English

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.

Keywords

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

R2 v1 2026-06-21T20:22:36.274Z