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PIERS Online
Vol. 3
No. 5
2007
pp: 633-636Principal Component Analysis (PCA) in the Context of Radar PolarimetryWolfgang-Martin Boerner, E. Luneburg, and Andreas Danklmayer doi:10.2529/PIERS061006085232 Downloads: 3827 Abstract:Statistical and computational techniques for revealing the internal structure that underlies the set of random correlated data exists in a great variety at present; and target decomposition theorems, either in the coherent or incoherent formulation, are well established. In spite of this fact a rather innovative and new concept is presented in this contribution. In turn the Principal Component Analysis (PCA) is considered to possibly add value to existing approaches, and it allows for an interpretation of polarimetric synthetic aperture radar measurements using variables obtained via linear transformation. Starting with the Sinclair backscatter matrix S which will be further transformed into the so called target feature vector by stacking column elements of S and generating the covariance matrices averaged over a certain pixel array, we show, how the Sinclair backscatter matrix is decomposed into the sum of a maximum of four 2 × 2 elementary point scatter matrices which are weighted by the principal components, whereas the variances of these components agree with the eigenvalues of the covariance matrix. This mathematical development defines a decomposition which expresses scattering mechanism from distributed targets in terms of scattering matrices via an incoherent step.References:1. Boerner, W.-M., H. Mott, E. Luneburg, B. Brisco, R. Brown, J. S. Paterson (authors); S. R. Cloude, E. Krogager, J. S. Lee, D. L. Schuler, J. J. van Zyl, D. Randall, and P. Budkewitsch (contributing authors), "Polarimetry in remote sensing: Basic and applied concepts," The Manual of Remote Sensing, 3rd Edition, American Society of Photogrammetry and Remote Sensing, Chap. 5, R. A. Reyerson, ed., ASPRS Publishing, Bethesda, MD, 1998. 2. Mott, H., "Antennas for radar and communications," A Polarimetric Approach, John Wiley and Sons, New York, 1992. 3. Luneburg, E., IEICE Transactions on Electronics (Special Issue on Electromagnetic Theory), E78-C 10, 1339, 1995. 4. Jolliffe, I. T., Principal Component Analysis, 2nd edn., Springer, New York, 2002. 5. Danklmayer, A., M. Chandra, and E. Lueneburg, "Principal component analysis in radar polarimetry," Advances in Radio Science, Vol. 3, URSI, Kleinheubacher Berichte 2004, in press, 2005. 6. Cloude, S. R. and E. Pottier, "A review of target decomposition theorems in radar polarimetry," IEEE Trans. GRS, Vol. 34, No. 2, 498-518, Mar., 1996. 7. Horn, R. A. and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985. 8. Luneburg, E. and W.-M. Boerner, "Statistical aspects of radar polarimetry," Fields, Networks, Computational Methods, and Systems in Modern Electrodynamics, P. Russer, M. Mongiardo (Editors), A Tribute to Leopold B. Felsen (the Proceedings of the Symposium on Fields, Networks and Computation: A Modern View of Engineering Electrodynamics, June 01-02, 2004, Technical University of Munich (in dedication to Leopold B. Felsen), Springer-Verlag Berlin-Heidelberg-New York, 2004. 9. Cloude, S. R., "Radar target decomposition theorems," Electronics Letters, Vol. 21, No. 1, 22-24, 1985. 10. Cloude, S. R., "Uniqueness of target decomposition theorems in radar polarimetry," Proceedings of the NATO Advances Research Workshop on Direct And Inverse Methods in Radar Polarimetry, Boerner, W.-M. et al. (eds), Bad Windsheim, Germany, September 18-24, 1988; Kluwer Academic Publishers, Dordrecht 1992; NATO ASI Series C, Vol. 350, 267-296, 1988. 11. Cloude, S. R., "Polarimetric optimization based on the target covariance matrix," Electronics Letters, Vol. 26, No. 20, 1990. 12. Swartz, A. A., H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, "Optimal polarizations for archiving maximum contrast in radar images," J. Geophys. Research, Solid Earth and Planets, Vol. 93, 15, 252-15, 260, 1988. 13. Cloude, S. R. and E. Pottier, "An entropy based classification scheme for land applications of polarimetric SAR," IEEE Trans. Geosci. Remote Sensing, Vol. 35, No. 1, 68-78, 1997. |
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