A characterization of the Non-Degenerate Source Condition in Super-Resolution

Vincent Duval 1
1 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
CEREMADE - CEntre de REcherches en MAthématiques de la DEcision, Inria de Paris
Abstract : In a recent article, Schiebinger et al. provided sufficient conditions for the noiseless recovery of a signal made of M Dirac masses given 2M + 1 observations of, e.g. , its convolution with a Gaussian filter, using the Basis Pursuit for measures. In the present work, we show that a variant of their criterion provides a necessary and sufficient condition for the Non-Degenerate Source Condition (NDSC) which was introduced by Duval and Peyré to ensure support stability in super-resolution. We provide sufficient conditions which, for instance, hold unconditionally for the Laplace kernel provided one has at least 2M measurements. For the Gaussian filter, we show that those conditions are fulfilled in two very different configurations: samples which approximate the uniform Lebesgue measure or, more surprisingly, samples which are all confined in a sufficiently small interval.
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https://hal.inria.fr/hal-01665805
Contributor : Vincent Duval <>
Submitted on : Monday, December 18, 2017 - 12:23:44 PM
Last modification on : Thursday, April 26, 2018 - 10:28:41 AM

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  • HAL Id : hal-01665805, version 1
  • ARXIV : 1712.06373

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Vincent Duval. A characterization of the Non-Degenerate Source Condition in Super-Resolution. 2017. ⟨hal-01665805⟩

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