CN104616250A - Self-snake diffusion and sparse representation based on Contourlet domain SAR image denoising method - Google Patents

Abstract

The invention discloses a self-snake diffusion and sparse representation based on Contourlet domain SAR image denoising method. The method comprises the steps of 1, inputting a noise-included SAR image; 2, circularly translating the noise-including SAR image in a certain distance, and performing Contourlet transformation to obtain a low-frequency sub-band and a high-frequency sub-band; 3, performing self-snake diffusion filter for the low-frequency sub-band, and estimating by using the filtered coefficients as local average values of the low-frequency sub-band; 4, filtering the high-frequency sub-band through a spare optimization model, and solving the spare coefficients of the high-frequency sub-band by the improved orthogonal matching pursuit algorithm; 5, fusing the filtered low-frequency sub-band and high-frequency sub-band coefficients, performing reverse Contourlet transformation and reversely translating, and then outputting the denoised SAR image. According to the technical scheme, the method has the advantages that the side edge information of the image can be effectively maintained, the denoising effect of the image can be improved, the operation is simple, and the speckle noise in the SAR image can be filtered and removed.

Description

A kind of based on the Contourlet territory SAR image denoising method from snake diffusion and rarefaction representation

Technical field

The present invention relates to technical field of image processing, be specifically related to a kind of based on the Contourlet territory SAR image denoising method from snake diffusion and rarefaction representation of synthetic-aperture radar (SAR) Image Denoising Technology field, the present invention can be used for the coherent speckle noise of filtering SAR image.

Background technology

The filtering of SAR image coherent speckle noise is the important topic of SAR image processing technology field always, is subject to the extensive concern of researcher, proposes multiple denoising method.Different according to adopted mathematical method, the denoising method of SAR image can be divided three classes: statistics class denoising method, transform domain class denoising method, partial differential diffusion class denoising method.Each class methods respectively have relative merits, and wherein most widely used is transform domain class denoising method.Rarefaction representation is the main information describing signal with less coefficient, has been successfully applied to the transform domain class denoising method of SAR image.Zhao Ruizhen [Zhao Ruizhen, Liu Xiaoyu, et al..Wavelet denoising via sparse representation [J] .Science in China Series F, 2009,52 (8): 1371-1377] rarefaction representation is applied to wavelet field, Denoising Problems is converted into optimal problem, utilizes the contaminated wavelet coefficient of method of steepest descent Iterative restoration, complete SAR image denoising.But because small echo directivity is limited, effectively can not represent line, face singularity, cannot catch the profile information of image, the SAR image denoising effect therefore for texture-rich is poor.For this reason, multi-scale geometric analysis method becomes first-selected.Liu Shuaiqi [Liu Shuaiqi, Hu Shaohai, Xiao Yang. based on the Shearlet territory SAR image denoising [J] of rarefaction representation. electronics and information journal, 2012,34 (9): 2110-2115] SAR image is transformed to Shearlet territory, solve optimization problem in conjunction with rarefaction representation, complete SAR image denoising, but algorithm have ignored the residual noise of low frequency sub-band, therefore effect is not very remarkable.Yang Meng [Meng Yang, Gong Zhang, SAR Image De-specklingUsing Over-complete Dictionary.Electronics Letters, 48 (10): 596-597, 2012] according to SAR image low frequency and high frequency sparsity structure information, by greedy algorithm reconstructed image low frequency component, small echo and shearing wave is utilized to carry out rarefaction representation to the some singularity of image high fdrequency component and line singularity, the high fdrequency component of SAR image is reconstructed by iteration optimization mode, fusion low frequency component and high fdrequency component realize SAR image denoising, effect is better, but algorithm have ignored the marginal information of low frequency sub-band large scale target, the image after denoising is caused to occur edge fog phenomenon.From snake diffusing filter [Weickert J, g.Fast Methods for Implicit Active Contour Models U.Geometric Level SetMethods in Imaging.Vision and Graphics, 2003, Part II:43-57] due to the minutia such as edge, texture of image can be kept while denoising, be applied in the denoising method of SAR image.Zhu Lei [Zhu Lei, water roc is bright, Wu Aijing. a kind of SAR image Speckle noise removal new method [J]. Xian Electronics Science and Technology University's journal (natural science edition), 2012,39 (2): 80-86] divide being applied to un-downsampling wavelet transform bag from snake diffusion the low frequency sub-band taken off, achieve SAR image denoising in conjunction with the L1-L2 combined optimization improved, effect is better, but Riming time of algorithm is longer.Do and Vetterli [M.N.Do and M.Vetterli: " Contourlets. " In Beyond Wavelet, J.Stoeckler and G.V.Welland, Eds.Academic press, New York. (2002) to appear, http://ww.ifp.uiuc.edu/ ~ minhdo/publications] the multiple dimensioned contourlet transformation in non-self-adapting direction that proposes, owing to make use of the geometrical property of image, have multiple dimensioned, multidirectional and anisotropy, the marginal information of image just effectively can be caught with a small amount of coefficient, significantly can reduce pseudo-Gibbs effect, can with rarefaction representation connected applications in SAR image denoising.But the low frequency sub-band of SAR image after contourlet transformation is decomposed still retains fraction residual noise, if ignore the filtering of low frequency sub-band, denoising effect certainly will be affected, therefore SAR image is transformed to Contourlet territory by the present invention, low frequency sub-band is adopted from snake diffusion filtering, the denoising of sparse optimization denoising model is adopted to high-frequency sub-band.

