Phase Unwrapping in Seconds: A Spectral ADMM Algorithm for Large-Scale InSAR.
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| Title: | Phase Unwrapping in Seconds: A Spectral ADMM Algorithm for Large-Scale InSAR. |
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| Authors: | Rouet-Leduc, Bertrand1 (AUTHOR) rouetleduc.bertrand.5s@kyoto-u.ac.jp, Hulbert, Claudia2 (AUTHOR) |
| Source: | Remote Sensing. Jun2026, Vol. 18 Issue 11, p1801. 17p. |
| Subjects: | Phase unwrapping (Digital image processing), Radar interferometry, Optimization algorithms, Time series analysis, Convex programming, Synthetic aperture radar |
| Abstract: | Highlights: What are the main findings? Phase unwrapping, one of the slowest steps in satellite radar interferometry, can be reformulated as a convex optimization problem that decomposes into trivially parallel operations on GPU. The resulting algorithm, FAUST-ADMM, matches the accuracy of established methods while being up to two orders of magnitude faster, reducing processing times from tens of minutes or even hours to seconds. What are the implications of the main findings? Phase unwrapping is no longer a computational bottleneck in InSAR processing: entire multi-year, multi-track SAR archives can now be routinely unwrapped on a single machine in hours instead of days. This enables exhaustive, automated InSAR time-series analysis at continental to global scales, supporting systematic monitoring of tectonic, volcanic, and anthropogenic ground deformation. Phase unwrapping, the recovery of a continuous signal from measurements known only modulo 2 π , 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 L 1 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | Highlights: What are the main findings? Phase unwrapping, one of the slowest steps in satellite radar interferometry, can be reformulated as a convex optimization problem that decomposes into trivially parallel operations on GPU. The resulting algorithm, FAUST-ADMM, matches the accuracy of established methods while being up to two orders of magnitude faster, reducing processing times from tens of minutes or even hours to seconds. What are the implications of the main findings? Phase unwrapping is no longer a computational bottleneck in InSAR processing: entire multi-year, multi-track SAR archives can now be routinely unwrapped on a single machine in hours instead of days. This enables exhaustive, automated InSAR time-series analysis at continental to global scales, supporting systematic monitoring of tectonic, volcanic, and anthropogenic ground deformation. Phase unwrapping, the recovery of a continuous signal from measurements known only modulo 2 π , 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 L 1 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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 20724292 |
| DOI: | 10.3390/rs18111801 |
