CN103020922A - PCA (principal component analysis) transformation based SAR (synthetic aperture radar) image speckle suppression method - Google Patents

Abstract

The invention discloses a PCA (principal component analysis) conversion based SAR (synthetic aperture radar) image speckle suppression method which mainly solves the problem that an existing PCA transform domain denoising method cannot be applied to SAR images with multiplicative noise models. The method includes the steps: taking pieces of an SAR image and selecting similar pieces from a training sample searching window to form a sample matrix; calculating a covariance matrix of the sample matrix, and solving eigenvalue and eigenvector; transforming the eigenvalue and eigenvector to obtain noise containing feature coefficient; using a minimum linear mean square error to estimate the noise containing feature coefficient; using the estimated feature coefficient to reconstruct the image pieces, and averaging repeatedly estimated pixels to obtain a basic denoising result; and repeating the process under basic filtering results to obtain satisfactory filtering effects. Point target and marginal texture detail information are maintained during speckle suppression, speckle suppression effects of SAR images are improved, and the method can be used for SAR image target recognition and terrain classification.

Description

Based on the relevant speckle suppression method of the SAR image of PCA conversion

Technical field

The invention belongs to image data processing technology field, specifically a kind of relevant speckle suppression method can be used for the inhibition of SAR Image Speckle noise.

Background technology

Synthetic-aperture radar SAR is a kind of high-resolution imaging radar.It has round-the-clock, multipolarization, and from various visual angles, many angles of depression data retrieval capabilities reaches the penetration capacity to some atural objects, not only is widely used in the military affairs, on agricultural, meteorology, topography and geomorphology, the condition of a disaster monitoring etc. are civilian a large amount of application is arranged also.But because SAR emission is coherent wave, these coherent waves through with the back scattering effect of the relevant effect, particularly atural object of atural object, make target echo signal produce decay, be exactly coherent speckle noise on the present image of this attenuation meter.Because the defective of principle, cause the SAR image to exist serious coherent speckle noise, affected follow-up image interpretation, therefore how to have suppressed the coherent speckle noise in the SAR image, improving the deciphering ability of image and obtaining more information becomes an important problem.The primary goal that SAR image coherent spot suppresses is in the filtering speckle noise, keeps as much as possible the detailed information of image.

The coherent speckle noise of SAR image is a kind of Multiplicative noise model of complexity, for this special character of speckle noise, in the recent two decades in the past, people have proposed the relevant speckle suppression method of SAR image of a lot of classics, such as Lee filtering, enhanced Lee filtering, Kuan filtering etc.These methods are to estimate the variance of local coherent speckle noise with a defined good wave filter window, and carry out filtering and process, and its result is the undue level and smooth edge details information of image usually, has obtained to a certain extent preferably effect.Except carry out the inhibition of image coherent spot in the spatial domain, nineteen ninety-five, American scholar Donoho is incorporated into wavelet theory in the image denoising, has proposed the wavelet soft-threshold method.The wavelet soft-threshold method has been started the beginning that transform domain carries out image denoising, and the outstanding achievement of having emerged in large numbers afterwards many transform domain denoisings comprises the image de-noising method of multi-scale transform.The wavelet soft-threshold method is a kind of nonlinear algorithm, still has the problem of destroying image detail information, and is also bad to the radiation characteristic maintenance of image.

The PCA conversion is widely used in a lot of fields as the related tool of a kind of Data Dimensionality Reduction and denoising, such as recognition of face etc.The existing people of PCA conversion is used for doing the denoising of natural image, the same with wavelet transformation, it also can catch the architectural feature of image, but the two-dimensional wavelet transformation of being opened by the one dimension wavelet basis, the optimum that is not image represents, with a fixing wavelet basis can't presentation video in a large amount of abundant partial structurtes, therefore based on the denoising method of small echo, can introduce visual cut, namely modal in the transform domain " ring " phenomenon.Some problems of bringing in order to overcome the Noise Elimination from Wavelet Transform method, the people such as Muresan and Parks have proposed the strategy of the PCA denoising of spatially adaptive for the first time.The people such as Lei Zhang in 2010 and Weisheng Dong have proposed the better method of performance on the algorithm basis of Muresan, this method is PLG-PCA, its effect is very nearly the same with the associating filtering BM3D method of at present very outstanding non-local mean method NLM and three-dimensional bits coupling, but above PCA algorithm only is applied in the natural image that noise model is additivity at present, and can not use noise model is in the SAR image of the property taken advantage of.

