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

```@article{Puy2015LinearEO,
title={Linear embeddings of low-dimensional subsets of a Hilbert space to Rm},
author={Gilles Puy and Mike E. Davies and R{\'e}mi Gribonval},
journal={2015 23rd European Signal Processing Conference (EUSIPCO)},
year={2015},
pages={469-473}
}```
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… CONTINUE READING