Breaking through the Thresholds: an Analysis for Iterative Reweighted $\ell_1$ Minimization via the Grassmann Angle Framework

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dc.creatorXu, Weiyu
dc.creatorKhajehnejad, M. Amin
dc.creatorAvestimehr, Salman
dc.creatorHassibi, Babak
dc.date2009-04-06
dc.date.accessioned2026-07-07T13:00:53Z
dc.date.available2026-07-07T13:00:53Z
dc.descriptionIt is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization algorithm. However, even though iterative reweighted $\ell_1$ minimization algorithms or related algorithms have been empirically observed to boost the recoverable sparsity thresholds for certain types of signals, no rigorous theoretical results have been established to prove this fact. In this paper, we try to provide a theoretical foundation for analyzing the iterative reweighted $\ell_1$ algorithms. In particular, we show that for a nontrivial class of signals, the iterative reweighted $\ell_1$ minimization can indeed deliver recoverable sparsity thresholds larger than that given in [1], [3]. Our results are based on a high-dimensional geometrical analysis (Grassmann angle analysis) of the null-space characterization for $\ell_1$ minimization and weighted $\ell_1$ minimization algorithms.
dc.descriptionSubmitted to ITW 2009 in Sicily
dc.identifierhttps://arxiv.org/abs/0904.0994
dc.identifierhttp://arxiv.org/abs/0904.0994
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225985
dc.subjectProbability
dc.subjectInformation Theory
dc.titleBreaking through the Thresholds: an Analysis for Iterative Reweighted $\ell_1$ Minimization via the Grassmann Angle Framework
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