Coherence and sufficient sampling densities for reconstruction in compressed sensing
Machine Learning
2013-11-05 v2 Information Theory
Algebraic Geometry
math.IT
Machine Learning
Abstract
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and measurement, and logarithmic in the ambient dimension where the signal is presented. We exemplify our approach by deriving sufficient sampling densities for low-rank matrix completion and distance matrix completion which are independent of the true matrix.
Cite
@article{arxiv.1302.2767,
title = {Coherence and sufficient sampling densities for reconstruction in compressed sensing},
author = {Franz J. Király and Louis Theran},
journal= {arXiv preprint arXiv:1302.2767},
year = {2013}
}
Comments
16 pages, 1 figure. v2 streamlines the exposition