group is reused to the sub-band images progress side
To decomposition, high frequency imaging coefficient of frequency and low-frequency image coefficient of frequency are respectively obtained.Wherein, the sub-band images include one low
Frequency image and K high frequency imaging.
In the present embodiment, five layers of multiple dimensioned two-dimensional discrete are carried out to noisy image and shear Wave Decomposition, first layer and the second layer
Each direction of two-stage high-frequency sub-band, third layer and each direction of the 4th layer of two-stage high-frequency sub-band, layer 5 is low frequency sub-band.
Wherein, when carrying out multiple dimensioned shearing wave conversion to noisy image, the shearing wave of use is transformed to G.R.Easley,
D.Labate, W.Q.Lim 2008 in " Applied and Computational Harmonic Analysis (application and
Calculate frequency analysis) " the 1st phase article delivered " the Sparse directional image of page 25~46 of volume 25
Representations using the discrete shearlet transform is (based on discrete Shearlet transformation
Image orientation rarefaction representation) " proposed in discrete non-lower sampling Shearlet transformation, the window function of selection is " Meyer ", should
Discrete Shearlet transformation has translation invariance and good directionality, can more effectively capture the geometrical characteristic of image.Institute
Stating shearing wave transformation for mula is
Wherein, a is scale parameter, and s is shear parameters, and t is translation parameters,Indicate parabolic linear content
Matrix,Indicate shearing matrix.
Then, it is respectively processed, including uses for the low-frequency image coefficient of frequency and high frequency imaging coefficient of frequency
Local Wiener filtering algorithm with directional window is filtered high frequency imaging coefficient of frequency, and using quickly bilateral
Filter is filtered low-frequency image coefficient of frequency.
High frequency imaging coefficient of frequency is filtered using the local Wiener filtering algorithm with directional window
Purpose is the noise for removing noisy image, and local Wiener filtering is a kind of simple and effective filtering method of spatially adaptive, is contained
Image of making an uproar mainly consists of two parts in the local Wiener filtering of transform domain.First centered on every bit high frequency imaging signal
All coefficient in transform domain in one directionality window averagely obtain the variance of the high frequency imaging signalI.e.
In formula, (0, x) ≡ max (x), W and #W respectively represent the number of directionality window and directionality window midpoint,It is noisy image by the transformed high frequency imaging of shearing wave.Then, pass through the part to noisy image coefficient in transform domain
Wiener filtering determines the coefficient in transform domain of original image, i.e.,
Most critical is exactly estimation to picture signal variance in local Wiener filtering, and present invention use is with directive
All values are averaged to estimate the variance of picture signal in window function, and the direction of directionality window is chosen is matched with shearing wave conversion
Frequency abstraction direction, compared to the variance that the window functions such as rectangular window can more accurately estimate signal.Directionality window W's determines
Justice are as follows:
Wherein, r, a > 0 controls the size of Directional Windows
And shape, θ ∈ [- π, π] determine the direction of Directional Windows.
Further, when being filtered using quick two-sided filter to low-frequency image coefficient of frequency, it is assumed thatIt represents input low-frequency image I and increases the three-dimensional image matrix obtained after dimension,Three-dimensional weight matrix is represented, then the structure of quick two-sided filter are as follows:
In formula, (x, y) is the coordinate of input image pixels point.Represent the linear convolution of matrix.Int erp is interpolation letter
Number, the major function of int erp is pairWithInterpolation arithmetic is carried out in three-dimensional space to find out in coordinateOn value, then result is assigned to IY (x, y) and EY (x, y).
G is the spatial neighbor degree factor G after linearisationsWith gray scale similarity factor GrProduct, i.e. gaussian kernel function.
Calculation amount can be accordingly increased later by increasing dimension, improve calculating by the way of down-sampling in the process of the present invention
Efficiency, wherein ssRepresent spatial domain sample rate, srPixel codomain sample rate is represented, three-dimensional matrice is just divided into several skies by this
Between size be ss×ss×srSmall three-dimensional space.
It is denoised after being handled using the local Wiener filtering with directional window high frequency imaging coefficient of frequency
Shearing wave coefficient afterwards, and after also obtaining denoising after equally handling using quick bilateral filtering low-frequency image coefficient of frequency
Shearing wave coefficient, the clean image after denoising in order to obtain carries out shearing wave inverse transformation to all shearing wave coefficient, can be with
Clean image after being denoised.
