Sparse recovery under weak moment assumptions
Statistics Theory
2016-02-22 v5 Probability
Statistics Theory
Abstract
We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible estimate -- exhibited by a random gaussian matrix. We also prove that this moment condition is necessary, up to a factor. Applications to the Compatibility Condition and the Restricted Eigenvalue Condition in the noisy setup and to properties of neighbourly random polytopes are also discussed.
Cite
@article{arxiv.1401.2188,
title = {Sparse recovery under weak moment assumptions},
author = {Guillaume Lecué and Shahar Mendelson},
journal= {arXiv preprint arXiv:1401.2188},
year = {2016}
}