## 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.

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 language | English |
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Number of pages | 5 |

Publication status | Published - 31 Aug 2015 |

Event | 23rd European Signal Processing Conference (EUSIPCO) 2015 - Nice, France Duration: 31 Aug 2015 → 4 Sep 2015 |

### Conference

Conference | 23rd European Signal Processing Conference (EUSIPCO) 2015 |
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Country | France |

City | Nice |

Period | 31/08/15 → 4/09/15 |