A Probabilistic-Cost Algorithm for Large-Scale 2D Phase Unwrapping

Abstract

Two-dimensional phase unwrapping can dominate computation and memory usage in wide-area Interferometric Synthetic Aperture Radar (InSAR) processing. Here we present Whirlwind, a minimum-cost-flow (MCF) unwrapper tailored for large interferograms of surface deformation. We derive fixed likelihood-ratio costs using multilook interferometric phase statistics, marginalizing uncertainty in the local phase-gradient and coherence estimates. A compact integer lookup table and parallel-augmenting successive-shortest-path solver with Dial bucket queues make the MCF solve efficient while avoiding flow-dependent cost relinearization. We test whether these improvements in speed and memory can be obtained without a loss of solution quality using multiple evaluation criteria for individual interferograms, at mission-production scale, and in end-to-end displacement time series solutions. On a 74-Mpixel Sentinel-1 interferogram of the 2019 Ridgecrest earthquakes, Whirlwind runs in 209 s, 28x faster than single-tile SNAPHU, while using 40% of the peak memory. Across 6,014 provisional NISAR geocoded unwrapped (GUNW) products, 93% agreed with the SNAPHU-derived results on more than 99% of valid pixels; on seven challenging 77-MHz Antarctic frames, Whirlwind ran a median 21x faster than SNAPHU while matching 99.4% of its integer-cycle assignments. Finally, in a complete Sentinel-1 time series experiment, Whirlwind improved the network-inversion consistency over SNAPHU, and in a high-resolution Capella time series of the Portuguese Bend landslide, it achieved the highest correlation with a dense GPS network among five unwrapping configurations. Whirlwind is provided as an open-source library capable of handling the growing volume of globally available InSAR data.