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

Gilles Puy, Mike Davies, Remi Gribonval
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
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
more » ... , which is based on a variable density sampling technique, is computationally more efficient, while potentially requiring more measurements.
doi:10.1109/eusipco.2015.7362427 dblp:conf/eusipco/PuyDG15 fatcat:2uuxzyunbfav7f3bd266ah7cmu