2005 IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications Proceedings

SPECKLE FILTERING OF POLARIMETRIC SAR IMAGE AND THE ENHANCEMENT FOR CLASSIFICATION* GUJing, CHEN Yilun, and YANG Jian Dept. of Electronic Engineering, Tsinghua University, Beijing 100084, China

ABSTRACT

In this paper, a new approach to speckle filtering of Syntietic Aperture Radar (SAR) data is presented. We define a parameter space consisting of two orthogonal subspaces - the signal subspace and the noise subspace. Then, the full polarimetric information from the signal subspace is obtained after speckle filtering. Moreover, edges of different kinds of targets are preserved. Using polarimetric SAR data, the effectiveness of the proposed method is not only validate by the standarddeviation-to mean ratio, but also by target classification

1. INTRODUCTION

Several methods for speckle filtering have been investigated in the past years. Lee et aL constructed a multiplicative noise model, and derived two algorithms that produced speckle-reduced images by using the criterion of the Minimum Mean-Square Error (MMSE) [1]. Novak and Burl derived the Polarimetric Whitening Filter (PWF) by using full polarimetric data to generate a single, minimum-speckle intensity image [2] [3]. Lopes et al [4] and Liu et alt [5] proposed a

PWF for Multilook processed data (MIWF). The methods of PWF and MPWF produce single-channel images, and the polarimetric information is lost in the result. Some other techniques using different criteria such as Maximum A Posteriori (MAP) probability and the statistical Maximum Likelihood (M) have also * This work was supported by the National Natural Science Foundation of China(4027 1077), by the National Important Fundamental Research Plan of China(2001CB30940 1), by

thie Science Foundation of National Defence of China, by the Research Fund for the Doctoral Program of Higher Education

suhspace,

respectively.

The

speckle

reduced

polarimetric inlformation can be obtained from the signal subspace, and the details such as edges between ifrn agt r rsre.Fnly h tnad dfeettresaepeeae.Fal,fi tnad

of China, by the Aerospace Technology Foundation of China, and by the Fundamental Research Foundation of Tsinghua University.

0-7803-9128-4/05/$20 .00 ©C 2005 IEEE .

been well studied [6]-[9]. In addition to the filtering of speckle, preservation of the detailed polarimetric information is also important, because one needs to use the filtered data for further applications such as classification [1 0] and edge extraction [1 1]. Conventional methods for speckle filtering are based on the local variance statistics estimation. The accuracy of the estimation requires local uniformity of the pixels in a considered window. In general, for a good speckle filtering, the window should be large, but for good preservation of details, the window should be small. Thus, a tradeoff must be made between these two conflicting requirements. Cloude [12] first considered an eigenvector-based decomposition of the scattering covariance matrix to identify the dominant scattering mechanism via extraction of the largest eigenvalue. This approach has also been used to generate a speckle reduced image [12]. But this method does not work properly if there is more than one target in the considered window. In some cases, there is no significant difference between the two largest eigenvalues. In other words, the polarimetric information is not only contained in the largest eigenvalue and the corresponding eigenvector. Some informatioin will be lost if one neglects any component contributed by smaller eigenvalues. In this paper, we propose a method for overcoming the above problem, based on the subspace decomposition. With this approach, it is no longer necessary to assume uniform features in the considered window. We use a high dimensional parameter vector to describe a pixel, thus more features representing a contribution provided by different targets in a window can be described by this parameter vector. The covariance matrix of this vector is decomposed into two kinds of matrices e corresponding column spaces are called the signazl subspace and the noise

378

large in high reflective areas compared with that of low reflective areas. In order to smooti this variation, tie elements of C before filtering are divided by the root square of the span of the corresponding pixel. For a typical target, there should be a corresponding parameter vector pointing with a typical direction characterizing tis target. The speckle effect would cause a slightly biased direction. This biased direction can be teated as a combination of he tpical direction with a large norm and a random oriented orthogonal direction with a small nom. When an area contains different kinds of targets, it is more likely to have more than one feature. Assuming that there are m (m<10) different typical targets in the area, there should be m linear independent directions for the parameter vectors which span an m-dimensional linear subspace. We call this mr-diensional subspace the "signal subspace". The orthogonal (1 0-m)-dimensional subspace (i.e., the residual subspace) called the ",noise subspace". Polarimetric information is mainly contained in the "signal subspace", while the residual "noise subspace" is useless and due to the speckle effect

deviation-to mean ratio and target classification are studied by polarimetric SAR data, validating the effectiveness of the proposed method 2. SPECKLE MODEL OF POLARIMETRIC DATA

The scattering matrix of a target in a linear horizontal (H) and vertical (V) polarization basis is expressed as:

IS] = L SHH SHV

(1)

In the reciprocal backscattering case SHw= sz. The three elements sH, sn', and sw may be used to define a complex scattering vector:

