Parameterized proximal-gradient algorithms for L1/L2 sparse signal recovery

TL;DR

This paper introduces a novel L1/L2 penalty model for sparse signal recovery and develops parameterized proximal-gradient algorithms with proven convergence, demonstrating superior efficiency over existing methods in noisy and noiseless scenarios.

Contribution

It proposes a new L1/L2 based penalty model and designs efficient proximal-gradient algorithms with convergence guarantees for sparse signal recovery.

Findings

Algorithms outperform state-of-the-art methods in experiments.

Proximity operator has a closed-form solution, enhancing efficiency.

Convergence of the algorithms is theoretically established.

Abstract

The ratio of L1 and L2 norms (L1/L2), serving as a sparse promoting function, receives considerable attentions recently due to its effectiveness for sparse signal recovery. In this paper, we propose an L1/L2 based penalty model for recovering sparse signals from noiseless or noisy observations. It is proven that stationary points of the proposed problem tend to those of the elliptically constrained L1/L2 minimization problem as the smoothing parameter goes to zero. Moreover, inspired by the parametric approach for the fractional programming, we design a parameterized proximal-gradient algorithm (PPGA) as well as its line search counterpart (PPGA_L) for solving the proposed model. The closed-form solution of the involved proximity operator is derived, which enable the efficiency of the proposed algorithms. We establish the global convergence of the entire sequences generated by PPGA and PPGA_L with monotone objective values by taking advantage of the fact that the objective of the proposed model is a KL function. Numerical experiments show the efficiency of the proposed algorithms over the state-of-the-art methods in both noiseless and noisy sparse signal recovery problems.