Multi-frequency Phase Unwrapping from Noisy Data: Adaptive Local Maximum Likelihood Approach

The paper introduces a new approach to absolute phase estimation from frequency diverse wrapped observations. We adopt a discontinuity preserving nonparametric regression technique, where the phase is reconstructed based on a local maximum likelihood criterion. It is shown that this criterion, applied to the multifrequency data, besides filtering the noise, yields a 2πQ-periodic solution, where Q > 1 is an integer. The filtering algorithm is based on local polynomial (LPA) approximation for the design of nonlinear filters (estimators) and the adaptation of these filters to the unknown spatially smoothness of the absolute phase. Depending on the value of Q and of the original phase range, we may obtain complete or partial phase unwrapping. In the latter case, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [1]. Simulations give evidence that the proposed method yields state-of-the-art performance, enabling phase unwrapping in extraordinary difficult situations when all other algorithms fail.