Simultaneous Diagonalization of Hermitian Matrices and Its Application in PolSAR Ship Detection

A challenging issue in the field of marine remote sensing is the application of polarimetric synthetic aperture radar (PolSAR) to small ship detection in complicated environments. Several outstanding polarimetric detectors (such as the optimal polarimetric detector, polarimetric whitening filter (PWF), and polarimetric notch filter (PNF)) have been effectively implemented in practical applications. A linear combination model based on quadratic optimization is summarized to establish a general framework for polarimetric detectors, transitioning the PolSAR ship target detection from a model-driven approach to a hybrid (model/data)-driven approach. However, the dimension of the covariance matrix may be high, and the computation cost will be large. The higher dimension of the covariance matrix requires a bigger data demand. As a result, when the sample size is small, the model performance will degrade. In this article, to decrease the computational complexity and improve the robustness, we propose a novel method called the simultaneous diagonalization transform (SDT). The proposed method enables an almost simplest representation of information from the covariance matrix providing a rapid detection algorithm. The simulation experiments demonstrate that polarimetric detectors based on SDT consistently outperform those based on other methods in terms of accuracy, efficiency, and sample size requirements across various complex backgrounds. Furthermore, the effectiveness, robust, and fastness of the polarimetric detector based on SDT is validated using real data collected by RadarSAT-2 (RS-2), GaoFen-3 (GF-3), and Sentinel-1A.