Spatial Domain Generation of Random Surface Using Savitzky-Golay Filter for Simulation of Electromagnetic Polarimetric Systems
Keywords:
Polarimetric SAR, rough surface generation, Savitzky-Golay filterAbstract
A spatial-domain algorithm is introduced for generating both isotropic and anisotropic natural rough surface models with predetermined statistical properties using Savitzky-Golay filter. Unlike the spectral-domain methods, the proposed method does not require the calculation of two-dimensional inverse Fourier transforms which constitute a computational burden for generating large ensembles of high-resolution surfaces. A comparative analysis between the proposed spatial-domain method and one of the conventional spectral-domain methods is presented. The comparison shows that the proposed spatial-domain method results in substantially improved computational performance. The fitness of the generated rough surface to the predetermined statistical properties is verified by calculating a variogram for numerical measurement of the variance and the correlation lengths. To demonstrate the importance of generating such a rough surface for simulation of electromagnetic polarimetric systems, a rough surface with anisotropic statistical properties is placed in the near field region of two antennas of orthogonal polarizations. It is shown that the self and mutual electromagnetic coupling coefficients of the two antennas can be used for measuring the orientation of the rough surface.
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M. Sugimoto, K. Ouchi, and Y. Nakamura, “Four-component scattering power decomposition algorithm with rotation of covariance matrix using ALOS-PALSAR polarimetric data,” Remote Sensing, vol. 4, no. 8, pp. 2199-2209, July 2012.
A. Nascimento, A. Frery, and R. Cintra, “Detecting changes in fully polarimetric SAR imagery with statistical information theory,” IEEE Transactions on Geoscience and Remote Sensing, vol. 4, Sep. 2018.
W. Wang, et al., “A fully polarimetric SAR imagery classification scheme for mud and sand Flats in intertidal zones,” IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 3, pp. 1734-1742, Mar. 2017.
Y. Zhang, Yu Li, X. San Liang, and J. Tsou “Comparison of oil spill classifications using fully and compact polarimetric SAR images,” Applied Sciences, vol 7, no. 2, pp. 193-214, Feb. 2017.
S. Uhlmann and S. Kiranyaz “Integrating color features in polarimetric SAR Image classification,” IEEE Transactions on Geoscience and Remote Sensing, vol. 52, no. 4, pp. 2197-2216, Apr. 2014.
L. Zhang, L. Sun, B. Zou, and W. Moon, “Fully polarimetric SAR image classification via sparse representation and polarimetric features,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 8, no. 8, pp. 3923-3932, Aug. 2015.
B. Zhang, W. Perrie, Paris W. Vachon, X. Li, W. Pichel, J. Guo, and Y. He, “Ocean vector winds retrieval from C-band fully polarimetric SAR measurements,” IEEE Transactions on Geoscience and Remote Sensing, vol. 50, no. 11, pp. 4252- 4261, Nov. 2012.
C. Hsieh, “Energy transition for depolarized backscatter from rough surfaces,” Journal of Microwave Power and Electromagnetic Energy, vol. 44, no. 3, pp. 132-138, Jan. 2010.
N. Sajjad, A. Khenchaf, and A. Coatanhay, “Depolarization of electromagnetic waves from sea surface,” In OCOSS. European Conf., June 2010.
A. Sentenac, H. Giovannini, and M. Saillard, “Scattering from rough inhomogeneous media: Splitting of surface and volume scattering,” JOSA A, vol. 19, no. 4, pp. 727-736, Apr. 2002.
K. O’Donnell and E. Mendez, “Experimental study of scattering from characterized random surfaces,” JOSA A, vol. 4, no. 7, pp. 1194-1205, July 1987.
M. Zubair, Z. Haider, S. Khan, and J. Nasir, “Atmospheric influences on satellite communications,” Przeglad Elektrotechniczny, vol. 87, no. 5, pp. 261-264, Jan. 2011.
G. Wolosinski, V. Fusco, and P. Rulikowski, “Broadband dual-polarized antenna with high port isolation and polarization purity,” In Antennas and Propagation (APSURSI), IEEE International Symposium on, pp. 1581-1582, June 2016.
C. Holler, A. Taylor, M. Jones, O. King, S. Muchovej, M. Stevenson, R. Wylde, et al., “A circularly symmetric antenna design with high polarization purity and low spillover,” IEEE Transactions on Antennas and Propagation, vol. 61, no. 1, pp. 117-124, Jan. 2013.
J. M. Ralston and E. L. Ayers, “Antenna effects on polarimetric imagery in ultrawide synthetic aperture radar,” Institute for Defense Analyses, No. IDA-D-2735, Alexandria, Virginia Sep. 2002.
Y. Cocheri and R. Vauzelle, “A new ray-tracing based wave propagation model including rough surfaces scattering,” Progress In Electromagnetics Research, vol. 75, pp. 357-381, 2007.
S. Coons, “Surfaces for computer aided design of space forms,” Massachusetts Inst. of Tech. Cambridge Project Mac, no. MAC-TR-41, June 1967.
M. Escobar and A. Meyerovich, “Applications and identification of surface correlations,” arXiv Preprint arXiv:1404.1291, vol. 2, Apr. 2014.
C. Mack, “Generating random rough edges, surfaces and volumes,” Applied Optics, vol. 52, no. 7, pp.1472-1480, 1 Mar. 2013.
A. Francisco and N. Brunetière, “A hybrid method for fast and efficient rough surface generation,” Proceedings of the Institution of Mechanical Engineers, vol. 230, no. 7, pp. 747-768, July 2016.
K. Uchida, J. Honda, and K. Y. Yoon, “An algorithm for rough surface generation with inhomogeneous parameters,” Journal of Algorithms & Computational Technology, vol. 5, no. 2, pp. 259-271, June 2011.
Y. Kuga and P. Phu, “Experimental studies of millimeter - wave scattering in discrete random media and from rough surfaces,” Progress In Electromagnetics Research, vol. 14, no. 7, pp. 37- 88, 1996.
K. Uchida, M. Takematsu, and J. Honda, “A discretization criterion for generating random rough surface based on convolution method,” Complex, Intelligent and Software Intensive Systems (CISIS), Eighth International Conference, IEEE, pp. 307-312, July 2014.
T. Jacobs, et al., “Quantitative characterization of surface topography using spectral analysis,” Surface Topography: Metrology and Properties, Vol. 5, no. 1 p. 013001, Jan. 2017.
S. Abraham and M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Analytical Chemistry, vol. 36 no. 8, pp. 1627-1639, July 1964.
R. Torala and A. Chakrabarti, “Generation of Gaussian distributed random numbers by using a numerical inversion method,” Computer Physics Communications, vol. 74, no. 3, pp. 327-334, Mar. 1993.
D. Thomas, W. Luk, P. Leong, and J. Villasenor, “Gaussian random number generators,” ACM Computing Surveys, vol. 39, no. 4, p. 11, Nov. 2007.
R. Ritabrata, “Comparison of Different Techniques to Generate Normal Random Variables,” Stochastic Signals and Systems (ECE 330: 541), Rutgers, The State University of New Jersey, Nov. 2002.
