A Multi-component Decomposition Method for Polarimetric SAR Data

Transcription

1 Chinese Journal of Electronics Vol.26, No.1, Jan A Multi-component Decomposition Method for Polarimetric SAR Data WEI Jujie 1, ZHAO Zheng 1, YU Xiaoping 2 and LU Lijun 1 (1. Chinese Academy of Surveying and Mapping, Beijing , China) (2. Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing , China) Abstract There are more unknowns than equations to solve for previous four-component decomposition methods. So they have to determine each scattering power with some assumptions and avoid negative powers in decomposed results with physical power constraints. This paper presents a multi-component decomposition for multi-look Polarimetric SAR (PolSAR) data by combining the Generalized similarity parameter (GSP) and the eigenvalue decomposition. It extends the existing fourcomponent decomposition by adding the diffuse scattering as the fifth scattering component considering additional cross-polarized power that could represent terrain effects and rough surface scattering. And unlike the previous methods, the new method determines the volume scattering contribution by a modified nonnegative eigenvalue decomposition method and utilizes the GSP to determine the negative powers of the three scattering contributions (i.e., odd-bounce, double-bounce, and diffuse scattering) directly without extra assumptions and constraints. By experiment, the new method is proved to be more straightforward and reasonable. Key words Multi-component decomposition, Polarimetric SAR (PolSAR), Generalized similarity parameter (GSP). I. Introduction Polarimetric target decomposition plays an important role in the interpretation of Polarimetric SAR (PolSAR) data. Freeman and Durden firstly proposed the original three-component decomposition, modeling the measured covariance matrix as a linear sum of three physical scattering mechanisms (i.e., surface scattering, double-bounce scattering, and volume scattering) under the reflection symmetry condition that the co- and cross-polarized correlations are close to zero for natural distributed media [1]. Then Yamaguchi et al. extends the three-component decomposition by adding helix scattering mechanism as the fourth component for non-reflection symmetric scattering case [2]. But there existed a fatal flaw in the two methods in that negative powers sometimes appear in decomposed results. Thus, Yajima et al. [3] and An et al. [4] modified both the approaches to eliminate these negative powers by some rigorous power constraints. Additionally, there are more unknowns than equations to solve for the previous model-based decomposition methods, which all have to suppose the magnitude of the parameter α in the double-bounce scattering model to be 1 ifre(s HH SVV ) to be positive or suppose β in the surface scattering model equal to +1 if Re(S HH SVV ) to be negative for determining their corresponding power contributions [1 7].Furthermore, they all ignore the diffuse scattering including additional cross-polarized power that could represent terrain effects and rough surface scattering. Thus, this paper presents a multi-component decomposition method using the combination of the Generalized similarity parameter (GSP) and the eigenvalue decomposition. It extends the existing four-component decomposition by adding the diffuse scattering as the fifth scattering component. II. The Generalize Similarity Parameter The GSP is an extension to the similarity parameter [8] for multi-look PolSAR data and is defined as R(A, B) = A, B = A F B F tr(a B) tr(a A)tr(B B) (1) where A and B denote respectively the coherence matrix having been rotated to zero orientation angle (i.e., deorientation [5,9] ); tr( ) is the trace of a matrix; is the inner product of two matrices, defined as A, B = Manuscript Received Jan. 5, 2015; Accepted July 5, This work is supported by the Special Fund by Surveying and Mapping and GeoInformation Research in the Public Interest (No ), the Project funded by China Postdoctoral Science Foundation (No.2016M591219), and the National Natural Science Foundation of China (No ). c 2017 Chinese Institute of Electronics. DOI: /cje