Summary of the invention

Technical matters

The invention provides a kind of Contourlet territory SAR image denoising method based on spreading sharp rarefaction representation from snake, can to the low frequency sub-band of SAR image after contourlet transformation is decomposed and high-frequency sub-band denoising respectively, both maintain the marginal information of image, turn improve denoising effect.

Technical scheme

In order to solve above-mentioned technical matters, a kind of Contourlet territory SAR image denoising method based on spreading sharp rarefaction representation from snake of the present invention specifically comprises the steps:

Step one a: width of input option comprises the SAR image of noise:

Step 2: first certain to noisy SAR image cycle spinning distance, what overcome contourlet transformation moves sex change, then contourlet transformation is carried out to the SAR image after translation, wherein LP structure adopts " 9-7 " biorthogonal wavelet to decompose, the direction number of DFB is 8, retain and extract SAR image low frequency sub-band coefficient profit 8 directions high-frequency sub-band coefficient;

Step 3: for not having openness low frequency sub-band, adopting, from snake diffusing filter, DIFFUSION TREATMENT being carried out to image, and the coefficient after filtering process is estimated as the local mean value of SAR image low frequency sub-band in Contourlet territory;

Step 4: for having openness high-frequency sub-band, adopts sparse representation model to construct the optimal model of denoising, utilizes the orthogonal matching pursuit algorithm improved to solve the sparse coefficient of high-frequency sub-band, specifically comprises the following steps:

Step 1: due to the high-frequency sub-band pairwise orthogonal in 8 directions, so first the high-frequency sub-band in 8 directions recombinated according to the orthogonal feature of correspondence, forms 4 directional subbands;

Step 2: the h getting each pixel in 4 directional subband images ₀× h ₀in neighborhood, column vector is end to end is rearranged to dimensional vector;

Step 3: choose the calculation matrix of Gaussian distribution as redundant dictionary Φ (M × (N/2), 1≤M < < (N/2)), respectively the directional subband column vector of 4 in step 2 is measured;

Step 4: at I ²each atom of normalization dictionary Φ under norm meaning; With the rarefaction representation coefficient of 4 direction high-frequency sub-band column vectors under dictionary Φ in the orthogonal matching pursuit algorithm calculation procedure 2 improved;

Step 5: 4 direction high-frequency sub-band filtering obtained recover to be reassembled as the high-frequency sub-band in 8 directions.

Step 5: low frequency coefficient filtering obtained and high frequency coefficient carry out Contourlet inverse transformation and oppositely translation, return to the ordering the same with original image, obtain the SAR image after denoising.

Technical scheme of the present invention proposes a kind of new SAR image denoising method.The method combines from snake diffusing filter and rarefaction representation denoising model, and applies it in the denoising method of SAR image contourlet transformation territory.First SAR image is transformed to Contourlet territory by it, decomposite low frequency sub-band and high-frequency sub-band, low frequency sub-band coefficient is adopted and carries out filtering process from snake diffusion, sparse optimization denoising model is adopted to carry out filtering process to high-frequency sub-band, low frequency sub-band coefficient after last fused filtering process and high-frequency sub-band coefficient, and carry out Contourlet inverse transformation, achieve SAR image denoising.

Beneficial effect

Method of the present invention overcomes in existing SAR image denoising method the contradiction that cannot keep picture edge characteristic simultaneously and improve image noise reduction effect, compared with other congenic method, implementation method is simple, both the filtering coherent speckle noise of SAR image, farthest remained again the edge feature of image object.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below.

