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

Abstract : We consider the problem of embedding a low-dimensional set, M, from an infinite-dimensional Hilbert space, H, to a finite-dimensional space. Defining appropriate random linear projections, we propose two constructions of linear maps that have the restricted isometry property (RIP) on the secant set of M with high probability. The first one is optimal in the sense that it only needs a number of projections essentially proportional to the intrinsic dimension of M to satisfy the RIP. The second one, which is based on a variable density sampling technique, is computationally more efficient, while potentially requiring more measurements.
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Communication dans un congrès
EUSIPCO - 23rd European Signal Processing Conference, Aug 2015, Nice, France. 2015
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Contributeur : Gilles Puy <>
Soumis le : lundi 8 juin 2015 - 14:17:23
Dernière modification le : mardi 16 janvier 2018 - 15:54:22

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  • HAL Id : hal-01116153, version 2

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Gilles Puy, Mike E. Davies, Rémi Gribonval. Linear embeddings of low-dimensional subsets of a Hilbert space to $\mathbb{R}^m$. EUSIPCO - 23rd European Signal Processing Conference, Aug 2015, Nice, France. 2015. 〈hal-01116153v2〉

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