2 206 Chinese Journal of Electronics 2017 tr(a B); stands for the transpose conjugate operator; F is the Frobenius norm of a matrix. And the GSP has some important properties [10],as follows: 1) The GSP is always greater than or equal to zero and holds rotation invariance about the line of sight of radar. Thus the GSP between two coherence matrices (T 1, T 2 )is equal to the GSP between their corresponding covariance matrices (C 1, C 2 ), i.e., R(T 1, T 2 )=R(C 1, C 2 ) 0; 2) If T 1, T 2, and T 3 are three non-zero coherence matrices, which satisfy R(T 1, T 2 )=R(T 1, T 3 )=R(T 2, T 3 ) (2) then for an arbitrary coherence matrix T, with the rank of one, we have R(T, T 1 )+R(T, T 2 )+R(T, T 3 )=1 (3) III. Multi-component Decomposition Scheme 1. Basic decomposition principle The measurable covariance matrix must be rotated firstly to minimize the cross-polarized component (HV) to discriminate vegetation against oriented buildings within the volume scattering for more accurate classification. Then the proposed method models the rotated covariance matrix [C] as a linear sum of five scattering mechanisms (i.e., odd-bounce scattering, double-bounce scattering, diffuse scattering, volume scattering, and helix scattering) as follow [C] =f odd [C] odd + f dbl [C] dbl + f diff [C] diff (4) + f vol [C] vol + f hlx [C] hlx where f i (i = odd, dbl, diff, vol, hlx) is the expansion coefficient to be determined. And [C] i corresponds to the known scattering model, i.e., odd-bounce scattering, double-bounce scattering, diffuse scattering, volume scattering, and helix scattering, respectively. For the existing model-based decomposition methods, the odd- and double-bounce scattering mechanisms are modeling as β 2 0 β α 2 0 α [C] odd = 0 0 0, [C] dbl = (5) β 0 1 α 0 1 where α and β are the unknown parameters to be determined; the superscript stands for the complex conjugate operator. Since the parameters α and β have to be individually supposed as 1 and +1 for the determination of the odd- and double-bounce scattering contributions, the proposed method directly utilizes the corresponding covariance matrices of the Pauli spin matrices {a, b, c} [11] for image analysis, as follows a = 1 [ ] 1 0 [C] odd = b = 1 [ ] 1 0 [C] dbl = 1 2 c = 1 [ ] 0 1 [C] diff = (6a) (6b) (6c) where a represents single scattering from a plane surface (odd-bounce scattering), b represents a dihedral scattering (double-bounce scattering) from corners with a relative orientation of 0,andcrepresents a dihedral with a relative orientation of 45, named diffuse scattering here, considering the cross-polarized returns that might come from terrain effects or rough surface scattering. For the volume scattering model, in order to further distinguish vegetation from oriented urban areas within the volume scattering mechanism for more accurate classification, the extended volume scattering model [6] (i.e. Eq.(7)) that accounts for the HV component for dihedral structures is also exploited for the proposed method except the other three vegetation volume scattering models mentioned in Ref.[2]. And the helix scattering model is described as the same to the previous four-component decomposition [2,3,5 7]. [C] vol = (7) Determination of the scattering powers The proposed method determines the powers of the five scattering components in the following order. 1) Helix scattering contribution The helix scattering contribution is determined as the existing four component decomposition methods, in that P hlx = f hlx =2 Im{ S HV (S HH S VV ) } (8) 2) Volume scattering contribution If the helix scattering is determined, the remainder matrix [C] 1 rd can be obtained after the helix component was subtracted from the measurable data and modeled as [C] 1 rd = a [C] vol + [C] 2 rd (9) where [C] vol represents the volume scattering model; the parameter a is the volume scattering power P vol to be determined. Then, the Eq.(9) can be rewritten as ξ 0 ρ ξ a 0 ρ a [C] 2 rd = 0 η 0 a 0 η a 0 (10) ρ 0 ζ ρ a 0 ζ a

3 A Multi-component Decomposition Method for Polarimetric SAR Data 207 Van Zyl et al. proposed the Nonnegative eigenvalue decomposition method (NNED) to determine the volume scattering power [12 14]. But owing to the proposed method also adopting the extended volume scattering model Eq.(8), the NNED is modified slightly to avoid the denominator ξ a ζ a ρ a 2 of a fractional expression from solving the parameter a to be zero in the data processing procedure. Then the parameter a is estimated as a max =min(a 1,a 2 ) (11) where ξζ ρ 2, if ξ a ζ a ρ a 2 =0 Z a 1 = Z Z 2 4(ξ a ζ a ρ a 2 )(ξζ ρ 2 ) 2(ξ a ζ a ρ a 2, ) otherwise a 2 = η/η a, Z = (ξζ a + ζξ a ) ρρ a ρ ρ a, ξ = S HH f hlx, ρ = S HH S VV f hlx, η = 2 S HV f hlx, ζ = S VV f hlx. Andξ a, ζ a, ρ a and η a are the known parameters in volume scattering models. 