$\ell^1$ penalty for ill-posed inverse problems

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dc.creatorLoubes, J. M.
dc.date2007-09-17
dc.date.accessioned2026-07-07T08:30:02Z
dc.date.available2026-07-07T08:30:02Z
dc.descriptionWe tackle the problem of recovering an unknown signal observed in an ill-posed inverse problem framework. More precisely, we study a procedure commonly used in numerical analysis or image deblurring: minimizing an empirical loss function balanced by an $l^1$ penalty, acting as a sparsity constraint. We prove that, by choosing a proper loss function, this estimation technique enables to build an adaptive estimator, in the sense that it converges at the optimal rate of convergence without prior knowledge of the regularity of the true solution
dc.identifierhttps://arxiv.org/abs/0709.2606
dc.identifierhttp://arxiv.org/abs/0709.2606
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138143
dc.subjectStatistics Theory
dc.title$\ell^1$ penalty for ill-posed inverse problems
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