Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems

Yingying Li, Jinchuan Zhou (), Zhongfeng Sun and Jingyong Tang
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Yingying Li: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
Jinchuan Zhou: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
Zhongfeng Sun: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
Jingyong Tang: School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

Mathematics, 2023, vol. 11, issue 12, 1-24

Abstract: We introduce a novel iterative algorithm, termed the Heavy-Ball-Based Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HBHTP), to reconstruct a sparse signal from a small number of magnitude-only measurements. Our algorithm is obtained via a natural combination of the Hard Thresholding Pursuit for sparse phase retrieval (SPR-HTP) and the classical Heavy-Ball (HB) acceleration method. The robustness and convergence for the proposed algorithm were established with the help of the restricted isometry property. Furthermore, we prove that our algorithm can exactly recover a sparse signal with overwhelming probability in finite steps whenever the initialization is in the neighborhood of the underlying sparse signal, provided that the measurement is accurate. Extensive numerical tests show that SPR-HBHTP has a markedly improved recovery performance and runtime compared to existing alternatives, such as the Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HTP), the SPARse Truncated Amplitude Flow (SPARTA), and Compressive Phase Retrieval with Alternating Minimization (CoPRAM).

Keywords: sparse phase retrieval; Heavy-Ball method; Hard Thresholding Pursuit; restricted isometry property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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