Closed-Form Expressions for InSAR Sample Statistics and Its Application to Non-Gaussian Data

Abstract

Aim of this article is to analytically derive the statistics of the magnitude and phase of the complex sample correlation coefficient between two Gaussian synthetic aperture radar (SAR) acquisitions, the foundation of interferometric SAR (InSAR), and polarimetric SAR. In particular, several novel closed-form expressions containing only elementary functions for the probability density functions (pdf) and the central moments are derived when the complex sample coherence is averaged over an integer number of independent samples (multilooking). Based on these rather simple expressions, a promising way to overcome the assumption of an underlying normal distribution for the InSAR data is proposed. Jointly, these two approaches permit a physically sound, robust, and highly accurate description of the InSAR statistics of severely heterogeneous scenes, a crucial prerequisite to many applications.