Accelerating gradient projection methods for $\ell_1$-constrained signal recovery by steplength selection rules
It provides a faster method for sparse signal recovery in compressed sensing and inverse problems, which is an incremental improvement over existing gradient projection methods.
The paper proposes a new gradient projection algorithm for ℓ₁-constrained sparse recovery that outperforms five state-of-the-art algorithms in both well-conditioned and ill-conditioned problems, achieving faster convergence through adaptive steplength selection.
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.