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.
Source Publication
Linear Algebra and its Applications
Recommended Citation
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
Comments
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Reviewed at MR2942359.
Previous version: arXiv:1202.4525 [math.FA].
Date of arXiv submission: 21 Feb 2012, updated 17 Apr 2012.