Robust Polyhedral Regularization

Samuel Vaiter 1 Gabriel Peyré 1 Jalal M. Fadili 2
2 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : 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.
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Submitted on : Monday, April 22, 2013 - 11:19:04 AM
Last modification on : Thursday, February 7, 2019 - 5:37:02 PM
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  • HAL Id : hal-00816377, version 1
  • ARXIV : 1304.6033


Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili. Robust Polyhedral Regularization. International Conference on Sampling Theory and Applications (SampTA), 2013, Bremen, Germany. ⟨hal-00816377⟩



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