Minimization of pseudo fountain penalty for sparse signal recovery

Abstract

In this paper, we propose a novel Pseudo-fountain (PF) penalty that builds upon and extends compressed sensing (CS) theory. The PF penalty optimizes dual parameters in coordination, enhancing its adaptability to the sparsity of signals. Meanwhile, leveraging the renowned RIP theory, we establish explicit conditions for the exact and robust recovery of signals. Additionally, we develop a Difference of Convex Algorithm-PF (DCA-PF) tailored for the constrained sparse signal recovery model formulated in this work. The experimental results demonstrate that the PF penalty outperforms its counterparts in terms of robustness, stability, and sparsity for sparse signal recovery.