CAPE : combinatorial absolute phase estimation Technical report , IT / IST Communications theory and Pattern Recognition Group

This paper introduces an absolute phase estimation algorithm for interferometric applications. The approach is Bayesian. Besides coping with the 2π-periodic sinusoidal non-linearity in the observations, the proposed methodology assumes a first order Markov random field (MRF) prior and a maximum a posteriori probability (MAP) viewpoint. For computing the MAP solution, we provide a combinatorial suboptimal algorithm that involves a multi-precision sequence. In the coarser precision, it unwraps the phase by using essentially the, previously introduced, PUMA algorithm [J. Bioucas-Dias and G. Valadão, IEEE Trans. Image Proc., vol. 16, no. 3, pp. 698-709 (2007)], which blindly detects discontinuities and yields a piecewise smooth unwrapped phase. In the subsequent increasing precision iterations, the proposed algorithm denoises each piecewise smooth region, thanks to the previously detected location of the discontinuities. For each precision, we map the problem into a sequence of binary optimizations, which we tackle by computing min-cuts on appropriate graphs. This unified rationale for both phase unwrapping and denoising inherits the fast performance of graph min-cuts algorithms. In a set of experimental results, we illustrate the effectiveness of the proposed approach.