Phase and amplitude phase restoration in synthetic aperture radar imaging

Methods for addressing two types of multiplicative noise in synthetic aperture radar (SAR) imaging are presented. The authors consider a multiplicative noise with a real phase (i.e. the SAR signal´s phase is contaminated but its amplitude is uncorrupted) that possesses unknown functional characteristics with respect to the radar signal´s temporal frequencies. A perturbation solution for phase reconstruction from amplitude is developed from a wave equation governing the SAR signal and a Riccati equation that relates the amplitude and phase functions of the SAR signal. This solution is converted into a noniterative analytical solution in terms of the moments and powers of the log amplitude function. Next, the authors consider a multiplicative noise with a complex phase (i.e. both the amplitude and phase of the SAR signal are contaminated) that varies linearly with respect to the radar signal´s temporal frequencies. The two wave equations governing the SAR signal at two temporal frequencies of the radar signal are combined to derive a method to reconstruct the complex phase error function