Proceedings of Asia-Pacific Microwave Conference 2007

A New SAR Despeckling Method Based on

Contour et Transform

Guozhong ChenDept. Electronic Engineering of Shanghai Jiao Tong

UniversityShanghai Jiao Tong University

Shanghai, P. R. Chinacgz5 1 ghotmail.com

Abstract-Synthetic Aperture Radar (SAR) image despeckling isan important problem in the SAR applications. The demand forthe speckle reduction of SAR images is to smooth the specklenoise while preserving the structure information of the originalimages. Because Contourlet is a new and more effective signalrepresentation tool than wavelet in many image applications, wepropose an improved despeckling method based on the hiddenMarkov tree (HMT) model in contourlet domain. In the newmethod, a parameter named inter-direction variation coefficientwhich takes advantages of both inter-direction dependency of thecontourlet coefficients and measurement of the sceneheterogeneity is developed to upgrade the performance.Experiments on the real SAR images show that the proposedmethod achieves better performance in contrary to otherdespeckling methods.

Keywords-Synthetic Aperture Radar (SAR); speckle; contourlet

I. INTRODUCTION

SAR is a kind of coherent imaging system that produces arandom pattern, named speckle, which degrades the merit ofthe SAR images and affects their further application seriously.To overcome this drawback in SAR images, it is essential toreduce the speckle before next procedures.

In recent years, the contourlet transform (CT), as a moreeffective two-dimensional tool than wavelet transform [1, 2], isintroduced into the Synthetic Aperture Radar (SAR) imagedespeckling application [4]. Based on the statistical features ofthe contourlet coefficients, Po and Do [2] proposed a contourlethidden Markov tree (CHMT) model for image denoising. Itmakes good use of the inter-scale and intra-scale dependencyof the contourlet coefficients but lacks in capturing sufficientinter-direction dependency. On the other hand, the HMT modelis good at describing a variety of smooth textures but performpoorly when sharp edges or point targets are to be preserved.So, in this paper, we introduce a parameter named inter-direction variation coefficient (IDVC) which takes advantagesof both inter-direction dependency of the contourletcoefficients and measurement of the scene heterogeneity intothe CHMT-based despeckling method to propose an improveddespeckling method.

Finally, we verify our method using the real SAR imagesand the experimental results show that our method can obtain

Xingzhao LiuDept. Electronic Engineering of Shanghai Jiao Tong

UniversityShanghai Jiao Tong University

Shanghai, P. R. Chinaxzhliugsjtu.edu.cn

better performance on the detail preservation of SAR imagescomparing with the other contourlet-based method. Because ofthe lack of the space, only one of the experiments is shown inthis paper.

The remainder of this paper is organized as follows. Section2 concisely reviews the knowledge of the contourlet transform.In section 3, we develop the parameter of IDVC and proposethe new CHMT-based despeckling method using the IDVC. Toverify our method, the experimental results on a real SARimage are exhibited to show the performance of our proposedmethod in section 4. Finally, conclusions are summarized insection 5.

II. CONTOURLET TRANSFORMThe contourlet transform [1] proposed by Minh Do and

Vetterli is a new extension to the wavelet transform in twodimensions. Contourlets not only possess the main features ofwavelets (namely, multiscale and time-frequency localization),but also offer a high degree of directionality and anisotropy [2].

Finest Scale Level

|Band Pass ContourletIrnage Output | Coefficients

h0 ILP No DFB 1-

Low Pass Output

X~~~~Bn PsCoffiients

Coarser Scale Level

Figure 1. Contourlet filter bank

Similar to wavelet, contourlet can decompose the imageinto different scales. But unlike the wavelet which can onlydecompose each scale into two directions, contourlet candecompose each scale into any arbitrarily power of two'snumber of directions and different scales can be decomposedinto different numbers of directions. So the contourlet uses adouble filter-bank structure, namely pyramidal directional filter

1-4244-0749-4/07/$20.00 w2007 IEEE.

banks (PDFB) which is composed of Laplacian Pyramid (LP)that implements the multiresolution decomposition andDirectional Filter Banks (DFB) that implements themultidirection decomposition. Figure 1 displays a blockdiagram of the PDFB structure of the contourlet transform. Thescheme can be iterated on the coarse image [1]. Figure 2illustrates an example of the contourlet transform for a realSAR image using two LP subband levels and 8 directions at thefinest level.

