CN101980286B - Method for reducing speckles of synthetic aperture radar (SAR) image by combining dual-tree complex wavelet transform with bivariate model - Google Patents

Abstract

The invention discloses a method for reducing the speckles of a synthetic aperture radar (SAR) image by combining dual-tree complex wavelet transform with a bivariate model, which mainly solves the problems that speckle noise cannot be well inhibited and part of edge information and detailed information are lost in the conventional method for reducing the speckles of the SAR image. The method comprises the following steps of: performing dual-tree complex wavelet decomposition on the original SAR image to obtain a real part and an imaginary part of a decomposition coefficient on each scale; solving the variance of a noise coefficient by using a non-logarithmic additive noise model; solving the edge variances of the real parts and the imaginary parts of the complex wavelet coefficient by using a local neighborhood window; solving a threshold contraction function by maximum posterior estimation and performing threshold contraction on the dual-tree complex wavelet decomposition coefficient; and performing dual-tree complex wavelet reconfiguration on the contracted coefficient to obtain an image of which the speckles are reduced. The method has the advantages of capability of effectively removing the speckle noise from the SAR image and high edge preserving performance, and can be used for reducing the speckles of the SAR images with abundant edge information and detailed information, particularly the airport, runway and road-containing SAR images.

Description

SAR image method for reducing speckle in conjunction with dual-tree complex wavelet and two-varaible model

Technical field

The invention belongs to technical field of image processing, relate to picture noise and suppress, specifically a kind of SAR image method for reducing speckle of multiple wavelet field can be used for the inhibition of the speckle noise of diameter radar image.

Background technology

Synthetic aperture radar (SAR) is a kind of high-resolution imaging radar.It has round-the-clock, multipolarization, from various visual angles, many angles of depression data retrieval capabilities and to the penetration capacity of some atural objects, not only be employed widely militarily, on agricultural, meteorology, topography and geomorphology, the condition of a disaster monitoring etc. are civilian, number of applications 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 the coherent spot spot noise on the present image of this attenuation meter.Therefore how to suppress the coherent speckle noise in the image, improving the deciphering ability of image and obtaining more information becomes an important problem.

The primary goal that spot falls in the SAR image is in the filtering speckle noise, keeps the detailed information of image as much as possible.Speckle noise is a kind of signal of multiplicative noise model of complicacy.For this special nature of speckle noise, in the recent two decades in the past, people have proposed the SAR method for reducing speckle of a lot of classics, like Lee filtering, and enhanced Lee filtering, Kuan filtering or the like.These methods are to estimate the variance of local speckle noise with a wave filter window that has defined, and carry out Filtering Processing, the level and smooth edge details information that its result is usually undue, and these methods have all been received effect preferably to a certain extent.Nineteen ninety-five, American scholar Donoho is incorporated into wavelet theory in the image denoising, has proposed small echo soft-threshold method.Small echo 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.

Wavelet transform owing to have lacks the shortcoming of translation invariance and relatively poor directional selectivity; People such as nearest Britain scholar Kingsbury have proposed the dual-tree complex wavelet conversion; Application in image denoising tentatively demonstrates its remarkable advantages: compare with wavelet transform; The dual-tree complex wavelet conversion effectively solves the ringing effect that occurs in the wavelet transform because it has approximate translation invariance and more directional selectivity.But this dual-tree complex wavelet conversion method for reducing speckle does not take into full account geometric properties and the SAR image of image in the statistical property of multiple wavelet field and the local correlations between the coefficient; The speckle noise filtering of falling the SAR image smoothing zone behind the spot is insufficient, the details and the marginal information partial loss of image simultaneously.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned prior art; A kind of SAR image method for reducing speckle that combines dual-tree complex wavelet and two-varaible model is proposed; The speckle noise in the SAR image smoothing zone behind the spot, the details and the marginal information of complete reservation image fall with abundant filtering.

