PURE: Scalable Phase Unwrapping with Spatial Redundant Arcs

TL;DR

This paper introduces PURE, a scalable phase unwrapping method that uses dual decomposition to efficiently solve large-scale problems, outperforming existing methods in runtime and memory usage while maintaining accuracy.

Contribution

The paper presents a novel dual decomposition approach for phase unwrapping that efficiently handles non-planar graphs and guarantees convergence to the global optimum.

Findings

Comparable accuracy to state-of-the-art methods

Improved runtime performance

Reduced memory footprint

Abstract

Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010) was shown to produce a more reliable solution by exploiting redundant differential estimates. However, this technique requires a commercial linear programming solver for large-scale problems. For a linear cost function, we propose a method based on Dual Decomposition that breaks the given problem defined over a non-planar graph into tractable sub-problems over planar subgraphs. We also propose a decomposition technique that exploits the underlying graph structure for solving the sub-problems efficiently and guarantees asymptotic convergence to the globally optimal solution. The experimental results demonstrate that the proposed approach is comparable to the existing state-of-the-art methods in terms of the estimate with a better runtime and memory footprint.