Numerically erasure-robust frames
Functional Analysis
2012-04-18 v2
Abstract
Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically erasure-robust frames. We first consider a variety of constructions, including random frames, equiangular tight frames and group frames. Later, we show that arbitrarily large erasure rates necessarily induce numerical instability in signal reconstruction. We conclude with a few observations, including some implications for maximal equiangular tight frames and sparse frames.
Cite
@article{arxiv.1202.4525,
title = {Numerically erasure-robust frames},
author = {Matthew Fickus and Dustin G. Mixon},
journal= {arXiv preprint arXiv:1202.4525},
year = {2012}
}
Comments
15 pages