A General Framework of Polarimetric Detectors Based on Quadratic Optimization

Ship detection is an important task in civil or military applications and we can use polarimetric synthetic aperture radar (PolSAR). Many polarimetric detectors were proposed and achieved good performances in particular environments, such as optimal polarimetric detector (OPD), polarimetric whitening filter (PWF), polarimetric notch filter (PNF), polarimetric detection optimization filter (PDOF), and diagonal loading detector (DLD). Up to now, the analytical links among different polarimetric detectors have not been found. In this work, the above polarimetric detectors are unified in mathematical forms and a general framework of polarimetric detectors based on quadratic optimization is presented. The mathematical forms are summarized as a trace of two matrices’ product. One is a detection transformation matrix and the other is the polarimetric covariance matrix of the pixel to be detected. We find that all these polarimetric detectors can be regarded as the optimization of such detection matrix, which is the key point of the general framework, and the difficulty turns to be a linear inseparable problem. A pocket perceptron linear algorithm (PPLA) is used to solve the linear inseparable problem. In the case of low resolution, target detection is almost an indivisible problem, and multilayer perceptron (MLP) cannot provide better detection results than PPLA. In the case of high resolution, target detection becomes a nonlinear separable problem, and MLP is gradually superior to PPLA. In addition, the optimal weights of the recent DLD are obtained to compare with other detectors in the general framework and the DLD is developed to a more general case [generalized DLD (GDLD)]. The experiments validate the general framework of polarimetric detectors. Different detectors in the general framework are utilized and compared in both simulated and measured PolSAR data. The results show that the optimal solution in the general framework can always reach the best performance, and the GDLD is the closest one to the optimal detector of the general framework.