A virtual resampling technique for algebraic two-dimensional phase unwrapping

Abstract

Two-dimensional (2D) phase unwrapping is a reconstruction problem of a continuous phase, defined over 2D-domain, from its wrapped samples. In our previous work, we presented a two-step phase unwrapping algorithm which first constructs, as the real and imaginary parts of a complex function, a pair of piecewise polynomials having no common zero over the domain, then estimates the unwrapped phase by applying the algebraic phase unwrapping. In this paper, we propose a preprocessing of the above algorithm for avoiding the appearance of zeros of the complex function in the first step. The proposed preprocessing is implemented by a convex optimization and resampling, and its effectiveness is shown in a terrain height estimation by the interferometric synthetic aperture radar.