Fast Implementation of ℓ 1-Greedy Algorithm

Petukhov, Alexander; Kozlov, Inna

doi:10.1007/978-1-4614-4565-4_25

Cited by 5 publications

(1 citation statement)

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“…The threshold is lowered after each iteration so that more and more large entries are weighted down by τ in each subsequent iteration step. Numerical experiments show that the l 1 greedy algorithm outperforms both the standard and reweighted l 1 -minimization algorithms in recovering random sparse signals [10,17].…”

Section: Introductionmentioning

confidence: 97%

Error analysis of reweightedl1greedy algorithm for noisy reconstruction

Zhu

Arroyo

et al. 2015

Journal of Computational and Applied Mathematics

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a b s t r a c tSparse solutions for an underdetermined system of linear equations Φx = u can be found more accurately by l 1 -minimization type algorithms, such as the reweighted l 1 -minimization and l 1 greedy algorithms, than with analytical methods, in particular in the presence of noisy data. Recently, a generalized l 1 greedy algorithm was introduced and applied to signal and image recovery. Numerical experiments have demonstrated the convergence of the new algorithm and the superiority of the algorithm over the reweighted l 1 -minimization and l 1 greedy algorithms although the convergence has not yet been proven theoretically. In this paper, we provide an error bound for the reweighted l 1 greedy algorithm, a type of the generalized l 1 greedy algorithm, in the noisy case and show its improvement over the reweighted l 1 -minimization.

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Section: Introductionmentioning

confidence: 97%