An absolute phase estimation algorithm for interferometric applications is introduced. The approach is
Bayesian. Besides coping with the 2pi-periodic sinusoidal nonlinearity in the observations, the proposed meth-
odology assumes a first-order Markov random field prior and a maximum a posteriori probability (MAP) view-
point. For computing the MAP solution, we provide a combinatorial suboptimal algorithm that involves a mul-
tiprecision sequence. In the coarser precision, it unwraps the phase by using, essentially, the previously
introduced PUMA algorithm [IEEE Trans. Image Proc. 16, 698 (2007)], which blindly detects discontinuities
and yields a piecewise smooth unwrapped phase. In the subsequent increasing precision iterations, the pro-
posed algorithm denoises each piecewise smooth region, thanks to the previously detected location of the dis-
continuities. 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 the graph min-cuts algorithms. In a set of experimental results, we illustrate
the effectiveness of the proposed approach.