Phase unwrapping, the recovery of a continuous signal from measurements known only modulo 2π, is a ubiquitous problem in coherent imaging, from medical MRI to radar remote sensing. In Interferometric Synthetic Aperture Radar (InSAR), phase unwrapping is both critical and computationally demanding: current methods require minutes to hours per interferogram and frequently fail on large images. We present FAUST-ADMM (Fast ADMM Unwrapping via Spectral Transforms), an algorithm that formulates phase unwrapping as a weighted L1 optimization and solves it efficiently on GPU using the Alternating Direction Method of Multipliers (ADMM). Each iteration reduces to a Poisson equation solved in closed form via the Discrete Cosine Transform, followed by element-wise soft thresholding, both trivially parallel. On 500 synthetic earthquake interferograms, FAUST-ADMM achieves 99% accuracy with reference-point correction, matching SNAPHU, MCF, and PUMA, while running 10 to 100× faster. On a full three-subswath Sentinel-1 interferogram of the 2019 Ridgecrest M7.1 earthquake (∼6500 × 8500 pixels), FAUST-ADMM agrees with SNAPHU on 99.7% of pixels in 35 s, a 74× speedup. Our method makes batch unwrapping of large InSAR time series practical on a single consumer GPU.
Rouet‐Leduc et al. (2026) studied this question.