The technical thought that realizes the object of the invention is translation invariance and the multi-direction selectivity that combines the dual-tree complex wavelet conversion; Utilize the real imaginary part two-varaible model of multiple wavelet coefficient that high frequency coefficient is decomposed in the dual-tree complex wavelet conversion and carry out the self-adaptation atrophy, obtain the SAR image of filtering speckle noise, reservation detailed information.Its concrete performing step comprises as follows:

(1) original SAR image I is carried out dual-tree complex wavelet and decompose, obtain the decomposition complex coefficient y on yardstick j _j, its real part and imaginary part are respectively y _{R, j}, y _{I, j}

(2) utilize non-logarithm additive noise model, find the solution the noise variance

on each yardstick

(3) utilize the local neighborhood window, find the solution the real part edge standard deviation sigma of multiple wavelet coefficient on yardstick j respectively _{R, j}With imaginary part edge standard deviation sigma _{I, j}

(4) respectively the real part of the complex coefficient on yardstick j and imaginary part are carried out threshold value and shrink, the nothing of the trying to achieve estimation wavelet coefficient

of making an uproar

(5), obtain falling the image

behind the spot to coefficient

the operation dual-tree complex wavelet reconstruct after the reduction

The present invention compared with prior art has following advantage:

1) the present invention is owing to adopt non-logarithm additive noise model, utilizes this model can avoid in the property taken advantage of model conversation during for additive model, the deficiency of bringing because of the operation of taking the logarithm to the radiation characteristic maintenance of original image.The radiation characteristic that therefore can keep original image more fully.

2) the present invention has fully taken into account the directivity characteristics and the local characteristics of SAR image itself owing to utilize the real imaginary part two-varaible model of multiple wavelet coefficient, has kept abundant image edge and detailed information more, fully filtering the regional speckle noise of SAR image smoothing.

3) simulation result shows, the inventive method is than the SAR image method for reducing speckle of other several kinds of existing classics, is all increasing significantly aspect the smooth effect of smooth region and the edge hold facility.

Description of drawings

Fig. 1 is a FB(flow block) of the present invention;

To be the present invention fall spot simulation result comparison diagram with existing two kinds of method for reducing speckle are applied to X-band amplitude SAR image to Fig. 2;

To be the present invention fall spot simulation result comparison diagram with existing two kinds of method for reducing speckle are applied to Ku band strength SAR image to Fig. 3.

Embodiment

With reference to Fig. 1, concrete performing step of the present invention is following:

Step 1 is carried out dual-tree complex wavelet to input SAR original image and is decomposed.

Import original SAR image and be designated as I, this SAR image itself is exactly by the image of speckle noise pollution, therefore need be as studying the natural image denoising; Add the noise of a random noise or certain specific character for former figure; Can directly fall spot and handle, the original SAR image I of input carried out dual-tree complex wavelet decompose, obtain one and a low-frequency image and J yardstick this image; Each yardstick has 6 high frequency imagings, and the multiple wavelet coefficient of high frequency imaging is designated as y on yardstick j _j

y _j＝y _r，j+i·y _i，j (1)

Y wherein _{R, j}Be multiple wavelet coefficient real part, y _{I, j}Be multiple wavelet coefficient imaginary part.

Step 2; Utilize non-logarithm additive noise model, find the solution the noise variance

on each yardstick

(2a) utilize non-logarithm additive noise model, be the original SAR graphical representation of importing:

I＝RX＝X+(R-1)X＝X+N (2)

Wherein R represents coherent spot; Its average is 1; Variance is that

X represents the true backscatter intensity of atural object, N be will filtering additive noise; Every bit from the original SAR image of input is got square window I (k), and window size is k * k, calculates the noise variance of each local square window:

${\mathrm{\σ}}_{N\left(k\right)}^2=({\mathrm{\σ}}_{I\left(k\right)}^2+m_{I\left(k\right)}^2)\·{\mathrm{\σ}}_R^2/({\mathrm{\σ}}_R^2+1)---\left(3\right)$

M wherein _{I (k)},

Average and the variance of representing local window I (k) respectively,

Be coherent spot R variance, the k value is 3,5,7;

(2b) noise variance

of each local square window is averaged, obtains that noise variance is on each yardstick:

${\mathrm{\σ}}_n^2=\mathrm{mean}\left({\mathrm{\σ}}_{N\left(k\right)}^2\right).---\left(4\right)$

