GraHTP: A Provable Newton-like Algorithm for Sparse Phase Retrieval

This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit (GraHTP), for sparse phase retrieval with complex sensing vector...

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Bibliographic Details
Main Authors Dai, Licheng, Lu, Xiliang, You, Juntao
Format Journal Article
LanguageEnglish
Published 05.10.2024
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
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Summary:This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit (GraHTP), for sparse phase retrieval with complex sensing vectors. GraHTP is theoretically provable and exhibits high efficiency, achieving a quadratic convergence rate after a finite number of iterations, while maintaining low computational complexity per iteration. Numerical experiments further demonstrate GraHTP's superior performance compared to state-of-the-art algorithms.
DOI:10.48550/arxiv.2410.04034