Non-signal components minimization for sparse signal recovery

Abstract

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.