Linear embeddings of low-dimensional subsets of a Hilbert space to Rm

Gilles Puy, Michael Davies, Remi Gribonval

Research output: Contribution to conferencePaperpeer-review

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.
Original languageEnglish
Number of pages5
Publication statusPublished - 31 Aug 2015
Event23rd European Signal Processing Conference (EUSIPCO) 2015 - Nice, France
Duration: 31 Aug 20154 Sep 2015

Conference

Conference23rd European Signal Processing Conference (EUSIPCO) 2015
CountryFrance
CityNice
Period31/08/154/09/15

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