Interferometric SAR coherence magnitude estimation using second kind statistics

Coherence magnitude is a fundamental parameter for the analysis of applications using interferometric synthetic aperture radar (InSAR). The coherence magnitude estimators are biased and need bias removal. The sample coherence magnitude estimation, computed on a window basis, depends on the number of independent samples and theoretical coherence. It has been shown that the sample coherence magnitude estimator is the maximum-likelihood one. It is a biased estimator, especially for low coherence values. In this paper, we present a novel coherence magnitude estimator obtained from the method of moments using "second kind statistics". Classical methods (with regular statistics) for coherence computation are based on a probability density function (pdf) model for estimating regular moments (first kind statistics) defined with the Fourier transform. The proposed approach is based on the same pdf model to compute the second kind statistics defined with the Mellin transform (log-moment). Thus, it is shown that the estimated coherence given by the first log-moment is less biased. Moreover, it is shown that the coherence magnitude estimation from complex coherence maps (interferometric data) using second kind statistics is the optimal estimation procedure of interferometric coherence. It gives the smallest bias near zero comparing with existing estimators. The developed estimation approaches have been applied to obtain coherence measurements from tandem European Remote Sensing 1 and 2 satellite interferometric data, collected over varying terrain with a variety of ground cover types (agriculture field, forest, lake, urban area, sea) in Tunisia, France, and Nepal