The Polarimetric Detection Optimization Filter and its Statistical Test for Ship Detection

Abstract

Ship detection via synthetic aperture radar (SAR) has been demonstrated to be very useful as polarimetric information helps discriminate between targets and sea clutter. Among the available polarimetric detectors, optimal polarimetric detection (OPD) theoretically provides the best detection performance under the assumption that the fully developed speckle hypothesis stands. This study proposes a polarimetric detection optimization filter (PDOF). The target clutter ratio (TCR) over the speckle variation was maximized using a matrix transform to derive the PDOF. The objective function based on a matrix transform instead of a vector transform is optimized to obtain synthetic effects by combining a polarimetric whitening filter (PWF) and a polarimetric matched filter (PMF). Subspace form of the PDOF (SPDOF) is also proposed, which gives performance comparable to the PDOF. Assuming a Wishart distribution, the exact and approximate expressions of the closed-form probability density function (PDF) of the PDOF are derived. The probability of false alarm (PFA) was derived in a closed-form expression, which allows obtaining the PDOF threshold analytically. Moreover, the gamma model is extended to a generalized gamma distribution ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{G}\Gamma \text{D}$ </tex-math></inline-formula> ) to adapt complicated resolutions and sea states. Experiments with simulated and real data validate the correctness and effectiveness of the results. The PDOF detector achieves the best performance in most virtual and real-world environments, especially in cases where the target statistics and clutter are not Wishart-distributed.