# Recipes for stable linear embeddings from Hilbert spaces to $\mathbb{R}^m$

1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA_D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : We consider the problem of constructing a linear map from a Hilbert space H (possibly infinite dimensional) to R^m that satisfies a restricted isometry property (RIP) on an arbitrary signal model, i.e., a subset of H. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP with high probability. We also describe a generic technique to construct linear maps that satisfy the RIP. Finally, we detail how to use our results in several examples, which allow us to recover and extend many known compressive sampling results.
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Article dans une revue
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2017, 〈10.1109/TIT.2017.2664858〉
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Littérature citée [34 références]

https://hal.inria.fr/hal-01203614
Contributeur : Gilles Puy <>
Soumis le : mardi 17 janvier 2017 - 13:11:01
Dernière modification le : mercredi 16 mai 2018 - 11:24:14

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Gilles Puy, Mike Davies, Rémi Gribonval. Recipes for stable linear embeddings from Hilbert spaces to $\mathbb{R}^m$. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2017, 〈10.1109/TIT.2017.2664858〉. 〈hal-01203614v2〉

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