Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization

TLDR

Two‑dimensional phase unwrapping is required in interferometric radar to recover unambiguous phase from data known only modulo 2π. The study aims to develop a MAP‑based algorithm that maximizes the conditional probability of the phase‑unwrapped solution using wrapped phase, image intensity, and interferogram coherence. The authors model joint statistics of estimated and observed signals, formulate generalized nonlinear cost functions, and use nonlinear network‑flow optimization to approximate MAP solutions, testing the algorithm on a rough‑terrain topographic interferogram and a differential interferogram of a large earthquake. The MAP algorithm produces complete, more accurate phase‑unwrapping results than other tested methods.

Abstract

Interferometric radar techniques often necessitate two-dimensional (2-D) phase unwrapping, defined here as the estimation of unambiguous phase data from a 2-D array known only modulo 2pi rad. We develop a maximum a posteriori probability (MAP) estimation approach for this problem, and we derive an algorithm that approximately maximizes the conditional probability of its phase-unwrapped solution given observable quantities such as wrapped phase, image intensity, and interferogram coherence. Examining topographic and differential interferometry separately, we derive simple, working models for the joint statistics of the estimated and the observed signals. We use generalized, nonlinear cost functions to reflect these probability relationships, and we employ nonlinear network-flow techniques to approximate MAP solutions. We apply our algorithm both to a topographic interferogram exhibiting rough terrain and layover and to a differential interferogram measuring the deformation from a large earthquake. The MAP solutions are complete and are more accurate than those of other tested algorithms.