;,F

x = (sw

S

(2)

is

by the covariance matrix (CM): C xx (3) where the superscript H denotes the conjugate transpose of a vector. Multilook polarimetric data are obtained by averaging CM, e.g.: -

"

C =-EC L

i=1

,

(4)

Table I: Definition of parameters.

where C, is the e single-look sample covariance matrix. A polarimetric SAR provides, in practice, three different images corresponding to the channels: EHH, HV, and VV. These three different data are usually correlated. For a typical target the colTelation allows us to concentrate the relevant informationl in a low dimensional space. On the other hand, speckle noise is uncorrelated with those features as said before. By extracting the dominant infonnation, tie speckle effect may be reduced.

parameter Pi P2 p3 P4

Ps

P6 p7

PI

sp

Plo

3. TIE PARAMETER VECTOR By means of the matrix C , one can construct a parameter vector: parameter vector: (5) p (pl, P2, ... Plo )T There are many possible choices of the parameters p, such as the elements of C, the span, the polarimetric entropy [15], the similarity parameters [16] and so on. In this paper, we define the parameter vector as shown in Table I. Here, is element of a C in the i h row and te j column. Inversely, one canl get the C if the parameter vector is knownl. As anticipated, speckle can be modeled as a signal dependent additive noise [14] for the multilook processed data. The variace of the additive noise is

cq,

379

definition cl /A

c221A

_C33/A

Re{c12}/A

Re {cl}/A

Re {c23 }/A

Imr{C12}/A

IM{C13/A _ the polarimetric entropy IM{c23}/A

A =(1 SHH 12 +21 Sgv 12 + s. 2) , Re(x) and Im{x) are the real and imaginary part of the variable x.

Let us denote with jup the mean vector of a parameter vector p. The covariance matrix of the

parameter vectorp is: (6) Cp=E{(p and may be decomposed as: (7) Cp = QAQT = where A diag ( A1, A2, ..., Alo ) and Al, A2, ..., Alo are the eigenvalues of Ce,. Since Cp, is semi-positive definite, the eigenvalues A, are nonnegative and can be arranged in decreasinlg order, as shown by: (8) Al A > .. >Ala

-1p) (p)T}

q-TAp-),i = 1, 2, ..., 10

The columns of the l -by-l 0 matrix Q in (10) consist of 10 orthogonal eigenvectors ql, q2, ..., qio of Cp that iS~ Q=(q1,q2, qlo) (9)

or equivalently:

These 10 orthogonal eigenvectors define the basis of the 1 0-dimensional linear space spaned by all the parameter vectors in a window. On e oerwherec parameter vector p = (pi, P2, ..., p10) derived from C may be expanded as a linear combination of the eigenvectors ql, q2, ..., qlo and the mean vector If there are m targets in the considered area, and if noise exits, then we would have m larger eigenvalues A1, A2, ..., Am, and (10-rn) smaller eigenvalues m+ii A,+2, ., Alo, where Am >>Am+. Thus, Q can be rewritten

(14) _ rQs(p - )'), ( Cs, p,) Q(pT CN) ..., CM C, C2, )T heec =(c,T2 cm onsists of the coefficients of the vectorp-Hp corresponding to the signal subspace, and CN = ( Cm+l, Cm+L ..., CIO )T csiss of te coeficients corresondi to te noise subsae. The noisy part should be removed and the signal part should be preserved Hence, we may reconstuct an "estimated" parameter vector ' as follows: m

..

c =

C=(

.A

Q =( QSQN) (10) where the 10-by-m matrix Qs is composed of the eigenector ql, q q2, q > .~q~cresodn the m eigenvectors > qm corresponding tooter larger eigenvalues, and the I O-by-(l 0-m) matrix Qy is composed of the remaining (10-m) eigenvectors qm+,.qm+21, .*, qlo corresponding to the (10-m) smaller eigenvalues. It is easy to show that the m-dimensional linear subspace based on the colunns of Qs is coincident with the "signal subspace", while the residual subspace based on the columns of QN is just the "noise subspace". The rank of the signal subspace (i.e., the number of targets) is assumed to be known,- but actually it needs to be estimated. In practice, the rank of the signal subspace can be estimated by counting how many eigenvalues are needed so that their sum is larger than a previously defmed threshold. This threshold may be defned as somne percentage of the sum of all the eigenvalues. The function to determine the rank is the following: 1 ftc n K = minCA lZ% (11) E >7 where K is the estimated rank, n = 10 in this paper and q e (0,1) is chosen according to a priori knowledge. 4. SUBSPACE FILTERING OF C

It may be shown that any parameter vector p = (pi, P2, ..., po )T derived from C may be expanded as a linear combination of the eigenvectors of t covarice matix of the parameter vector and the mean vector: 10 P = zx + # (12) ,=1 The coeffilcients Cj of te expansion are defined by means of the inner product:

From F

the

Cl) =Q (P

C2c

+

as:

(13)

c,q

first 9 elements of the

easily obtains the estimated C.

