Abstract
The polarimetric calibration of synthetic aperture radar (SAR) imagery requires the equalization of a multiple-input, multiple-output (MIMO) distortion system. For wide-band, wide-angle SAR systems, the distortion is frequency and angle dependent and can be accurately modelled as a two-dimensional finite impulse response (FIR) filter bank. This paper presents a design algorithm, using a Gröbner basis, to compute a FIR filter bank that exactly inverts the multi-channel distortion. The results presented for polynomial inversion of MIMO FIR systems hold for sampled data signals of arbitrary dimension.
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References
C.A. Berenstein and A. Yger, “On Explicit Solutions to the Bezout Equation,” Systems & Control Letters, vol. 4, February 1984, pp. 33–39.
D.A. Cox, J. Little, and D. O'shea, Ideals, Varieties, and Algorithms, Springer-Verlag, 1992.
J.H. Davenport, Y. Siret, and E. Tournier, Computer Algebra, Academic Press, 1988.
E. Ertin and L.C. Potter, “Polarimetric Calibration for Wide Band Synthetic Aperture Radar Imaging,” IEEE Proceedings-Radar, Sonar and Navigation, vol. 145, no. 5, October 1998, pp. 275–280.
E. Ertin and L.C. Potter, “Polarimetric Classification of Scattering Centers Using M-ary Bayesian Decision Rules,” IEEE Transactions on Aerospace and Electronic Systems, vol. 36, no. 3 Part: 1, July 2000, pp. 738–749.
N. Fitchas and A. Galligo, “Nullstellensatz Effectif et Conjecture de Serre (Théorème de Quillen-Suslin) pour le Calcul Formel,” Math. Nachr., vol. 149, 1990, pp. 231–253.
E. Fornasini and M.E. Valcher, “Multidimensional Systems with Finite Support Behaviors: Signal Structure, Generation, and Detection,” SIAM Journal on Control and Optimization, vol. 36, no. 2, 1998, pp. 760–769.
A. Freeman and J. van Zyl, J. Klein, H. Zebker, and Y. Shen, “Calibration of Stokes and Scattering Matrix Format Polarimetric SAR Data,” IEEE Transactions on Geoscience and Remote Sensing, vol. 30, no. 3, May 1992, pp. 531–539.
G. Harikumar and Y. Bresler, “FIR Perfect Signal Reconstruction from Multiple Convolutions: Minimum Deconvolver Orders,” IEEE Transactions on Signal Processing, vol. 46, no. 1, January 1998, pp. 215–218.
G. Harikumar and Y. Bresler, “Exact Image Deconvolution from Multiple FIR Blurs,” IEEE Transactions on Image Processing, vol. 8, no. 6, June 1999, pp. 215–218.
J.H. Justice, “A Levinson-Type Algorithm for Two-Dimensional Wiener Filtering Using Bivariate Szegö Polynomials,” Proceedings of the IEEE, vol. 65, no. 6, June 1977, pp. 882–886.
J. Kollar, “Sharp Effective Nullstellensatz,” Journal of the American Mathematical Society, vol. 1, no. 4, October 1988, pp. 963–975.
E. Mayr and A. Meyer, “The Complexity of the Word Problem for Commutative Semigroups and Polynomial Ideals,” Advances in Mathematics, vol. 46, 1982, pp. 305–329.
L. Novak, S. Halversen, G. Owirka, and M. Hiett, “Effects of Polarization and Resolution on SAR ATR,” IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 1, January 1997, pp. 102–116.
R. Rajagopal and L. Potter, “MIMO FIR Equalizers and Orders,” in ICASSP 2001 Proceedings, 2001.
R. Rau and J.H. McClellan, “Analytic Models and Postprocessing Techniques for UWB SAR,” IEEE Transactions on Aerospace and Electronic Systems, vol. 36, no. 4, October 2000, pp. 1058–1074.
G.A. Showman and J.H. McClellan, “Blind Polarimetric Equalization of UWB SAR Imagery,” in Proceedings of 2000 International Conference on Image Processing, 2000, pp. 673–676.
M. Soumekh, “Reconnaissance with Ultra Wideband UHF Synthetic Aperture Radar,” IEEE Signal Processing Magazine, vol. 12, no. 4, July 1995, pp. 21–40.
W. Steedly and R. Moses, “High Resolution Exponential Modeling of Fully Polarized Radar Returns,” IEEE Transactions on Aerospace and Electronic Systems, vol. 27, no. 3, May 1991, pp. 459–469.
L. Tong, G. Xu, and T. Kailath, “Blind Identification and Equalization Based on Second-Order Statistics: A Time Domain Approach,” IEEE Transactions on Information Theory, vol. 40, no. 2, March 1994, pp. 340–349.
J.J. van Zyl, “Calibration of Polarimetric Radar Images Using Only Image Parameters and Trihedral Corner Reflector Responses,” IEEE Transactions on Geoscience and Remote Sensing, vol. 28, no. 3, 1990, pp. 337–347.
M. Wax and T. Kailath, “Efficient Inversion of Toeplitz-Block Toeplitz Matrix,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. 31, no. 5, October 1983, pp. 1218–1221.
H. Zebker, J. Van Zyl, S. Durden, and L. Norikane, “Calibrated Imaging Radar Polarimetry: Technique, Examples, and Applications,” IEEE Transactions on Geoscience and Remote Sensing, vol. 29, no. 6, November 1991, pp. 942–961.
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Rajagopal, R., Potter, L. Multi-Channel Multi-Variate Equalizer Design. Multidimensional Systems and Signal Processing 14, 105–118 (2003). https://doi.org/10.1023/A:1022273009065
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DOI: https://doi.org/10.1023/A:1022273009065