Papers › Iteratively Reweighted Least Squares for Phase Unwrapping

Iteratively Reweighted Least Squares for Phase Unwrapping

18 Jan 2024arXiv:2401.09961links table onlyarchive 2025-07-28

Benjamin Dubois-Taine, Roland Akiki, Alexandre d'Aspremont

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The 2D phase unwrapping problem seeks to recover a phase image from its observation modulo 2π, and is a crucial step in a variety of imaging applications. In particular, it is one of the most time-consuming steps in the interferometric synthetic aperture radar (InSAR) pipeline. In this work we tackle the L¹-norm phase unwrapping problem. In optimization terms, this is a simple sparsity-inducing problem, albeit in very large dimension. To solve this high-dimensional problem, we iteratively solve a series of numerically simpler weighted least squares problems, which are themselves solved using a preconditioned conjugate gradient method. Our algorithm guarantees a sublinear rate of convergence in function values, is simple to implement and can easily be ported to GPUs, where it significantly outperforms state of the art phase unwrapping methods.

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