(15)

estimated k, r

one

5. EXPERIMENTAL RESULTS OF SPECKLE FILTERING

The proposed algorithm was evaluated using a fourlook polarimetric image acquired over the San Francisco Bay area by the NASA/JPL airborne L-band polarimetric SAR. We use part of this image which includes sea surface, grass areas and city. Experimental results show that the 10 parameter Plo (the polarimetric entropy) should be appropriately weighted to obtain good performances. This weight is regarded as a balance between two different measurements, and the weight for PAo is 5 in this paper. It is not sensitive for the method to change ite weight from 36, but the effectiveness decreases a bit if the

The original span image is shown in Fig.1 (a). A 9-by-9 moving window is used to obtain the local covariance matrix of the parameter vector. The mean of the parameter vector is calculated over the window. We choose two different values with 70%, 50% as q in (14). The filtered span images based on the proposed method and Lee's method (MMSE) are shown in Fig.1

(b)I(Inc)ande(d). order

to quantiativel evaluate the perfornances of the proposed method, the, standarddeviation-to mean ratios (SMR) in different kinds of areas are calculated for the orig-inalimage and the filtered aies. aData based on Lee's method (MMSE) is ~~~~~~alsogiven fo canparisca. The corresponding results are shownin Table II.

380

Table II: Comparison of the standard-deviation-to mean ratios (a/m) between dlTfferent methods.

From the Fig.1 and Table II, we find the effectiveness of speckle filtering by using the proposed method. The resolution of the filtered SAR image becomes lower when we choose smaller 17, but some detail infonnation of targets such as the streets in the city area and coastlines is still preserved. For preserving more detail characteristics of targets, it is better to select larger q. It is interesting to notice that

City

span O

ij=700/a

the SMR is smaller for the proposed method with q = 50% compared with Lee's method for the city area, while the opposite situation for the sea area. It is probably caused by different procedures of smoothing for these two methods. For the city area i.e., high reflective area, speckle noise is stronger than the sea area which is low reflective. Speckle noise would contribute little to the signal subspace, but would influence more on the estimated local statistics such as local mean and local variation. For Lee's method, the averaging effect is best in low reflective or homogenous region. In higher reflective or heterogeneous region, however, his method will almost maintain the original pixel value. Therefore, the proposed method works better in the city area, but worse in the sea area than Lee's method.

(a)

, MMSE

. 1.532 .

1.372

Grass HH

Span

0.579

0.340

HH Span _ . . 1.789 0.482 .

Sea

HH

0.473

.

1.708 0.450 0.584 0.225 0.343

6. ENHANCEMENT FOR CLASSIFICATION

Speckle filtering can be used to enhance the separation of all polarized channels and improve the performance of classification [10]. The data is used for classification based on the Bayes maximum likelihood classification algorithm proposed in [19]. The multilook scattering covariance matrix has been verified to satisfy the Wishart distribution [20]. Therefore, the distance measure is given by, d(C, co° )=nlI Cm +Tr(C;1C) (16) cor Where is the mth class, Cm is the nominal scattering covariance matrix for class m, which can be obtained by averaging the samples of training data. Tr represents the trace of a matrix. The same distance measure is applied to the original data and the filtered data. The corresponding confusion matrices are given in Table III (a) and (b), respectively. The improvement in classification using the filtered data is evident, especially for the city area. Table III: Comparison of the results of classification accuracy by using original data and

(b)

filtered data. (a) Confusion matrix for the original data Sea area City area Grass area

Sea area

City

area

Grass area

98.72%

0

1.28%

0%

67.95%

0

13.27

32.05% 86.73%

(b) Confusion matrix for the filtered data

(d) (c) Fig. 1: L-band four-look span image of the San Francisco Bay area using (a) original data, (b) filtered data with the proposed method (q=70%/o), (c) flltered data with the proposed method (q=50%) and (d) flltered data with Lee's method.

sea area

Sea area

City area Grass area

381

99.880/o

0.28% 0

City area 0

83.01%

08.55%

Grass area

0.12%

16.70%

91.45%

7. CONCLUIION

A new method for speckle filtering of the multilook SAR data has been proposed based on the subspace decomposition. This method is different from the conventional speckle filters which need to device the edge-aligned pixel windows to get the knowledge of the local statistics of polarimetric data in a homogenous region. The proposed method does not require uniform property of the polarimetric data in a window. The speckle reduced polarimetric information can be obtained from the signal subspace. Detail characteristics such as edges of different targets are preserved after filtering. The calculation results have demonstrated the effectiveness of the proposed method. From Table III, we have illustrated that this method is helpful for target classification.

REFERENCE

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