Non-signal components minimization for sparse signal recovery

• Published in: Signal processing Vol. 226; p. 109617
• Main Authors: Xiang, Min, Zhang, Zhenyue
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2025
• Subjects: Compressed sensing; Proximal gradient; Sparse signal recovery; Sparsity increment; Proximal gradient; Sparse signal recovery; Sparsity increment; Compressed sensing
• ISSN: 0165-1684
• DOI: 10.1016/j.sigpro.2024.109617

Sparse signal recovery is a challenging task. This paper focuses on the technique of non-signal components minimization for recovering the latent sparsest signal behind observations from two viewpoints: minimizing the residual subject to the sparsity level and minimizing the sparsity subject to the residual constraint. A successive sparsity increment method is proposed to address these two closely related tasks. This method yields two algorithms: SINSM for residual minimization and SISP for sparsity minimization. Additionally, an improved accelerated proximal gradient algorithm is provided to solve each non-signal components minimization problem penalized by the residual. The convergence of the improved algorithm is guaranteed. Numerical experiments demonstrate the superior performance of SINSM and SISP on both synthetic and real-world data. •Theoretical equivalence of non-signal components minimization and signal pursuing.•Sparsity increment overcomes the weakness of frequently meeting local minima.•Improved accelerated PG solves the successive minimization problem and converges.•SINSM and SISP minimize residual or sparsity via incremental sparsity.•SINSM and SISP significantly outperform the compared sparse algorithms numerically.