Phase unwrapping via diversity and graph cuts

Abstract

Many imaging techniques, e.g., interferometric synthetic aperture radar, magnetic resonance imaging, diffraction tomography, yield interferometric phase images. For these applications, the measurements are modulo-2p, where p is the period, a certain real number, whereas the aimed information is contained in the true phase value. The process of inferring the phase from its wrapped modulo-2p values is the so-called phase unwrapping (PU) problem. In this paper we present a graph-cuts based PU technique that uses two wrapped images, of the same scene, generated with different periods p1, p2. This diversity allows to reduce the ambiguity effect of the wrapping modulo-2p operation, and is extensible to more than two periods. To infer the original data, we assume a first order Markov random field (MRF) prior and a maximum a posteriori probability (MAP) optimization viewpoint. The employed objective functionals have nonconvex, sinusoidal, data fidelity terms and a non isotropic total variation (TV) prior. This is an integer, nonconvex optimization problem for which we apply a technique that yields an exact, low order polynomial complexity, global solution. At its core is a non iterative graph cuts based optimization algorithm. As far as we know, all the few existing period diversity capable PU techniques for images, are either far too simplistic or employ simulated annealing, thus exponential complexity in time, optimization algorithms.