The above embodiments are merely illustrative of the technical solutions of the present invention, rather than is limited；Although referring to aforementioned reality
Applying example, invention is explained in detail, for those of ordinary skill in the art, still can be to aforementioned implementation
Technical solution documented by example is modified or equivalent replacement of some of the technical features；And these are modified or replace
It changes, the spirit and scope for claimed technical solution of the invention that it does not separate the essence of the corresponding technical solution.
Claims (7)
1. the image de-noising method based on shearing wave conversion and with directionality local Wiener filtering, which is characterized in that the image is gone
Method for de-noising includes the following steps:
Step 1: reading noisy image, multiple dimensioned two-dimensional discrete is carried out to the noisy image first and shears Wave Decomposition, the noisy figure
K+1 sub-band images are obtained as carrying out multiple dimensioned two-dimensional discrete shearing Wave Decomposition, the sub-band images include a low-frequency image
With K high frequency imaging, Directional Decomposition then is carried out to the sub-band images using shearing wave filter group, respectively obtains high frequency figure
Picture frequency rate coefficient and low-frequency image coefficient of frequency；
Step 2: using the local Wiener filtering algorithm with directional window to high frequency imaging frequency obtained in the step 1
Coefficient is filtered, the shearing wave coefficient after being denoised；
Step 3: low-frequency image coefficient of frequency obtained in the step 1 is filtered using quick two-sided filter,
Shearing wave coefficient after being denoised；
Step 4: shearing wave inverse transformation is carried out to the shearing wave coefficient in the shearing wave coefficient and the step 3 in the step 2
Processing, the clean image after being denoised.
2. the image de-noising method based on shearing wave conversion and with directionality local Wiener filtering as described in claim 1,
Be characterized in that, in the step 1 using non-lower sampling pyramid filter group to the noisy image carry out it is multiple dimensioned two dimension from
Dissipate shearing Wave Decomposition.
3. the image de-noising method based on shearing wave conversion and with directionality local Wiener filtering as described in claim 1,
Be characterized in that, in the step 1 using non-lower sampling pyramid filter group to the noisy image carry out it is multiple dimensioned two dimension from
Shearing Wave Decomposition is dissipated, Directional Decomposition then is carried out to the sub-band images using shearing wave filter group and realizes that direction localizes.
4. the image de-noising method based on shearing wave conversion and with directionality local Wiener filtering as claimed in claim 1 or 2,
It is characterized in that, carrying out multiple dimensioned shearing wave conversion to noisy image in the step 1, the shearing wave transformation for mula is
Wherein, a is scale parameter, and s is shear parameters, and t is translation parameters,Indicate parabola Scale Matrixes,Indicate shearing matrix.
5. the image de-noising method based on shearing wave conversion and with directionality local Wiener filtering as described in claim 1,
It is characterized in that, the method being filtered in the step 2 to high frequency imaging coefficient of frequency includes two parts: first with each
All coefficient in transform domain in a directionality window centered on point high frequency imaging signal averagely obtain the high frequency imaging signal
VarianceI.e.
In formula, (0, x) ≡ max (x), W and #W respectively represent the number of directionality window and directionality window midpoint, and y~(i,
It j) is noisy image by the transformed high frequency imaging coefficient of frequency of shearing wave；Directionality window W's is defined as:
Wherein, r, a > 0 controls the size and shape of Directional Windows
Shape, θ ∈ [- π, π] determine the direction of Directional Windows；
Then, the coefficient in transform domain of original image is determined by the local Wiener filtering to noisy image coefficient in transform domain, i.e.,
6. the image de-noising method as claimed in claim 1 or 5 based on shearing wave conversion and with directionality local Wiener filtering,
It is characterized in that, the frequency abstraction direction for being matched with shearing wave conversion is chosen in the direction of the directionality window.
7. the image de-noising method based on shearing wave conversion and with directionality local Wiener filtering as described in claim 1,
It is characterized in that, when being filtered in the step 3 to low-frequency image coefficient of frequency, it is assumed thatIt represents input low-frequency image I and increases the three-dimensional image matrix obtained after dimension,Three-dimensional weight matrix is represented, then the structure of quick two-sided filter are as follows:
In formula, (x, y) is the coordinate of the low-frequency image pixel of input,The linear convolution of matrix is represented, interp is interpolation letter
Number, G are the spatial neighbor degree factor G after linearisationsWith gray scale similarity factor GrProduct；ssRepresent spatial domain sample rate, sr
Represent pixel codomain sample rate.
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| CN111242856A (en) * | 2020-01-06 | 2020-06-05 | 西安工程大学 | Dual image denoising method based on shear wave |
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