Unscrambling Nonlinear Dynamics in Synthetic Aperture Radar Imagery

In analyzing single-channel synthetic aperture radar (SAR) imagery, three interrelated questions often arise. First, should one use the detected or the complex-valued image? Second, what is the `best´ statistical model? Finally, what constitutes the `best´ signal processing methods? This paper addresses these questions from the overarching perspective of the generalized central limit theorem, which underpins nonlinear signal processing. A novel procedure for characterizing the nonlinear dynamics in SAR imagery is proposed. To apply the procedure, three complementary 1-D abstractions for a 2-D SAR chip are introduced. Our analysis is demonstrated on real-world datasets from multiple SAR sensors. The nonlinear dynamics are found to be resolution dependent. As the SAR chip is detected, nonlinear effects are found to be obliterated (i.e., for magnitude-detection) or altered (i.e., for power-detection). In the presence of extended targets (i.e., nonlinear scatterers), it is recommended to use the complex-valued chip rather than the detected one. Furthermore, to exploit the intrinsic nonlinear statistics, it is advised to utilize relevant nonlinear signal analysis techniques.