Summary of the invention

The object of the invention is to propose the relevant speckle suppression method of a kind of SAR image based on the PCA conversion, the PCA transform domain denoising method of excellent performance is expanded in the SAR image that noise model is the property taken advantage of holding point target and edge details information when realizing the abundant filtering of SAR image.

For achieving the above object, technical solution of the present invention comprises the steps:

(1) gets a pixel x of SAR image, centered by pixel x, get the neighborhood window of 7 * 7 sizes, be designated as image block v;

(2) getting 21 * 21 large window centered by pixel x is training sample search window, and chooses the image block s similar to image block v in training sample search window, jointly forms sample matrix X;

(3) calculate the covariance matrix Ω of sample matrix X, obtain eigenwert and the proper vector of covariance matrix Ω;

(4) eigen vector is carried out the PCA conversion, be about to the eigenwert of covariance matrix Ω by arranging from big to small, obtain New Characteristics value V, the corresponding proper vector of eigenwert is also rearranged, obtain New Characteristics vector P;

(5) by the centralization matrix of sample matrix X

Transposed matrix P with proper vector P ^T, try to achieve noisy characteristic coefficient: $Y=\stackrel{\‾}{X}{P}^T;$

(6) with the first row Y of linear minimum mean-squared error method to noisy characteristic coefficient Y ₁Estimate the characteristic coefficient after obtaining estimating

(7) with the characteristic coefficient after estimating

The reconstructed image piece obtains the image block after the denoising

Wherein, μ is the average of sample matrix X;

(8) image block that each pixel of SAR image is corresponding carries out step (2)-step (7) and processes, and to the pixel that some repeat to estimate, is averaged, and obtains basic denoising result;

(9) on basic denoising result, upgrade noise level, repeat again a step (1)-step (8), obtain final squelch result.

The present invention compared with prior art has the following advantages:

1, the present invention is in SAR image coherent spot process of inhibition, the characteristic coefficient that adopts the PCA conversion to obtain is rebuild image, can effectively separate clean picture signal and noise signal, make the more abundant also edge details of image filtering and texture information keep good;

2, the present invention is by choosing the similar image piece, overcome wavelet soft-threshold filtering because of can't presentation video a large amount of abundant partial structurtes, the pseudo-Gibbs' effect that produces during to squelch, i.e. ringing;

3, the present invention is by choosing the similar image piece and with characteristic coefficient image being rebuild, and at the smooth effect of smooth region, the reservation aspect of edge details and texture information is all more desirable than the relevant speckle suppression method of other existing SAR image.

Description of drawings

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

Fig. 2 is the SAR image of the artificial composograph simulation of two width of cloth of emulation use of the present invention;

Fig. 3 is the SAR image of the barbara natural image simulation of emulation use of the present invention;

Fig. 4 is the SAR image of the optical imagery simulation of emulation use of the present invention;

Fig. 5 is the real amplitude SAR image that emulation of the present invention is used;

Fig. 6 is the real strength S AR image that emulation of the present invention is used;

Fig. 7 is the as a result figure after using existing method and the present invention to the SAR image filtering of the artificial composograph simulation of first width of cloth;

Fig. 8 is the as a result figure after using existing method and the present invention to the SAR image filtering of the artificial composograph simulation of second width of cloth;

Fig. 9 is the as a result figure after using existing method and the present invention to the SAR image filtering of barbara natural image simulation;

Figure 10 is the as a result figure after using existing method and the present invention to the SAR image filtering of optical imagery simulation;

Figure 11 is the as a result figure after using existing method and the present invention to real amplitude SAR image filtering;

Figure 12 is the as a result figure after using existing method and the present invention to real strength S AR image filtering.

