Title

Numerically Erasure-robust Frames

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

The "Link to Full Text" button on this page loads the open access article version of record, hosted at Elsevier. The publisher retains permissions to re-use and distribute this article.

Reviewed at MR2942359.

Previous version: arXiv:1202.4525 [math.FA].
Date of arXiv submission: 21 Feb 2012, updated 17 Apr 2012.

DOI

10.1016/j.laa.2012.04.034

Source Publication

Linear Algebra and its Applications

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