Robust Polyhedral Regularization
Vaiter, Samuel; Peyré, Gabriel; Fadili, Jalal (2013), Robust Polyhedral Regularization, International Conference on Sampling Theory and Applications (SampTA), 2013, Bremen, GERMANY
TypeCommunication / Conférence
External document linkhttps://hal.archives-ouvertes.fr/hal-00816377
Conference titleInternational Conference on Sampling Theory and Applications (SampTA), 2013
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Abstract (EN)In this paper, we establish robustness to noise perturbations of polyhedral regularization of linear inverse problems. We provide a sufficient condition that ensures that the polyhedral face associated to the true vector is equal to that of the recovered one. This criterion also implies that the $\ell^2$ recovery error is proportional to the noise level for a range of parameter. Our criterion is expressed in terms of the hyperplanes supporting the faces of the unit polyhedral ball of the regularization. This generalizes to an arbitrary polyhedral regularization results that are known to hold for sparse synthesis and analysis $\ell^1$ regularization which are encompassed in this framework. As a byproduct, we obtain recovery guarantees for $\ell^\infty$ and $\ell^1-\ell^\infty$ regularization.
Subjects / Keywordsinverse problem; polyhedral regularization; noise robustness
Showing items related by title and author.
Fadili, Jalal; Dossal, Charles; Peyré, Gabriel; Deledalle, Charles-Alban; Vaiter, Samuel (2013) Article accepté pour publication ou publié