The implementation step

With reference to Fig. 1, specific implementation step of the present invention is as follows:

Step 1 is got a pixel x of SAR image, gets the neighborhood window of 7 * 7 sizes centered by pixel x, is designated as image block v.

Step 2, getting 21 * 21 large window centered by pixel x is training sample search window, and chooses the image block s similar to image block v in training sample search window, jointly forms sample matrix X:

2a) choosing 250 larger corresponding image blocks of value of d (v, s) in training sample search window is similar image block s, the similarity degree between d (v, s) presentation video piece v and the image block s wherein, and two image blocks are more similar, and value is more near 0,

Similarity degree for two image blocks of amplitude SAR image is calculated as follows:

$d(v,s)=2L(k\ln 2+\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\ln |v_i|+\ln |s_i|-\ln |v_i^2+s_i^2\left|\right),$

For the similarity degree of two image blocks of strength S AR image, its computing formula is:

$d(v,s)=L(2k\ln 2+\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\ln |v_i|+\ln |s_i|-2\ln |v_i+s_i\left|\right),$

Wherein, L is the number of looking of SAR image, v _iI the pixel of presentation video piece v, s _iI the pixel of expression similar image piece s, k is the number of pixel in the image block, value is 49;

2b) image block v is pulled into the first row that row consist of sample matrix X by row, similar image piece s is pulled into other row that row consist of sample matrix X by row.

Step 3 is calculated the covariance matrix Ω of sample matrix X, obtains eigenwert and the proper vector of covariance matrix Ω:

3a) establishing a line number is m, and columns is the sample matrix X of n:

$X=\left[\begin{array}{cccc}{x}_1^1& x_1^2& \·\·\·& x_1^n\\ x_2^1& x_2^2& \·\·\·& x_2^n\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ x_m^1& x_m^2& \·\·\·& x_m^n\end{array}\right],$

Wherein,

An element of the capable q row of expression sample matrix X p, 1≤p≤m, 1≤q≤n;

3b) the take a sample p of this matrix X is capable $X_p=\left[\begin{array}{cc}{x}_p^1& x_p^2\·\·\·x_p^n\end{array}\right],$ Calculate X _pAverage:

3c) by average μ _p, obtain the capable X of p of sample matrix X _pThe centralization matrix:

3d) all row of sample matrix X are pressed step 3b)-step 3c) process, obtain the centralization matrix of sample matrix X

3e) by the centralization matrix Obtain covariance matrix: Wherein,

Expression centralization matrix

Transposition.

Step 4 is pressed from big to small arrangement with the eigenwert of covariance matrix Ω, obtains New Characteristics value V, and the corresponding proper vector of eigenwert is also rearranged, and obtains New Characteristics vector P.

Step 5 is by the centralization matrix of sample matrix X

Transposed matrix P with proper vector P ^T, try to achieve noisy characteristic coefficient: $Y=\stackrel{\‾}{X}{P}^T.$

Step 6 is with the first row Y of linear minimum mean-squared error method to noisy characteristic coefficient Y ₁Estimate the characteristic coefficient after obtaining estimating $\hat{Y}:\hat{Y}=w{Y}_1,$ Wherein, $w=\frac{{\mathrm{\σ}}_l^2}{{\mathrm{\σ}}_l^2+{\mathrm{\σ}}^2}$ The expression weight coefficient, ${\mathrm{\σ}}_l^2=\max [0,{{\mathrm{\μ}}_{Y,d}}^2-{\mathrm{\σ}}^2]$ Represent desirable SAR Characteristic of Image parameter variance, μ _{Y, d}The capable average of d of representation feature coefficient Y,

The additive noise variance of expression SAR picture signal,

With

Variance and the average of noisy SAR image,

Be the coherent spot variance of SAR image, several L calculate by looking of SAR image, for its coherent spot variance of amplitude SAR image by formula namely

Calculate, for its coherent spot variance computing formula of strength S AR image be: ${\mathrm{\σ}}_z^2=(4/\mathrm{\π}-1)/L.$

Step 7 is with the characteristic coefficient after estimating The reconstructed image piece obtains the image block after the denoising

Wherein, μ is the average of sample matrix X.

