2-D PHASE UNWRAPPING AND INSTANTANEOUS FREQUENCY ESTIMATION

The phase of complex signals is wrapped since it can only be measured modulo-2 pi; unwrapping searches for the 2 pi-combinations that minimi ze the discontinuity of the unwrapped phase, as only the unwrapped pha se can be analyzed and interpreted by further processing. Given an est imate of the phase gradient (i.e,, of the instantaneous frequency), th e 2-D unwrapped phase can be obtained as a solution of a variational p roblem. The analysis of unwrapping is done quite separately from insta ntaneous frequency estimation so that the reliability of both steps ca n be assessed independently, Various methods for evaluating 2-D instan taneous frequency are presented and compared in the presence of noise and amplitude variations. A study has also been made on aliasing arisi ng in areas where, with respect to instantaneous frequency, spatial sa mpling is insufficient, The presence of noise in the data further comp licates phase aliasing analysis since there is no way to distinguish b etween the aliasing due to noise or that due to steep phase slopes.