Year: 2024
Type: article
Abstract: We consider a least absolute deviation (LAD) approach to the robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. To solve the resulting non-convex optimization problem, we propose a robust alternating minimization (Robust-AM) derived as an unconstrained Gauss-Newton method. To solve the inner optimization arising in each step of Robust-AM, we adopt two computationally efficient methods. We provide a non-asymptotic convergence analysis of these practical algorithms for Robust-AM under the standard Gaussian measurement assumption. These algorithms, when suitably initialized, are guaranteed to converge linearly to the ground truth at an order-optimal sample complexity with high probability while the support of sparse noise is arbitrarily fixed and the sparsity level is no larger than$1/4$. Additionally, through comprehensive numerical experiments on synthetic and image datasets, we show that Robust-AM outperforms existing methods for robust phase retrieval offering comparable theoretical performance guarantees.
Authors: Seonho Kim, Kiryung Lee
Institution: The Ohio State University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Award: G2760107292
OpenAlex ID: W4405231932