Scale Mixture of Gaussian Modelling of Polarimetric SAR Data
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Research Article Scale Mixture of Gaussian Modelling of Polarimetric SAR Data Anthony P. Doulgeris and Torbjørn Eltoft The Department of Physics and Technology, University of Tromsø, 9037 Tromsø, Norway Correspondence should be addressed to Anthony P. Doulgeris, [email protected] Received 1 June 2009; Accepted 28 September 2009 Academic Editor: Carlos Lopez-Martinez Copyright © 2010 A. P. Doulgeris and T. Eltoft. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper describes a flexible non-Gaussian statistical method used to model polarimetric synthetic aperture radar (POLSAR) data. We outline the theoretical basis of the well-know product model as described by the class of Scale Mixture models and discuss their appropriateness for modelling radar data. The statistical distributions of several Scale mixture models are then described, including the commonly used Gaussian model, and techniques for model parameter estimation are given. Real data evaluations are made using airborne fully polarimetric SAR studies for several distinct land cover types. Generic scale mixture of Gaussian features is extracted from the model parameters and a simple clustering example presented.
1. Introduction It is well known that POLSAR data can be non-Gaussian in nature and that various non-Gaussian models have been used to fit SAR images—firstly with single channel amplitude distributions [1–3] and later extended into the polarimetric realm where the multivariate K-distributions [4, 5] and Gdistributions [6] have been successful. These polarimetric models are derived as stochastic product models [7, 8] of a non-Gaussian texture term and a multivariate Gaussianbased speckle term, and can be described by the class of models known as Scale Mixture of Gaussian (SMoG) models. The assumed distribution of the texture term gives rise to different product distributions and the parameters used to describe them. In this paper we only investigate the semisymmetric zeromean case, which is expected for scattering in the natural terrain, and the more general scale mixture model includes a skewness term to account for a dominant or coherent scatterer and a mean value vector. Extension to the nonsymmetric case or expanding to a multitextural/nonscalar product will be addressed in the future. It is worth noting that these methods are general multivariate statistical techniques for covariate product model analysis and can be generally applied to single, dual, quad, and combined (stacked) dual frequency SAR images, or any type of coherent
imaging system. The significance and interpretation of the parameters, however, may be different in each case. The scale mixture models essentially describe the probability density function giving rise to the measured complex scattering coefficients. They therefore model at the scattering vector level, that is, Single-Look Complex (SLC) data set
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