Parallel algorithms for phase unwrapping based on Markov random field models

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Abstract
A general framework is presented for the design of parallel algorithms for two-dimensional, path-independent phase unwrapping of locally inconsistent, noisy principal-value phase fields that may contain regions of invalid information. This framework is based in Bayesian estimation theory with the use of Markov random field models to construct the prior distribution, so that the solution to the unwrapping problem is characterized as the minimizer of a piecewise-quadratic functional. This method allows one to design a variety of parallel algorithms with different computational properties, which simultaneously perform the desired pathindependent unwrapping, interpolate over regions with invalid data, and reduce the noise. It is also shown how this approach may be extended to the case of discontinuous phase fields, incorporating information from fringe patterns of different frequencies.