A Pseudo-Inverse-Based Hard Thresholding Algorithm for Sparse Signal Recovery

Wen, Jinming; He, Haitao; He, Zihao; Zhu, Fumin

doi:10.1109/tits.2022.3172868

Cited by 10 publications

(1 citation statement)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is a close relationship between the phase recovery problem and the compressed sensing problem [28][29][30]. Compressed sensing, also known as compressed sampling, is a new information technology used to find sparse solutions to underdetermined linear systems.…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Sun

et al. 2023

Mathematics

View full text Add to dashboard Cite

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).

show abstract

Section: Introductionmentioning

confidence: 99%