Accelerating gradient projection methods for $\ell_1$-constrained signal recovery by steplength selection rules

TL;DR

This paper introduces a new gradient projection algorithm with adaptive steplength rules that outperforms existing methods in sparse signal recovery tasks, especially in noisy and ill-conditioned scenarios.

Contribution

The paper presents a novel gradient projection method utilizing line-search and adaptive steplength strategies based on Barzilai-Borwein rules for improved sparse recovery.

Findings

Outperforms five existing algorithms in computational tests

Effective in both well-conditioned and ill-conditioned problems

Demonstrates favorable convergence properties

Abstract

We propose a new gradient projection algorithm that compares favorably with the fastest algorithms available to date for $\ell_1$-constrained sparse recovery from noisy data, both in the compressed sensing and inverse problem frameworks. The method exploits a line-search along the feasible direction and an adaptive steplength selection based on recent strategies for the alternation of the well-known Barzilai-Borwein rules. The convergence of the proposed approach is discussed and a computational study on both well-conditioned and ill-conditioned problems is carried out for performance evaluations in comparison with five other algorithms proposed in the literature.