A Discrete/Continuous Minimization Method in Interferometric Image Processing

Abstract

Ts 2D absolute phase estimation problem, in interferometric applications, is to infer absolute phase (not simply modulo-2#)from incomplete, noisy, and modulo-2# image observations.Ton is known to be a hard problem as the observation mechanism is nonlinear. In this paper we adopt the Bayesian approach.T he observation density is 2#-periodic and accounts for the observation noise; the aprioriproba- bility of the absolute phase is modeled by a first order noncausal Gauss MarkI random field (GMRF) tailored to smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) estimate. Each iteration embodies a discrete optimization step (Z-step), implemented by network programming techniques, and an iterative conditional modes (ICM) step (#-step). Accordingly, we name the algorithm Z#M, where letter M stands for maximization. A set of experimental results, comparing the proposed algorithm with other techniques, illustrates the e#ectiveness of the proposed method.