NOISE-INDUCED SLOPE DISTORTION IN 2-D PHASE UNWRAPPING BY LINEAR ESTIMATORS WITH APPLICATION TO SAR INTERFEROMETRY

This paper explains the underestimation of phase slope and the consequ ent distortion of the phase surface, observed in two-dimensional (2-D) phase unwrapping by linear estimators. like least squares methods app lied to synthetic aperture radar (SAR) interferometry. These methods m inimize the difference between the gradient of the unwrapped phase and the wrapped differences of the measured wrapped phase. Using the prob ability distributions of phase noise and phase differences for a given coherence, the probability of a phase gradient error giving rise to a nonconservative vector field is derived. It is shown that this phase gradient error has nonzero mean in the presence of phase slopes. Linea r phase estimators cannot distinguish the mean phase gradient error fr om a true phase slope; hence, the unwrapped phase shows a slope bias, This bias is quantified as a function of coherence and the number of i ndependent samples that are averaged. The theoretical results are conf irmed by simulations.