Step 3 is utilized the local neighborhood window, finds the solution the real part edge standard deviation sigma of multiple wavelet coefficient on yardstick j respectively _{R, j}With imaginary part edge standard deviation sigma _{I, j}

Respectively to answering the real part y of wavelet coefficient on the j yardstick _{R, j}With imaginary part y _{I, j}In each point get square window N (l), window size is l * l, utilizes following formula to calculate on yardstick j the real part edge standard deviation sigma of multiple wavelet coefficient respectively _{R, j}With imaginary part edge standard deviation sigma _{I, j}:

${\mathrm{\σ}}_{r,j}=\sqrt{\max (1/M\·{\mathrm{\Σ}}_{m\∈N\left(l\right)}{y}_{r,j}^2\left(m\right)-{\mathrm{\σ}}_n^2,0)}---\left(5\right)$

${\mathrm{\σ}}_{i,j}=\sqrt{\max (1/M\·{\mathrm{\Σ}}_{m\∈N\left(l\right)}{y}_{i,j}^2\left(m\right)-{\mathrm{\σ}}_n^2,0)}---\left(6\right)$

Wherein M is the number of coefficient among the square window N (l), and the l value is 3,5,7.

Step 4; Respectively the real part of the complex coefficient on the j yardstick and imaginary part are carried out threshold value and shrink, the nothing of the trying to achieve estimation wavelet coefficient

of making an uproar

(4a) establish that real part and the imaginary part of multiple wavelet coefficient of arbitrary yardstick is approximate to satisfy following the distribution:

$p_y\left(y\right)=\frac{3}{2{\mathrm{\π\σ}}^2}\·\exp (-\frac{\sqrt{3}}{\mathrm{\σ}}\sqrt{y_{r,j}^2+y_{i,j}^2})---\left(7\right)$

Wherein σ is multiple wavelet coefficient edge standard deviation, y _{R, j}With y _{I, j}Be respectively the real part and the imaginary part of multiple wavelet coefficient on the j yardstick;

The maximum a posteriori of (4b) finding the solution no noise cancellation signal on yardstick j estimates that MAP estimates, obtains the contracting function

of multiple wavelet coefficient real part on the j yardstick and the contracting function

of imaginary part and is respectively:

${\hat{w}}_{r,j}=\frac{\mathrm{soft}(\sqrt{y_{r,j}^2+y_{r,j}^2}-\frac{\sqrt{3}{\mathrm{\σ}}_n^2}{\mathrm{\σ}})}{\sqrt{y_{r,j}^2+y_{r,j}^2}}\·y_{r,j}---\left(8\right)$

${\hat{w}}_{i,j}=\frac{\mathrm{soft}(\sqrt{y_{i,j}^2+y_{i,j}^2}-\frac{\sqrt{3}{\mathrm{\σ}}_n^2}{\mathrm{\σ}})}{\sqrt{y_{i,j}^2+y_{i,j}^2}}\·y_{i,j}---\left(9\right)$

Wherein soft (g) is defined as:

$\mathrm{soft}\left(g\right)=\left\{\begin{array}{cc}0& g<0\\ g& g\&GreaterEqual;0\end{array}\right.;---\left(10\right)$

(4c) find the solution multiple small echo real part threshold value T on yardstick j _{R, j}With imaginary part threshold value T _{I, j}In higher value T _j

T _j＝max(T _r，j，T _i，j) (11)

Wherein

σ _{R, j}, σ _{I, j}Be respectively the real part edge standard deviation and the imaginary part edge standard deviation of multiple wavelet coefficient on the j yardstick;

(4d) on the j yardstick, utilize following formula to carry out threshold value and shrink, calculate multiple wavelet coefficient on the j yardstick after the reduction:

${\hat{w}}_j=\mathrm{soft}\left(\right|y_j|-T_j)\&CenterDot;e^{i\&CenterDot;\mathrm{\&theta;}\left(y_j\right)}---\left(12\right)$

θ (y wherein _j) expression y _jThe radian value of direction.

Step 5; High frequency coefficient and the low-frequency image of 6 directions of J yardstick after the reduction are imported dual-tree complex wavelet reconfigurable filter group carry out reconstruct, what finally obtain reconstruct falls spot image

Effect of the present invention can further specify through following simulation result.

