Robust Phase Unwrapping by Convex Optimization

TL;DR

This paper introduces a convex optimization method for robust 2-D phase unwrapping that simultaneously denoises and unwraps phase images, outperforming existing techniques especially under noisy conditions.

Contribution

It proposes a novel convex optimization framework that unifies phase unwrapping and denoising, addressing noise and discontinuities more effectively than prior methods.

Findings

Outperforms state-of-the-art techniques in noisy scenarios

Effectively unwraps and denoises phase images simultaneously

Uses Chambolle-Pock primal-dual algorithm for optimization

Abstract

The 2-D phase unwrapping problem aims at retrieving a "phase" image from its modulo $2\pi$ observations. Many applications, such as interferometry or synthetic aperture radar imaging, are concerned by this problem since they proceed by recording complex or modulated data from which a "wrapped" phase is extracted. Although 1-D phase unwrapping is trivial, a challenge remains in higher dimensions to overcome two common problems: noise and discontinuities in the true phase image. In contrast to state-of-the-art techniques, this work aims at simultaneously unwrap and denoise the phase image. We propose a robust convex optimization approach that enforces data fidelity constraints expressed in the corrupted phase derivative domain while promoting a sparse phase prior. The resulting optimization problem is solved by the Chambolle-Pock primal-dual scheme. We show that under different observation noise levels, our approach compares favorably to those that perform the unwrapping and denoising in two separate steps.