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Conference Papers Year : 2015

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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Dates and versions

hal-01116153 , version 1 (26-02-2015)
hal-01116153 , version 2 (08-06-2015)

Identifiers

  • HAL Id : hal-01116153 , version 2

Cite

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. ⟨hal-01116153v2⟩
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