Approximation for the Statistics of the Optimal Polarimetric Detector in K-Wishart model

Abstract

Generally there are three mechanisms in ship detection in the Polarimetric Synthetic Aperture Radar (PolSAR), such as the optimal polarization, polarization decomposition and ship wake. The optimal polarimetric detector (OPD) provides the best possible detection performance achievable under ideal conditions. But it is very hard to derive the threshold in the constant false alarm rate (CFAR) process, because the expression of the probability of false alarm (PFA) is difficult to calculate. In this paper an approximation of the statistics of the OPD is presented, and the PFA and the probability of detection (PD) are both derived. This makes the threshold easy to be obtained via the bisection method. The derivations are validated by the simulated data and are helpful to the application of the OPD in PolSAR image.