Fig. 1 is the process flow diagram of SAR image denoising method of the present invention;

Fig. 2 is the filtering results contrast figures of employing four kinds of denoising methods to actual measurement SAR image 1 coherent speckle noise;

Fig. 3 is the filtering results contrast figures of employing four kinds of denoising methods to actual measurement SAR image 2 coherent speckle noise;

Fig. 4 is under different noise level, and four kinds of denoising methods are to the filtering performance quantitation curves figure of noise.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is further described:

As shown in Figure 1, the method for the present embodiment adopts different filtering methods to carry out denoising to the low frequency sub-band after the decomposition of SAR image contourlet transformation and high-frequency sub-band respectively.

The method of the present embodiment specifically comprises the following steps:

Step one: input picture.

One width of input option comprises the synthetic-aperture radar SAR image of noise.

Step 2: contourlet transformation is carried out to noisy SAR image.

First to two dimension noisy SAR image I (x, the y) cycle spinning of a width N × N, definition cycle spinning operator is as shown in (1) formula.Because cycle spinning operator is one to one, be reversible, it is inverse such as formula shown in (2).The object of cycle spinning image is the ordering by changing image, thus the change position of singular point in whole image reaches the oscillation amplitude reducing or eliminate pseudo-Gibbs phenomenon, improves reconstruction quality.

C _i，j(I)＝I[mod(x+i，N)，mod(y+j，N)] (1)

[C _i，j(I)] ^-1C _-i，-j(I) (2)

Carry out 1 layer of Contourlet to the SAR image after translation to decompose, wherein LP structure adopts " 9-7 " biorthogonal wavelet to decompose, and the direction number of DFB is 8, obtains the low frequency sub-band coefficient of SAR image and the high-frequency sub-band coefficient in 8 directions.

Step 3: low frequency sub-band is adopted and processes from snake diffusing filter.

If the low frequency sub-band of SAR image I after Contourlet changes is A, undertaken from the process of snake diffusing filter by formula (3), the low frequency sub-band image warp after process divide into two parts from snake diffusing filter, wherein for the direction with Edge-stopping is spread, for the shock-diffusion with edge humidification.Edge indicator function g is with gradient parameter for input, the g function adopted in the present invention is such as formula shown in (4), and wherein R is the contrast parameter of tolerance edge gradient.Coefficient after filtering process is estimated as the local mean value of SAR image low frequency sub-band in Contourlet territory.

$\frac{\&PartialD;A}{\&PartialD;t}=\left[\mathrm{div}\left(g\left(\right|\&dtri;A\left|\right)\frac{\&dtri;A}{|\&dtri;A|}\right)\right]|\&dtri;A|=g\left(\right|\&dtri;A\left|\right)|\&dtri;A|\mathrm{div}\left(\frac{\&dtri;A}{|\&dtri;A|}\right)+\&dtri;g\left(\right|\&dtri;g\left|\right)\&CenterDot;\&dtri;A---\left(3\right)$

g(r)＝1/(1+(r/R) ²) (4)

Step 4: adopt sparse optimization denoising model to process to high-frequency sub-band.

For having openness high-frequency sub-band, utilizing sparse representation model to construct the optimal model of denoising, utilizing the orthogonal matching pursuit algorithm improved to solve the sparse coefficient of high-frequency sub-band, specifically comprising the following steps:

Step 1: due to the high-frequency sub-band pairwise orthogonal in 8 directions, so first the high-frequency sub-band in 8 directions recombinated according to the orthogonal feature of correspondence, forms 4 directional subbands;

Step 2: the h getting each pixel in 4 directional subband images ₀× h ₀in neighborhood, column vector is end to end is rearranged to dimensional vector f;

Step 3: choose the calculation matrix of Gaussian distribution as redundant dictionary Φ (M × (N/2), 1≤M < < (N/2)), respectively the directional subband column vector f of 4 in step 2 is measured;

Step 4: at I ²each atom of normalization dictionary Φ under norm meaning; With the rarefaction representation coefficient of the directional subband column vector f of 4 in orthogonal matching pursuit algorithm calculation procedure 2 under dictionary Φ:

(1) initialization: surplus r ₀=f, stage initial value s=1, step-length is 1, iterations initial value m=1, and step-length is 1, threshold value g ₀(0 < g ₀< 1), μ (0 < μ < 1), index value set

(2) related coefficient μ={ μ is calculated _j| μ _j=| < r, Φ _j> |, j=1,2 ... N};

(3) atom is selected: determine candidate index collection Γ, meet formula | < r _m-1, Φ _j> |>=g _m-1× max| < r _m-1, Φ _j> |, wherein indexed set Γ meets $\left|\mathrm{\&Gamma;}\right|\&le;N-\left|{\mathrm{\&Lambda;}}_{m-1}\right|;$

