Abstract / Description of output
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 |
|---|---|
| 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 Sept 2015 |
Conference
| Conference | 23rd European Signal Processing Conference (EUSIPCO) 2015 |
|---|---|
| Country/Territory | France |
| City | Nice |
| Period | 31/08/15 → 4/09/15 |