Two-dimensional phase unwrapping using semidefinite relaxation

In many imaging applications, the continuous phase information of the measured signal is wrapped to a single period of 2pi, resulting in phase ambiguity. In this paper we consider the two-dimensional phase unwrapping problem and propose a maximum a posteriori (MAP) framework for estimating the true phase values based on the wrapped phase data. In particular, assuming a joint Gaussian prior on the original phase image, we show that the MAP formulation leads to a binary quadratic minimization problem. The latter can be efficiently solved by semidefinite relaxation (SDR). We compare the performances of our proposed method with the existing L¹/L²-norm minimization approaches. The numerical results demonstrate that the SDR approach significantly outperforms the existing phase unwrapping methods.