Step 8, the image block that each pixel of SAR image is corresponding carries out step (2)-step (7) and processes, and repeats the pixel estimated with linear minimum mean-squared error in a plurality of image blocks to being included in, be averaged, obtain basic denoising result.

Step 9 on basic denoising result basis, is upgraded noise level, namely changes the number of looking of image, image is looked number be updated to: L2=10 * L, and wherein, L is the number of looking of original image; Repeat again a step (1)-step (8), obtain final squelch result.

Effect of the present invention can further specify by following emulation experiment:

1. experiment condition

Experiment simulation environment: MATLAB2009a, Intel (R) Pentium (R) 1CPU2.4GHz, Window XP Professional.

The experiment simulation image: the SAR image of the artificial composograph of two width of cloth simulation, added all that to look number be 2 amplitude coherent spot noise, the size of image is 256 * 256; The SAR image of barbara natural image simulation has added that to look number be 4 amplitude coherent spot noise, and the image size is 512 * 512; The SAR image of optical imagery simulation has added that to look number be 8 amplitude coherent spot noise, and the image size is 512 * 512; Real amplitude SAR image is from the defence SAR of office of Britain country, X-band, and 3m resolution, the farmland, a place of England Bedfordshire, it is 3 that image is looked number, the image size is 256 * 256; Real strength S AR image is from the defence SAR of office of Britain country, X-band, and 3m resolution, near the Britain Bedford, it is 6 that image is looked number, the image size is 256 * 256.

Experiment control methods: enhanced Lee filtering, the improvement non-local mean filtering of grand proposition dawn of the phoenix of wavelet soft-threshold filtering and Xian Electronics Science and Technology University's Intellisense and key lab of the image understanding Ministry of Education, front two kinds of methods are the most representative methods in SAR image airspace filter and the frequency domain filtering, and the third method has represented the cutting edge technology that present SAR image coherent spot suppresses.

Experimental result is estimated: make an uproar than PSNR and structural similarity sex index SSIM with peak value, the degree of two indexs reflection squelch and to the maintenance of picture structure, PSNR is larger better to the coherent spot inhibition, the ideal value of SSIM is 1, more the retentivity near 1 pair of picture structure is better, in addition, can also use the equivalent number ENL of smooth region as evaluation criterion for real SAR image, ENL is larger, and smooth effect to the zone is better, also can judge the quality of coherent spot inhibition with subjective visual effect.

2. experiment content and result

Emulation 1, utilize existing enhanced Lee method, wavelet soft-threshold method, improve non-local mean method and the inventive method, SAR image to the artificial composograph simulation of first width of cloth shown in Fig. 2 (a) carries out filtering, filtered result as shown in Figure 7, wherein, Fig. 7 (a) is the filtering figure as a result of enhanced Lee, Fig. 7 (b) is the filtering figure as a result of wavelet soft-threshold, the filtering of Fig. 7 (c) improvement non-local mean is figure as a result, and Fig. 7 (d) is as a result figure of filtering of the present invention.

As can be seen from Figure 7, the present invention will be better than first three methods far away to the noise suppression effect of homogeneous region, and edge keeps good.

Emulation 2, utilize existing enhanced Lee method, wavelet soft-threshold method, improve non-local mean method and the inventive method, SAR image to the artificial composograph simulation of second width of cloth shown in Fig. 2 (b) carries out filtering, filtered result as shown in Figure 8, wherein, Fig. 8 (a) is the filtering figure as a result of enhanced Lee, Fig. 8 (b) is the filtering figure as a result of wavelet soft-threshold, the filtering of Fig. 8 (c) improvement non-local mean is figure as a result, and Fig. 8 (d) is as a result figure of filtering of the present invention.

As can be seen from Figure 8, the present invention will be better than first three methods far away to the noise suppression effect of homogeneous region, and edge keeps good.

Emulation 3, utilize existing enhanced Lee method, wavelet soft-threshold method, improve non-local mean method and the inventive method, SAR image to barbara natural image simulation shown in Figure 3 carries out filtering, filtered result as shown in Figure 9, wherein, Fig. 9 (a) is the filtering figure as a result of enhanced Lee, and Fig. 9 (b) is the filtering figure as a result of wavelet soft-threshold, the filtering of Fig. 9 (c) improvement non-local mean is figure as a result, and Fig. 9 (d) is as a result figure of filtering of the present invention.

