Nonlinearity and the effect of detection on single-channel synthetic aperture radar imagery

When signals exhibit non-Gaussian statistics, nonlinear signal processing techniques offer advantages over their linear counterparts. Nonlinearity in high-resolution synthetic aperture radar (SAR) imagery is an intrinsic phenomenon often overlooked in the radar literature. In this paper, we study the nonlinear dynamics, and the effect of detection, in SAR imagery. To this end, two complementary methods for exposing the nonlinear statistics are presented. The first method utilizes histogram fitting with relevant statistical models. The second method is based on hypothesis testing. Our results are demonstrated on real-world Radarsat-2 target chips. It is found that in the presence of extended targets (e.g., ships), the nonlinear effect in the SAR chip is predominant. Nonlinearity is observed to be negligible in the absence of extended targets. As the SAR chip is detected, the nonlinear dynamics are either diminished/altered (i.e., for power-detection) or obliterated (i.e., for magnitude-detection). To take full advantage of nonlinear statistics, it is recommended to utilize the complex-valued SAR image rather than the detected one. Furthermore, the Student's T location-scale distribution is seen to offer an excellent model for the SAR chip.