A Factor-Two Approximation Algorithm for Two-Dimensional Phase Unwrapping

Abstract

Two-dimensional phase unwrapping is the problem of deducing unambiguous "phase" from values known only modulo 2π. Many authors agree that the objective of phase unwrapping should be to find a (weighted) minimum of the number of places where adjacent discretized phase values differ by more than π. This problem, which is known to be NP-hard, is of considerable practical interest, largely due to its importance in interpreting data acquired with synthetic aperture radar (SAR) interferometry. Consequently, many heuristic algorithms for its approximate solution have been proposed. Here we present a novel approach to this problem, based on the local-ratio principle, which guarantees a solution whose cost is at most twice the minimum sought.