As can be seen from Figure 9, the effect of enhanced Lee filtering and wavelet soft-threshold filtering is not ideal, especially can't be satisfactory to the maintenance of texture, and improved non-local mean filter effect promotes greatly, but texture keeps still not as good as the present invention.

Emulation 4, utilize existing enhanced Lee method, wavelet soft-threshold method, improve non-local mean method and the inventive method, SAR image to optical imagery simulation shown in Figure 4 carries out filtering, filtered result as shown in figure 10, wherein, Figure 10 (a) is the filtering figure as a result of enhanced Lee, and Figure 10 (b) is the filtering figure as a result of wavelet soft-threshold, the filtering of Figure 10 (c) improvement non-local mean is figure as a result, and Figure 10 (d) is as a result figure of filtering of the present invention.

As can be seen from Figure 10, enhanced Lee filtering and wavelet soft-threshold filtering effect on grain details information keeps is undesirable and with edge fog, the present invention in the maintenance of edge details and texture information with to improve the non-local mean method very nearly the same.

Emulation 5, utilize existing enhanced Lee method, wavelet soft-threshold method, improve non-local mean method and the inventive method, real amplitude SAR image shown in Figure 5 is carried out filtering, filtered result as shown in figure 11, wherein, Figure 11 (a) is the filtering figure as a result of enhanced Lee, and Figure 11 (b) is the filtering figure as a result of wavelet soft-threshold, Figure 11 (c) is the filtering figure as a result that improves non-local mean, and Figure 11 (d) is as a result figure of filtering of the present invention.

As can be seen from Figure 11, although enhanced Lee filtering can be played certain noise inhibiting ability, but unsatisfactory in the maintenance of edge and grain details, there is the problem of cut in the method for wavelet soft-threshold, the edge keeps slightly being better than enhanced Lee filtering, and no matter improved non-local mean is the squelch to homogeneous zone, or the maintenance of edge all is very outstanding, maintenance to point target is also good, and visually method of the present invention and improved non-local mean are very nearly the same.

Emulation 6, utilize enhanced Lee, wavelet soft-threshold and the present invention carry out filtering to real strength S AR image shown in Figure 6, filtered result as shown in figure 12, wherein, Figure 12 (a) is the filtering figure as a result of enhanced Lee, and Figure 12 (b) is the filtering figure as a result of wavelet soft-threshold, and Figure 12 (c) is as a result figure of filtering of the present invention.

As can be seen from Figure 12, with the filtered result of the inventive method, its texture, edge, point target are all high-visible, and be also very good to the squelch in homogeneous zone, and other two kinds of methods always exist some to make us unacceptable problem.

The peak value of the simulation SAR image after the distinct methods squelch made an uproar compare result such as table 1 than PSNR and structural similarity sex index SSIM.

PSNR and the SSIM of the simulation SAR image after the table 1 distinct methods squelch compare

Table 1 data show that it all is optimum making an uproar the present invention's peak value in being applied to different images than PSNR and structural similarity sex index SSIM.

Average, variance and the equivalent number ENL of the smooth region of the true amplitude SAR image behind the different noise suppressing methods are compared result such as table 2.

Average, variance and the ENL of the smooth region of the true amplitude SAR image after the table 2 distinct methods squelch

Zone 1 in the table 2, zone 2, zone 3 is the Three regions that mark among Fig. 5.

As seen from Table 2, coherent spot to amplitude SAR image suppresses, it is best that the enhanced Lee filtering method keeps in average, and the present invention is also very approaching, the respond well improvement non-local mean of subjective vision obviously has larger deviation on average keeps, all be optimum in the present invention on the standard deviation generally in these methods, and improved non-local mean takes second place, enhanced Lee filtering and wavelet soft-threshold filtering are all poor, and the present invention is best in all methods on final equivalent number ENL.

