A statistical description of polarimetric and interferometric synthetic aperture radar data

Abstract

This paper provides a nearly complete analysis of the key distributions encountered in single- and multi-look polarimetric synthetic aperture radar data under the bivariate Gaussian and K -distribution models. It contains new analytic results on the moments of the amplitude and phase difference in single look data and on the moments of the amplitude in multi-look data. As yet no analytic results for the moments of multi-look phase difference have been found, except in limiting cases. The maximum likelihood estimators of the covariance matrix elements of two jointly Gaussian channels are derived, together with their asymptotic variances. The problems in extending this analysis to the bivariate K distribution are also discussed.

Statistical assessment of eigenvector-based target decomposition theorems in radar polarimetry

“…Consequently, the process to derive the marginal distribution of the sample eigenvalues, denoted as , must be divided into two steps. First, the transformation (14), along with the determinant of its Jacobian, must be introduced into the Wishart distribution (5). Second, the parameters of , i.e., the parameters which determine the eigenvectors must be integrated in order to derive .…”

“…Thus, turns into an -dimensional random variable [13] which can not be employed to characterize a distributed target without an assessment of the consequences of the speckle noise component [34]. For homogeneous data, under the Gaussian scattering assumption and on the basis of the central limit theorem, is described by a zero-mean, multidimensional, complex Gaussian pdf [5], [6] (2)…”

“…In (4), the vectors for correspond to the target vectors of every one of the averaged samples. The statistics of are completely characterized by the Wishart distribution [5], [6], [38] (5) where is the exponential of the trace of the matrix , and the multivariate gamma function is defined as follows: (6) In (6), is the gamma function.…”

“…For one-dimensional (1-D) SAR systems, speckle noise has been completely characterized by a multiplicative noise model due to the exponential probability density function (pdf) of the SAR image intensity [2], [3]. In the case of multidimensional SAR systems, and for polarimetric SAR (PolSAR) systems in particular, the characterization and reduction of the speckle noise component has been an important area of research since it represents one of the key limitations of this technology [5]- [8]. Recently, it has been demonstrated that the speckle noise component for multidimensional SAR data, under a covariance matrix formulation, must be modeled through a combination of multiplicative and additive noise sources [9].…”

Log-cumulants of the finite mixture model and their application to statistical analysis of fully polarimetric UAVSAR data

“…There are many options for the distributions of the mixing components, but here we mainly focus on the mixture of Wishart distributed components, since the Wishart distribution is widely used in PolSAR data modeling (Goodman 1963;Lee, Mitchell, and Kwok 1994;Tough, Blacknell, and Quegan 1995;López-Martínez and Fabregas 2003;Alonso-González, López-Martínez, and Salembier 2012). For different mixing components in the same image, the number of looks L is supposed to be consistent.…”