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

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arxiv 2410.04034 v2 pith:4EZM26TQ submitted 2024-10-05 math.NA cs.NA

Licheng Dai , Xiliang Lu , Juntao You This is my paper
classification math.NAcs.NA
keywords grahtpsparsephaseretrievalalgorithmprovablequadraticachieving
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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.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Sparse Signal Recovery From Quadratic Systems with Full-Rank Matrices

    cs.IT 2025-07 conditional novelty 6.0 of 10

    A new Sparse Gauss-Newton method recovers s-sparse signals from about O(s log n) quadratic measurements in its refinement stage, with quadratic convergence.

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