(4) postsearch screening: according to formula | μ (i)≤2| μ (j) | regularization screening is carried out to Candidate Set, determines subset Γ ₀, upgrade support set wherein ${\mathrm{\&Lambda;}}_m={\mathrm{\&Lambda;}}_{m-1}\&cup;{\mathrm{\&Gamma;}}_0;$

(5) surplus upgrades: applying equation $\hat{f}=\arg \min {\left|\right|y-{\mathrm{\&Phi;}}_{{\mathrm{\&Lambda;}}_m}f\left|\right|}_2,r_m=y-{\mathrm{\&Phi;}}_{{\mathrm{\&Lambda;}}_m}\hat{f}$ Obtain and r _m;

(6) the ‖ r that satisfies condition is judged whether _m‖ ₂≤ ε ₁if meet, then iteration ends, exits circulation; If do not meet, judge whether abs (the ‖ r that satisfies condition _m‖ ₂-‖ r _m-1‖ ₂)/‖ r _m-1‖ ₂< ε ₂if meet, then enter the next stage, and revise threshold value g _m=g _m-1μ ^s-1, turn (3); Otherwise enter next iteration, turn (2);

Step 5: obtain 4 direction high-frequency sub-band are recovered the high-frequency sub-band being reassembled as 8 directions.

Step 5: output image.

Low frequency sub-band coefficient profit high-frequency sub-band coefficient filtering obtained carries out Contourlet inverse transformation and oppositely translation, returns to the ordering the same with original image, obtains the SAR image that denoising is later.

Below by way of the denoising effect of experimental analysis the present embodiment method and additive method, and carry out comparative descriptions.

A width actual measurement SAR image is chosen in experiment one, the airport SAR image (3 meters of resolution) that the International airport, area, Albuquerque, New Mexico as shown in (a) in Fig. 2 obtains.Adopt the different transform domain denoising methods in conjunction with rarefaction representation to airport SAR image denoising respectively, the denoising image obtained is as shown in (b), (c), (d) He (e) in Fig. 2.The denoising method adopted comprises: the Shearlet-SP method that the Wavelet-SP method that rarefaction representation and small echo combine, rarefaction representation and shearing wave combine, rarefaction representation with little involve that Wavelet-Shearlet-SP method that shearing wave is combined and the present invention propose based on spreading from snake and the Contourlet territory denoising method of rarefaction representation.

Another width actual measurement SAR image is chosen in experiment two, the city SAR image (1 meter of resolution) that the stud-farm, area, Albuquerque, New Mexico as shown in (a) in Fig. 3 obtains.Adopt Wavelet-SP method, Shearlet-SP method, Wavelet-Shearlet-SP method and the inventive method to city SAR image denoising respectively, obtain the SAR image after coherent speckle noise filtering as shown in (b), (c), (d) He (e) in Fig. 3.

In order to the superior function of denoising method of the present invention is described better, the present invention calculates the various Performance Evaluating Indexes of four kinds of denoising methods to airport SAR image denoising, comprise mean square deviation (Mean Square Error, MSE), equivalent number (Equivalent Number of Looks, ENL), edge strength index (Edge strength Index, ESI), performance parameter value is as shown in table 1.

The size of MSE represents the number of SAR image quantity of information, and computing formula is such as formula shown in (5), and wherein I is former SAR image, it is SAR image after denoising.Mean square deviation is larger, illustrates that the information that it reflects is more.

$\mathrm{MSE}=\frac{1}{\mathrm{MN}}\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{|I(i,j)-\stackrel{\&OverBar;}{I}(i,j)|}^2---\left(5\right)$

ENL is the index weighing SAR image coherent speckle noise relative intensity, the coherent speckle noise filtering ability of reflection wave filter, computing formula such as formula shown in (6), wherein μ and σ ²be respectively SAR image after Speckle reduction the average of smooth region pixel and variance.ENL is larger, represents that the coherent speckle noise in SAR image is more weak.

$\mathrm{ENL}=\frac{{\mathrm{\&mu;}}^2}{{\mathrm{\&sigma;}}^2}---\left(6\right)$

ESI defines such as formula shown in (7), wherein it is SAR image after Speckle reduction the average of i-th homogeneous region, be the average of i-th homogeneous region of former SAR image I, ESI is larger, and edge keeps better.

