Recursive-Tail-Fista for Sparse Signal Recovery

Abstract

Recovering a sparse target vector with reduced sparsity from a given observation vector is a major challenge in many applications. The well-known tail-minimization approaches tackle this challenge by minimizing the tail part of the target vector. Building upon this, recent development, the tail fast iterative soft thresholding algorithm (Tail-FISTA) formulates the tail-minimization problem as an unconstrained l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -minimization problem and solves it with the FISTA method. Motivated by Tail-FISTA and the tail-minimization approaches, in this paper, we propose a sparse signal recovery algorithm called the recursive-tail-FISTA (R-Tail-FISTA). We employ a two-step procedure for R-Tail-FISTA: 1. We consider the tail-minimization problem and formulate it as an unconstrained l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -minimization problem. 2. We solve it by using the Tail-FISTA approach. We demonstrate that the R-Tail-FISTA method performs better in terms of sparse signal recovery compared to state-of-the-art algorithms. Additionally, we demonstrate the superiority of R-Tail-FISTA by recursively applying the tail-minimization technique to the tail part of the target vector twice. Furthermore, we numerically show that the convergence rate is better for R-Tail-FISTA than that of Tail-FISTA.