1. experiment content

Experiment 1, spot falls in the amplitude SAR image that the method for reducing speckle and the method for reducing speckle of the present invention of existing Gamma-MAP method for reducing speckle, classical two-varaible model is applied to X-band.

Experiment 2, spot falls in the strength S AR image that the method for reducing speckle and the method for reducing speckle of the present invention of Gamma-MAP method for reducing speckle, classical two-varaible model is applied to the Ku wave band.

The present invention utilizes equivalent number ENL, and image average M and standard deviation V are as estimating the objective standard that the spot performance falls in the SAR image.ENL is high more, explain smooth region to fall the spot performance good more, the average of falling behind the spot is good more near the original image average more, spot falls and after standard deviation low more, explain that smooth effect is good more.Comparing result further illustrates the superiority of the present invention aspect noise reduction.

2. experimental result

The result of experiment 1 is as shown in Figure 2, and wherein Fig. 2 (a) is former SAR image, and Fig. 2 (b) falls the spot result for the Gamma-MAP method, and Fig. 2 (c) falls spot figure for the method for classical two-varaible model, and Fig. 2 (d) falls spot figure as a result for the present invention.Rectangular area 1,2 shown in Fig. 2 (a) is to calculate the required homogeneous region of ENL in the table 1, and table 1 has been listed average, variance and the equivalent number comparing result of the simulation result gained of emulation content 1.

Table 1: different method for reducing speckle objective indicators are estimated: equivalent number ENL, average M, standard deviation V

Can find out that from table 1 the present invention has obtained the equivalent number higher than existing additive method, fall image average behind the spot very near the original image average, the standard deviation of falling behind the spot is minimum.Therefore the present invention obtained than other method for reducing speckle more excellent the spot effect smoothly falls.

The result of experiment 2 is as shown in Figure 3, and wherein Fig. 3 (a) is former SAR image, and Fig. 3 (b) falls the spot result for classical Gamma-MAP method, and Fig. 3 (c) falls spot figure for the method for classical two-varaible model, and Fig. 3 (d) falls spot figure as a result for the present invention.Rectangular area 3,4 shown in Fig. 3 (a) is to calculate the required homogeneous region of ENL in the table 2.Table 2 has been listed average, variance and the equivalent number comparing result of the simulation result gained of emulation content (2).

Table 2: different method for reducing speckle objective indicators are estimated: equivalent number ENL, average M, standard deviation V

Can find out that from table 2 the present invention has obtained the equivalent number higher than additive method, fall image average behind the spot very near the original image average, the standard deviation of falling behind the spot is minimum.Therefore the present invention obtained than other method for reducing speckle more excellent the spot effect smoothly falls.

Claims (1)

1. One kind combine dual-tree complex wavelet and two-varaible model SAR image method for reducing speckle, comprise the steps:

   (1) original SAR image I is carried out dual-tree complex wavelet and decompose, obtain the decomposition complex coefficient y on yardstick j _j, its real part and imaginary part are respectively y _{R, j}, y _{I, j}

   (2) utilize non-logarithm additive noise model, find the solution the noise variance

   

   on each yardstick

   (2a) according to non-logarithm additive noise model, the every bit of I in the original image is got square window I (k), window size is k * k, asks the noise variance of each local square window:

   ${\mathrm{\&sigma;}}_{N\left(k\right)}^2=({\mathrm{\&sigma;}}_{I\left(k\right)}^2+m_{I\left(k\right)}^2)\&CenterDot;{\mathrm{\&sigma;}}_R^2/({\mathrm{\&sigma;}}_R^2+1)$

   M wherein _{I (k)},

   

   Average and the variance of representing local window I (k) respectively,

   

   Be the coherent speckle noise variance of former figure I, k gets 3,5, and 7;

   (2b) noise variance

   

   of each local square window is averaged, obtains the noise variance on each yardstick:

   ${\mathrm{\&sigma;}}_n^2=\mathrm{mean}\left({\mathrm{\&sigma;}}_{N\left(k\right)}^2\right);$