$\mathrm{ESI}=\frac{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}|R_j^j-R_{\stackrel{\&OverBar;}{I}}^j|}{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}|R_I^j-R_I^j|}---\left(7\right)$

The denoising performance index of table 1 four kinds of denoising methods

Denoising method	MSE	ENL	ESI
				Wavelet-SP method	0.1768	7.3552	0.7645
Shearlet-SP method	0.1658	7.4369	0.8026
				Wavelet-Shearlet-SP method	0.1428	8.6875	0.8132
The inventive method	0.1256	9.2147	0.8707

Experiment three is discussed under different noise level, and four kinds of SAR image denoising methods are to the quantitative comparison of the rejection of noise.In general, after denoising, the Y-PSNR of SAR image is larger, and denoising method performance must be better.Y-PSNR definition is such as formula shown in (8).

$\mathrm{PSNR}=10{\log }_{10}\left(\frac{{255}^2}{\mathrm{MSE}}\right)---\left(8\right)$

To the experiment SAR image I shown in Fig. 4 (a), respectively with added noise variance for independent variable, take Y-PSNR as dependent variable, obtain Wavelet-SP method, Shearlet-SP method, Wavelet-Shearlet-SP method and the inventive method to SAR image denoising performance comparison curves, as shown in Fig. 4 (b).

Can find out based on above three experiments, still comprise more noise spot in the SAR image after the denoising of Wavelet-SP method, it is fuzzy that point target also exists to a certain degree.Shearlet-SP method can select threshold parameter adaptively, has good edge sharpening effect.Wavelet-Shearlet-SP method utilizes sparse Optimized model and greedy algorithm to obtain the low frequency component of SAR image, utilize band limit, non-sampling, compactly supported wavelet and band limit, compact schemes shearing wave to achieve the Speckle reduction process of high fdrequency component center line characteristic sum point patterns, effect is better.The present invention then considers the non-openness of low frequency sub-band, a small amount of noise should be filtered out and keep large scale marginal information again, adopt and carry out filtering from snake diffusion, consider the openness of high-frequency sub-band, adopt sparse optimization denoising model to complete the coherent spot filtering of SAR image.As can be seen from the denoising performance evaluation index of table 1, denoising method of the present invention is better than other similar three methods in many aspects, not only eliminates the coherent speckle noise of SAR image, and farthest remains the marginal information of image.

Claims (2)

1., based on the Contourlet territory SAR image denoising method from snake diffusion and rarefaction representation, it is characterized in that, comprise the following steps:

Step one a: width of input option comprises the SAR image of noise, its dimension is N × N;

Step 2: first certain to noisy SAR image cycle spinning distance, what overcome contourlet transformation moves sex change, then Contourlet decomposition is carried out to the SAR image after translation, wherein LP structure adopts " 9-7 " biorthogonal wavelet to decompose, the direction number of DFB is 8, retains and extracts the low frequency sub-band coefficient of SAR image and the high-frequency sub-band coefficient in 8 directions;

Step 3: for not having openness low frequency sub-band, utilizing, from snake diffusing filter, DIFFUSION TREATMENT being carried out to image, and the coefficient after filtering process is estimated as the local mean value of SAR image low frequency sub-band in Contourlet territory;

Step 4: for having openness high-frequency sub-band, utilizes sparse representation model to construct the optimal model of denoising, utilizes the orthogonal matching pursuit algorithm improved to solve the sparse coefficient of high-frequency sub-band;

Step 5: the low frequency coefficient estimating to obtain and high frequency coefficient are carried out Contourlet inverse transformation and oppositely translation, returns to the ordering the same with original image, obtain the SAR image after denoising.

2. a kind of based on the Contourlet territory SAR image denoising method from snake diffusion and rarefaction representation as claimed in claim 1, it is characterized in that: step 4 specifically comprises the following steps:

Step 1: due to the high-frequency sub-band pairwise orthogonal in 8 directions, so first the high-frequency sub-band in 8 directions recombinated according to the orthogonal feature of correspondence, forms 4 directional subbands;

Step 2: the h getting each pixel in 4 directional subband images ₀× h ₀in neighborhood, column vector is end to end is rearranged to dimensional vector;

Step 3: choose the Gauss measurement matrix of stochastic distribution as redundant dictionary Φ, its dimension is wherein respectively the directional subband column vector of 4 in step 2 is measured;

Step 4: at I ²each atom of normalization dictionary Φ under norm meaning, with the rarefaction representation coefficient of 4 directional subband column vectors under dictionary Φ in the orthogonal matching pursuit algorithm calculation procedure 2 improved;

Step 5: obtain 4 direction high-frequency sub-band are recovered the high-frequency sub-band being reassembled as 8 directions.