Bayesian approaches to phase unwrapping: theoretical study

The problem of phase unwrapping of two-dimensional (2-D) phase signals has gained a considerable interest in recent years. It deals with the problem of estimating (reconstructing) an absolute phase from the observation of its noisy principal (wrapped) values. This is an ill-posed problem since many possible solutions correspond to a given observation. Many phase unwrapping algorithms have been proposed relying on different constraints for the phase signal sampling process or the nature (e.g., smoothness, regularity) of the phase signal. We look at these algorithms from the Bayesian point of view (estimation theory) and analyze the role of the prior assumptions, studying their equivalencies to the regularization constraints already used. This study lead to the development of the two new phase unwrapping algorithms, presented in the last section of this paper, which are able to work in quite difficult conditions of aliasing and noise. The theoretical study of the analyzed schemes is illustrated by some experiments on synthetic phase signals.