3) Other three scattering contributions After the helix and volume scattering powers have been determined, the second remainder matrix [C] 2 rd only contains odd-bounce scattering, double-bounce scattering, and diffuse scattering. Then, the GSP is utilized to determinate the three scattering powers with the matrix. But the rank of [C] 2 rd is not equal to one. In order to combine the GSP with the three orthogonal scattering models Eq. (6) for determining their corresponding scattering contributions, the eigenvalue decomposition [11,15] is firstly exploited for the matrix [C] 2 rd to get three different single scatters [C] i with its rank of one, as follow P dbl = f dbl = P diff = f diff = λ i R([C] i, [C] dbl ) λ i R([C] i, [C] diff ) IV. Experimental Results (15b) (15c) 1. Verification of the proposed method In this section, an ascending Rardarsat-2 fully polarimetric dataset acquired on 9th April 2008, was used for verifying the performance of the new method. The experimental area chosen for analysis covers San Francisco, which mainly includes urban areas, islands, bridges (e.g. thegoldengatebridge,thebaybridge),parks(e.g. the Golden Gate Park), lakes (e.g. the Lake Merced), significant stretches of the Pacific Ocean and San Francisco Bay, etc. And this PolSAR image has been multi-look processed by 2 4(Range Azimuth) in that the image resolution on the ground become the same (19.4m 19.4m). Then the proposed scheme is applied for the PolSAR data with the sliding window 3 3 and the decomposed results are shown in Fig.1. [C] 2 rd = λ i u i u i = λ 1[C] 1 + λ 2 [C] 2 + λ 3 [C] 3 (12) where λ i 0(i =1, 2, 3) are the real eigenvalues of the remainder covariance matrix and u i are the corresponding eigenvectors. Then by combining the properties of the GSP (i.e., Eqs.(2) and (3)) with Eq.(12), we can get R([C] i, [C] odd )+R([C] i, [C] dbl )+R([C] i, [C] diff )=1 (13) λ i = λ i {R([C] i, [C] odd )+R([C] i, [C] dbl )+R([C] i, [C] diff )} (14) Then the three scattering powers can be estimated as P odd = f odd = λ i R([C] i, [C] odd ) (15a) Fig. 1. The experimental area and the decomposed results Fig.1(a), (b), (c) and(d) show the google optical image, the decomposed color-coded RGB image (Red: f dbl, Green: f vol,blue:f odd ), the helix scattering power image (db), and the diffuse scattering power image(db), respectively. It is seen in the Fig.1(b) that the double-bounce scattering mechanism is very strong in some urban areas (e.g. the areasb and D), the odd-bounce scattering mechanism is predominant for water bodies (e.g. the area C,

4 208 Chinese Journal of Electronics 2017 San Francisco Bay, and Lake Merced, etc.), and the volume scattering in the area E covered by forest and vegetation is predominant. It is indicated that the decomposed results are acceptable and reasonable. And Fig.1(c) shows that some helix scattering powers are equal to zero in the urban areas where the building blocks are completely parallel to SAR flight pass, but some become relatively strong in the skew urbans where produce a rather predominant HV component. As mentioned in Refs.[2,3], this also means that the helix scattering is mainly caused by man-made objects with oriented dihedral structures. Besides, according to Fig.1(d), the diffuse scattering power is so small for the sea that it can be ignored in the decomposed results. But it becomes large especially for the skew urban where include a rather predominant cross-polarized (HV) power even though the deorientation has been done for the measurable matrix. of sight of radar, i.e., theareab circled by the dotted black line in Fig.2(a), the value of the volume scattering power became stronger and sometimes the volume scattering appears predominant even though the observation have been deoriented. 2. Comparison with previous decomposition methods In order to further validate the new method, two advanced four-component decomposition methods (i.e., Sato4 [6] and 4 [7] ) are examined for scattering power decomposition. And we also chose the transect indicated in the Fig.2(a) for quantitative comparison among the three methods by utilizing the three components (i.e., odd-bounce scattering, double-bounce scattering, and volume scattering) (See Fig.3). Inspection of Fig.3, the decomposed results of the proposed method are more close to that of the 4 method. And the volume scattering contribution of the proposed method sometimes is different from that of Sato4. It is caused by the different branch condition (i.e. C 1 = T 11 (θ) T 22 (θ) 1 2 f hlx for Sato4, C 1 = T 11 (θ) T 22 (θ)+ 7 8 T 33(θ) f hlx for the proposed method and 4) used for selecting the dihedral volume scattering model. Fig. 2. The quantitative examination of the proposed method Aditionally, because the diffuse scattering is very small and the helix scattering is determined as the same to the previous four-component decomposition, we only examine the other three decomposed components (i.e., odd-bounce scattering, double-bounce scattering, and volume scattering) for the validity of the proposed method more clearly. We zoomed up the small area A