Sparse recovery using expanders via hard thresholding algorithm

• Published in: Signal processing Vol. 227; p. 109715
• Main Authors: Wen, Kun-Kai, He, Jia-Xin, Li, Peng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2025
• Subjects: Combinatorial compressed sensing; Hard thresholding; Heavy ball method; Lossless expanders; Sparse signal recovery; 94A15; Heavy ball method; Hard thresholding; 90C26; Lossless expanders; Sparse signal recovery; 94A12; Combinatorial compressed sensing
• ISSN: 0165-1684
• DOI: 10.1016/j.sigpro.2024.109715

Expanders play an important role in combinatorial compressed sensing. Via expanders measurements, we propose the expander normalized heavy ball hard thresholding algorithm (ENHB-HT) based on expander iterative hard thresholding (E-IHT) algorithm. We provide convergence analysis of ENHB-HT, and it turns out that ENHB-HT can recover an s-sparse signal if the measurement matrix A∈{0,1}m×n satisfies some mild conditions. Numerical experiments are simulated to support our two main theorems which describe the convergence rate and the accuracy of the proposed algorithm. Simulations are also performed to compare the performance of ENHB-HT and several existing algorithms under different types of noise, the empirical results demonstrate that our algorithm outperform a few existing ones in the presence of outliers. •Propose the expander normalized heavy ball hard thresholding algorithm.•Convergence rate and accuracy of proposed algorithm are provided.•Our method achieves good numerical performance, especially in the presence of outliers.