Information Reconstruction-Based Polarimetric Covariance Matrix for PolSAR Ship Detection

In the last decades, how to detect ships with polarimetric synthetic aperture radar (PolSAR) has become one hot topic. Unfortunately, most of the existing ship detection methods cannot well detect small ships with weak backscattering. To deal with this issue, a ship detection matrix named complete polarimetric covariance matrix [CP] was recently proposed from the perspective of spatial information utilization. Although it is able to improve small ships’ target-to-clutter ratio (TCR) values, its calculation strategy still needs to be rethought due to the possible information loss of some ships. Besides, its mathematical characteristic (i.e., not positive semidefinite) also limits the successful applications of some existing polarimetric theories to it. To overcome these two drawbacks, we here develop an information reconstruction-based polarimetric covariance matrix [IC]. In brief, one new difference calculation strategy is first performed on the Sinclair matrix [ $S$ ], so as to reconstruct its information, by which a feature vector $v$ is subsequently extracted with the Lexicographic matrix basis. Then, via further performing an outer product operation on $v$ , the matrix [IC] is proposed. Meanwhile, to demonstrate the effectiveness of [IC] in ship detection, two different [IC]-based intensity detectors, respectively, named SPANIC and PEDIC, are designed as well. Experiments carried out on three GF-3 PolSAR datasets show that: 1) the proposed matrix [IC] has a better performance than [CP] and the original polarimetric covariance matrix [ $C$ ] in ship detection and 2) compared to the total power detector SPAN and geometrical perturbation-polarimetric notch filter (GP-PNF), both SPANIC and PEDIC can better detect ships, especially the small ships.