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

Licheng Dai

doi:10.1109/tsp.2026.3729607

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

2026-09-01

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DOI：10.1109/tsp.2026.3729607

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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.

Keywords:

Sparse phase retrieval

phaseless recovery

gradient hard thresholding pursuit

Gauss-Newton method

quadratic convergence

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

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