In sum, the relevant speckle suppression method of the SAR image based on the PCA conversion that the present invention proposes, can be good at keeping marginal information, grain details and the point target of SAR image, and the smooth effect to smooth region is also very desirable, so the present invention is remarkable to the inhibition of SAR image coherent speckle noise.

Claims (4)

1. based on the relevant speckle suppression method of the SAR image of PCA conversion, comprise the steps:

(1) gets a pixel x of SAR image, centered by pixel x, get the neighborhood window of 7 * 7 sizes, be designated as image block v;

(2) getting 21 * 21 large window centered by pixel x is training sample search window, and chooses the image block s similar to image block v in training sample search window, jointly forms sample matrix X;

(3) calculate the covariance matrix Ω of sample matrix X, obtain eigenwert and the proper vector of covariance matrix Ω;

(4) eigen vector is carried out the PCA conversion, be about to the eigenwert of covariance matrix Ω by arranging from big to small, obtain New Characteristics value V, the corresponding proper vector of eigenwert is also rearranged, obtain New Characteristics vector P;

(5) by the centralization matrix of sample matrix X

Transposed matrix P with proper vector P ^T, try to achieve noisy characteristic coefficient:

(6) with the first row Y of linear minimum mean-squared error method to noisy characteristic coefficient Y ₁Estimate the characteristic coefficient after obtaining estimating

(7) with the characteristic coefficient after estimating

The reconstructed image piece obtains the image block after the denoising

Wherein, μ is the average of sample matrix X;

(8) image block that each pixel of SAR image is corresponding carries out step (2)-step (7) and processes, and to the pixel that some repeat to estimate, is averaged, and obtains basic denoising result;

(9) on basic denoising result, upgrade noise level, repeat again a step (1)-step (8), obtain final squelch result.

2. the relevant speckle suppression method of the SAR image based on the PCA conversion according to claim 1, wherein step (2) is described chooses the image block s similar to image block v in training sample search window, carry out as follows:

2a) in training sample search window, choose d (v, s) 250 larger corresponding image blocks of value are similar image block s, wherein, d (v, s) similarity degree between presentation video piece v and the image block s, two image blocks are more similar, and value is more near 0, are calculated as follows for the similarity degree of two image blocks of amplitude SAR image:

For the similarity degree of two image blocks of strength S AR image, its computing formula is:

Wherein, L is the number of looking of SAR image, v _iI the pixel of presentation video piece v, s _iI the pixel of expression similar image piece s, k is the number of pixel in the image block, value is 49;

2b) first row of sample matrix X is that image block v pulls into a row composition by going, and other row of sample matrix X are that similar image piece s pulls into a row composition by row.

3. the relevant speckle suppression method of the SAR image based on the PCA conversion according to claim 1, the covariance matrix Ω of the described calculating sample matrix of step (3) X wherein, carry out as follows:

3a) establishing a line number is m, and columns is the sample matrix X of n:

Wherein,

1≤q≤n represents an element of the capable q row of sample matrix X p;

3b) the take a sample p of this matrix X is capable

Calculate X _pAverage:

3c) by average μ _p, obtain the capable X of p of sample matrix X _pThe centralization matrix:

3d) all row of sample matrix X are pressed step 3b)-step 3c) process, obtain the centralization matrix of sample matrix X

3e) by the centralization matrix

Obtain covariance matrix:

Wherein,

Expression centralization matrix

Transposition.

4. the relevant speckle suppression method of the SAR image based on the PCA conversion according to claim 1, wherein step (6) is described estimates the characteristic coefficient after obtaining estimating with the linear minimum mean-squared error method to noisy characteristic coefficient Y

Undertaken by following formula:

Wherein,

The expression weight coefficient,

Represent desirable SAR Characteristic of Image parameter variance, μ _{Y, d}The capable average of d of representation feature coefficient Y,

The additive noise variance of expression SAR picture signal,

With

Variance and the average of noisy SAR image,

Be the coherent spot variance of SAR image, several L calculate by looking of SAR image, for its coherent spot variance of amplitude SAR image by formula namely

Calculate, for its coherent spot variance computing formula of strength S AR image be:

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