We propose a new gradient projection algorithm that compares favorably with the fastest algorithms available to date for ℓ1-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.

Accelerating gradient projection methods for $ell_1$-constrained signal recovery by steplength selection rules / Loris, I; Bertero, M; DE MOL, C; Zanella, Riccardo; Zanni, Luca. - In: APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS. - ISSN 1063-5203. - STAMPA. - 27:2(2009), pp. 247-254. [10.1016/j.acha.2009.02.003]

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