Document Type

Article

Publication Date

9-15-2012

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.

Comments

Sourced from the e-print (version 2) at arXiv:1202.4525v2 [math.FA]. https://arxiv.org/abs/1202.4525
Date of arXiv submission (version 2): 17 Apr 2012.

The publisher version of record for this article is at ScienceDirect:
Fickus, M., & Mixon, D. G. (2012). Numerically erasure-robust frames. Linear Algebra and Its Applications, 437(6), 1394–1407. https://doi.org/10.1016/j.laa.2012.04.034

DOI

10.1016/j.laa.2012.04.034

Source Publication

Linear Algebra and its Applications

Included in

Algebra Commons

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