   (3) utilize the local neighborhood window, find the solution the real part edge standard deviation sigma of multiple wavelet coefficient on yardstick j respectively _{R, j}With imaginary part edge standard deviation sigma _{I, j}:

   Respectively to answering the real part y of wavelet coefficient on the j yardstick _{R, j}With imaginary part y _{I, j}In each point get square window N (l), window size is l * l, finds the solution on yardstick j the real part edge standard deviation sigma of multiple wavelet coefficient respectively _{R, j}With imaginary part edge standard deviation sigma _{I, j}

   ${\mathrm{\&sigma;}}_{r,j}=\sqrt{\max (1/M\&CenterDot;{\mathrm{\&Sigma;}}_{m\&Element;N\left(l\right)}{y}_{r,j}^2\left(m\right)-{\mathrm{\&sigma;}}_n^2,0)}$

   ${\mathrm{\&sigma;}}_{i,j}=\sqrt{\max (1/M\&CenterDot;{\mathrm{\&Sigma;}}_{m\&Element;N\left(l\right)}{y}_{i,j}^2\left(m\right)-{\mathrm{\&sigma;}}_n^2,0)}$

   Wherein M is the number of coefficient among the square window N (l), and l gets 3,5,7;

   (4) respectively the real part of the complex coefficient on yardstick j and imaginary part are carried out threshold value and shrink, the nothing of the trying to achieve estimation wavelet coefficient

   

   of making an uproar

   (4a) establish that real part and the imaginary part of multiple wavelet coefficient of arbitrary yardstick is approximate to satisfy following the distribution:

   $p_y\left(y\right)=\frac{3}{2\mathrm{\&pi;}{\mathrm{\&sigma;}}^2}\&CenterDot;\exp (-\frac{\sqrt{3}}{\mathrm{\&sigma;}}\sqrt{y_{r,j}^2+y_{i,j}^2})$

   Wherein σ is multiple wavelet coefficient edge standard deviation, y _{R, j}With y _{I, j}Be respectively the real part and the imaginary part of multiple wavelet coefficient on the j yardstick;

   (4b) find the solution the maximum a posteriori that yardstick j goes up no noise cancellation signal and estimate, the contracting function

   

   that obtains answering on the j yardstick wavelet coefficient real part contracting function and imaginary part is respectively:

   ${\hat{w}}_{r,j}=\frac{\mathrm{soft}(\sqrt{y_{r,j}^2+y_{r,j}^2}-\frac{\sqrt{3}{\mathrm{\&sigma;}}_n^2}{\mathrm{\&sigma;}})}{\sqrt{y_{r,j}^2+y_{r,j}^2}}\&CenterDot;y_{r,j}$

   ${\hat{w}}_{i,j}=\frac{\mathrm{soft}(\sqrt{y_{i,j}^2+y_{i,j}^2}-\frac{\sqrt{3}{\mathrm{\&sigma;}}_n^2}{\mathrm{\&sigma;}})}{\sqrt{y_{i,j}^2+y_{i,j}^2}}\&CenterDot;y_{i,j}$

   Wherein soft (g) is defined as:

   $\mathrm{soft}\left(g\right)=\left\{\begin{array}{cc}0& g<0\\ g& g\&GreaterEqual;0\end{array}\right.$

   (4c) find the solution multiple small echo real part threshold value T on yardstick j _{R, j}With imaginary part threshold value T _{I, j}In higher value T _j

   T _j＝max(T _r，j，T _i，j)

   Wherein

   

   

   σ _{I, j}Be respectively the real part edge standard deviation and the imaginary part edge standard deviation of multiple wavelet coefficient on the j yardstick;

   (4d) on the j yardstick, utilize following formula to carry out threshold value and shrink, calculate the multiple wavelet coefficient after the reduction:

   ${\hat{w}}_j=\mathrm{soft}\left(\right|y_j|-T_j)\&CenterDot;e^{i\&CenterDot;\mathrm{\&theta;}\left(y_j\right)}$

   θ (y wherein _j) expression y _jThe radian value of direction;

   (5), obtain falling image behind the spot to coefficient

   

   the operation dual-tree complex wavelet reconstruct after the reduction

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