and chose a transect, i.e., the white dotted line (See Fig.2(a)), to see the actual correspondence with the contributing scattering structures. The transect includes sea, beach, forest, grassland, football filed, museum buildings and urban from left to right. Inspection of Fig.2(b), the power f odd is rather dominant for sea and beach. Then in the Golden Gate Park, the volume scattering mechanism appears rather dominant for forest and grassland, the odd-bounce scattering is dominant for the football field, and the double-bounce scattering appears relatively dominant for the De Yong Museum buildings. And for the urban orthogonal to radar illumination, it appears a mixture scattering of odd-bounce (for building walls or floors) and double-bounce (for the structure of ground-wall). When urban oriented about the line Fig. 3. Comparison with previous decomposition method Additionally, the existing four component usually utilize physical power constraints to avoid negative powers in decomposed results. This compulsory mean seems to be unreasonable. For example, if the odd-bounce scattering power P odd is less than zero, it has to be enforced as zero. And then the double-bounce scattering power P dbl is re-calculated by P dbl = span P vol P hlx. But it is not necessary to exploit the physical power constraints for nonnegative decomposed powers by the new method. We chose some part of the transect from sample 582 to 591, which is closed-up with black dot line (named F, See Fig.2) for comparison test. The decomposed results are shown in Fig.4. And taken the 4 method for example, the specific calculation results of the sample 584 and 589 are listed in Table 1. For the sample 584, the odd- and double-bounce scattering contributions are calculated respectively as and previously. And for the sample 589, the both scattering powers are calculated respectively as and , previously. To avoid the negative powers, the odd-bounce scattering contributions are enforced to be zero and the double-bounce scattering

5 A Multi-component Decomposition Method for Polarimetric SAR Data 209 powers are recalculated as and respectively. Inspection of Fig.4(a) and(b), the sample 584 and 589 is individually located in some trees and oriented buildings, where the volume scattering is predominant. In this case, the odd-bounce scattering can not be completely neglected, even if the odd-bounce scattering for trees or oriented buildings is very low. But for the proposed method, any of the odd-bounce scattering contributions are not equal to zero. Besides, the new method also consider the diffuse scattering contribution, separately as and By contrast, it is proved that the decomposed results of the proposed method is more reasonable. The area B includes highly oriented dense urban, the patch C locates in the Pacific Ocean, the patch D mainly includes the urban orthogonal to radar illumination, and the patch E is covered by forest, which is close to Daly city. By those methods, the decomposition mean power contributions of areas are calculated and shown in Table 2. According to the table, the decomposed results of the proposed method are nearly identical to that of the previous methods and it agrees with the ground truth data well. And the diffuse scattering power is very small in the area D and E, and become as zero in the area C, where is covered by sea. In this case, the diffuse scattering can be ignored, so the five-component decomposition can be reduced as four-component decomposition automatically. But for the area B including highly skew building blocks, the diffuse scattering power becomes large, the diffuse scattering can not be neglected. Fig. 4. Comparison between 4 and the proposed method In addition, we selected four areas with obvious ground object features for a quantitative comparison of the two methods versus the proposed method. The areas were closed-up with the black line box shown in Fig.1(a). Table 1. Comparison between 4 and new method Sample Method P odd P dbl P vol P hlx P diff ant sca Domin- -ttering Doublebounce (Pre-) 584 (Post-) Volume New Volume (Pre-) Volume 589 (Post-) Volume New Volume Table 2. Quantitative comparison of the two previous methods versus the proposed method Area Method P odd P dbl P vol P hlx P diff Span from results Span from data Dominant scattering New B Sato Double-bounce New C Sato Odd-bounce New E D Sato Double-bounce New E E Sato Volume V. Conclusion A multi-component polarimetric target decomposition method has been proposed in this paper. It extends the existing four-component decomposition by adding the diffuse scattering as the fifth scattering component, which can not be neglected for oriented building blocks