Linear embeddings of low-dimensional subsets of a Hilbert space to $\mathbb{R}^m$

Gilles Puy; Mike E. Davies; Rémi Gribonval

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Linear embeddings of low-dimensional subsets of a Hilbert space to $\mathbb{R}^m$

Gilles Puy ¹ Mike E. Davies ² Rémi Gribonval ¹

1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio

IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE, Inria Rennes – Bretagne Atlantique

2 Institute for Digital Communication Joint Research Institute for Signal & Image Processing School of Engineering and Electronics - University of Edinburgh

Abstract : We consider the problem of embedding a low-dimensional set, M, from an infinite-dimensional Hilbert space to a finite-dimensional space. Defining appropriate random linear projections, we construct a linear map which has the restricted isometry property on the secant set of M, with high probability for a number of projections essentially proportional to the intrinsic dimension of M.

Keywords : Box-counting dimension Compressed Sensing Restricted Isometry Property

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Documents associated with scientific events

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Computer Science [cs] / Signal and Image Processing

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https://hal.inria.fr/hal-01157992
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Submitted on : Friday, May 29, 2015 - 11:14:01 AM
Last modification on : Thursday, January 20, 2022 - 5:28:50 PM
Long-term archiving on: : Monday, April 24, 2017 - 5:39:13 PM

Linear embeddings of low-dimensional subsets of a Hilbert space to $\mathbb{R}^m$

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Linear embeddings of low-dimensional subsets of a Hilbert space to $\mathbb{R}^m$

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