I INC,dV1 (n) =1 EE(DjNk (n))

d k=(1 l)Ncd +l

(1)

where Dj,k (n) is the contourlet coefficients of k-directionsubband at j-scale; n = (x, y) denotes the spatial position of thecoefficients and 1, ..., Ncj .

Then the IDVC parameter can be defined as

IDVCj (n) = EVNc (n) E(Aj (n))11j

(2)

where A, (n) is the coefficients of the low-passed subband at j-scale. All the expectation values E () are estimated in a

corresponding local window.

Direction k

Figure 2. Contourlet decomposition of a SAR image

Based on the statistics for contourlet coefficients of naturalimages, Po and Do [2] proposed a contourlet hidden Markovtree (CHMT) model to incorporate the properties of contourletcoefficients. Although the CHMT model makes good use of theinter-scale and intra-scale dependency of the contourletcoefficients, it lacks in capturing sufficient inter-directiondependency. On the other hand, HMT model is good atdescribing a variety of smooth textures but perform poorlywhen sharp edges or point targets are to be preserved. So, somemeasures can be done to improve the performance of theCHMT model.

III. THE PROPOSED METHOD

A. The inter-direction variation coefficient (ID VC)parameterIn the study of [2], it reveals the strong inter-direction

dependencies of contourlet coefficients; however the CHMTmodel can only capture part of inter-direction dependencies. Asshown in Figure 3, the existing inter-direction dependencies ofCHMT are linked by pair-arrow solid line and that the absentinter-direction dependencies are linked by pair-arrow dashed atj-scale. The j = 1,..., J is the decomposition scale. Forconvenient, we call the existing inter-direction dependencies asa clique and NC j denotes the number of the cliques at the j-scale. From the Figure 3, we can see that the number ofdirections included in each clique is equal, which is denotedas NC d . To compensate for the absent inter-directiondependencies, we introduce a parameter named IDVC.

First, the variation for /-th clique at j-scale is calculated,denoted as V1 (n)

C,j

a)

c)V2

j

2

3

4

< > the existing inter-direction dependencies

<--> the absent inter-direction dependencies

Figure 3. Dependency links between subbands of the contourletdecomposition with 4, 4, 8, and 16 directions from coarse to fine scales

B. Proposed methodIn the original SAR image, speckle-noise is modeled as

multiplicative noise Z = S F, where Z denotes the observedsignal, S denotes the noise-free signal and F represents speckle-noise whose mean is 1. The CF which denotes the normalized

standard deviation of speckle noise equals /IL (where L is

the number of looks) for intensity images and C(412T -1)/L for

amplitude images. One convenient way to deal with themultiplicative model is to define a pseudo additive noise U

Z =S+S(F-1)= S+USince CT is linear, from (3) we have

Az'j (n) = As'j (n) + A'yj(n)DIzi k] (n) = D[yj,k] (n) + D[j k] (n)

(3)

(4)

-W

where the A$jl (n) represent the approximation coefficientsand only the contourlet coefficients Dj k] (n) are processed.The IDVC can be used to measurement of the sceneheterogeneity. According to the analysis in [5] and because ofthe magnitudes of the contourlet coefficients of real-worldimages decaying exponentially across scale [6], we define twothresholds as

IDVCjmin= CFj(1) (5)

IDVCj max = q CFj(1) (6)

where q > 1 is an empirical constant weighting factor. Thenshrink the contourlet coefficients DzJ k] (n) as the followingrules. The D"k](n) denotes the estimation of the noise-freecoefficient DVj k] (n).

Firstly, ifID VCj (n) < ID VCj min it indicates homogeneous

areas and DJk](n) = 0;

Secondly, if ID VC1 (n) > ID VCJ1max' it indicates point or

edge areas and D Jk] (n) = Dzjk] (n) remain unchanged;

The variance (ot[jk](n)) can be calculated with 0 and

(0f[4, ](n)) [2].

(12)

where (x)+ = x for x> 0 and (x)+ = 0 for x < 0 . In the formulasabove, all the parameters of the observed data Z including

Cz and j ,k, (n) can be estimated in a corresponding localwindow.

At last, the application of the inverse CT on the shrinkagecoefficients and the approximation coefficients can get finaldespeckling image.

IV. EXPERIMENTAL RESULTSWe tested our method on the real SAR images and only an

experiment of a four-look SAR image is shown here to makecomparison with the other contourlet-based methods, such asCHMT method [2] and SCT-MMSE method [4]. The ENL(Effective Number of Looks) is used to evaluate theeffectiveness in speckle suppression (for two regions). TheENL is defined as

Thirdly, if ID VCJ(n) e [ID VCj min' ID VCj max] , DZ k](n)are shrunk using the contourlet HMT model proposed in [2].