and is very small for urban orthogonal to the radar illumination. But the diffuse scattering becomes as zero for water body. In this case, the diffuse scattering can be ignored so that the new method becomes as a four-component decomposition automatically. And it takes full advantage of the important characteristic of the GSP and the modified NNED method to avoid the negative powers in the image analysis automatically without any physical power constraints. By experiments, it is proved that the method can yield accurate and/or similar decomposition images compared with the previous decomposition methods and it works more reasonable, straightforward, and convenient. Besides, because the GSP between two covariance matrices is identical to that between their corresponding co-

6 210 Chinese Journal of Electronics 2017 herence matrices, this method is also applicable to the coherence matrix. In addition, the Pauli matrix is used for coherent decomposition. So the proposed method also establishes the more close relationship between coherent target decomposition for single look POLSAR data and incoherent decomposition for multi-look POLSAR data by the GSP. In some sense, the new method also extend the Pauli decomposition. References [1] A. Freeman and S.L. Durden, A three-component scattering model for polarimetric SAR data, IEEE Transactions on Geoscience and Remote Sensing, Vol.36, No.3, pp , [2] Y. Yamaguchi, T. Moriyama, M. Ishido, et al., Fourcomponent scattering model for polarimetric SAR image decomposition, IEEE Transactions on Geoscience and Remote Sensing, Vol.43, No.8, pp , [3] Y. Yajima, Y. Yamaguchi, R. Sato, et al., PolSAR image analysis of wetlands using a modified four-component scattering power decomposition, IEEE Transactions on Geoscience and Remote Sensing, Vol.46, No.6, pp , [4] W.T. An, Y. Cui and J. Yang, Three-component model-based decomposition for polarimetric SAR data, IEEE Transactions on Geoscience and Remote Sensing, Vol.48, No.6, pp , [5] Y. Yamaguchi, A. Sato, W.M. Boerner, et al., Four-component scattering power decomposition with rotation of coherency matrix, IEEE Transactions on Geoscience and Remote Sensing, Vol.49, No.6, pp , [6] A. Sato, Y. Yamaguchi, G., et al., Four-component scattering power decomposition with extended volume scattering model, IEEE Geoscience and Remote Sensing Letters, Vol.9, No.2, pp , [7] G., Y. Yamaguchi and S.E. Park, General fourcomponent scattering power decomposition with unitary transformation of coherency matrix, IEEE Transactions on Geoscience and Remote Sensing, Vol.51, No.5, pp , [8] J. Yang, Y.N. Peng and S.M. Lin, Similarity between two scattering matrices, Electronics Letters, Vol.37, No.3, pp , [9] J.S. Lee and T.L. Ainsworth, The effect of orientation angle compensation on coherency matrix and polarimetric target decompositions, IEEE Transactions on Geoscience and Remote Sensing, Vol.49, No.1, pp.53 64, [10] W.T. An, W.J. Zhang, J. Yang, et al., On the similarity parameter between two targets for the case of multi-look polarimetric SAR, Chinese Journal of Electronics, Vol.18, No.3, pp , [11] J.S. Lee and E. Pottier, Polarimetric Radar Imaging: From Basics To Applications, CRC Press Llc, Boca Raton, New York, USA, pp , [12] J.J. Van, K. Yunjin and M. Arii, Requirements for model-based polarimetric decompositions, Proc. of IEEE Symposium on Geoscience and Remote Sensing IGARSS 2008, Boston,Massachusetts, USA, pp.v-417 V-420, [13] J.J. Van, M. Arii and K. Yunjin, Model-based decomposition of polarimetric SAR covariance matrices constrained for nonnegative eigenvalues, IEEE Transactions on Geoscience and Remote Sensing, Vol.49, No.9, pp , [14] J.J. Van, Application of Cloude s target decomposition theorem to polarimetric imaging radar data, Proc. of Progress In Electromagnetics Research Symposium (PIERS), San Diego, California, USA, pp , [15] S.R. Cloude and E. Pottier, A review of target decomposition theorems in radar polarimetry, IEEE Transactions on Geoscience and Remote Sensing, Vol.34, No.2, pp , WEI Jujie was born in Pingtan country, Fujian Province, China, in He received the B.E. degree in Liaoning Technical University and the Ph.D. degree in Wuhan University. His current research work focuses on polarimetric synthetic aperture radar data processing. ( weijujie0417@gmail.com) ZHAO Zheng wasborninxiangfan city, Hubei, China, in She received the B.E. degree in Wuhan Technical University of Surveying and Mapping, the M.A. degree in Chinese Academy of Surveying and Mapping and the Ph.D. degree in Wuhan University. Her current research work focuses on interferometric synthetic aperture radar data processing and information extraction. ( zhaozheng@casm.ac.cn)