-[j,k] k]I(Ds (x,y) = E"p (S[jk] (n) =mSfDz/J 2](n),D0

m=O

( f[j,k] (n))2 (7x (r- lys 'n \)' / D[+(k] (n)

where S'j,k](n) is the state for D[Jk](n)p(S[jk] (n) = m DVJk] (n),0) stands for a probability mass

function (pmf) of state S[j,k] (n) = m . 0 is the parameter vectorof contourlet HMT model, which can be calculated using anexpectation maximization (EM) algorithm [2]. The variance ofthe noisy coefficient can be estimated [3], [4]

(Ja,k] )2 2= k]82C2(1 +C2) (8)

where ps and Cs are the mean and coefficients of variation ofSrespectively and they can be calculated as below [3]

PS = /'/I'F =A (9)12 C2

C2 _;Z CF1 + CF (10)

S2j,k] iS computed from the high frequency filter response of

the contourlet transform yf4j,k] [4]

k] =(Yi[k]) (11)

2

ENL =A"2 A {11for intensity imagefor amplitude image (1)

where ,u and c& are the mean and the variance measured withina homogeneous region.

For the assessment of structural feature retention, we adoptthe Pratt's figure of merit (FOM) [7].

FOM 1 (14)max(NA,NI) j=1+d7I(14)

where NA and NI are the number of the original and filterededge pixels respectively, d, is the Euclidean distance betweenthe original edge pixel i and the nearest filtered edge pixel, and,6 is a constant typically set to 1/9 . FOM ranges between 0and 1, with unity for idea edge detection.

Two uniform regions in the real SAR image are selected forthe ENL analysis, which is shown in figure 4(a). The finalexperimental results of the SCT-MMSE method, the CHMTmethod and our proposed method are shown in figure 4(b),figure 4(c) and figure 4(d) respectively. The values ofENL andFOM are listed in Table I.

V. CONCLUSIONThis paper proposed an improved contourlet HMT-based

method for SAR image despeckling by considering the inter-direction dependencies and scene heterogeneity. The real SARimages are tested to verify our method and experimental resultsshow that our method can obtain better performance on boththe speckle suppress and the detail preservation of SAR images.For the future work, we will introduce Markov random fieldmodeling into our method.

-'J"k] 2=

( o-, j, k, )2_ (0-,j',k] )2

(ODSI. (n)) D, ,(n) D, (n)

REFERENCES

[1] Do, MN., and Vetterli, M., "The contourlet transform: an efficientdirectional multiresolution image representation," IEEE Trans. ImageProcess., 2005, 14, (12), pp. 2091-2016.

[2] Po, D.D.-Y., and Do, MN., "Directional multiscale modeling of imagesusing the contourlet transform," IEEE Trans. Image Process., 2006, 15,(6), pp. 1610 1620.

[3] S. Foucher, G.B. Bnie and J.-M. Boucher, "Multiscale NMAP Filteringof SAR Images," IEEE Trans. Image Proc., vol. 10, no. 1, pp. 49 6,2001.

[4] Foucher, S., Farage, G., and Benie, G., "SAR Image Filtering based onthe Stationary Contourlet Transform," In Proc IGARSS 2006, July 2006,pp.4021 -4024.(a b

[5] F. Argenti and L. Alparone, "Speckle removal from SAR images in the (a) (b)undecimated wavelet domain," IEEE Trans. Geosci. Remote sens., vol.40, no. 11, pp. 2363-2374,Nov. 2002.

[6] 5. Mallat, "A Wavelet Tour of Signal Processing," New York:Academic, 1998.

[7] Yongjian Yu, Scott T. A., "Speckle reducing anisotropic diffusion,"IEEE Trans. Image Processing, 11(11). 927-935, 2002.

TABLE I. THE ENL AND FOM VALUES

ENL

Region 1 Region 2 FOM (c) (d)

The original 7Z112 6.946 Figure 4. the experimental results of the real SAR image. (a) is the originalimage; (b) is the result of the SCT MMSE method; (c) is the result of the

SCT-MMSE 64.13 60.54 0.621 CHMT method; (d) is the result of the proposed method.

CHMT-based Filter 70.01 69.23 0.703

The proposed method 76.43 74.26 0.826