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arXiv · 1202.4525

Numerically erasure-robust frames

Matthew Fickus·Dustin G. Mixon
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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.

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Matthew Fickus, Dustin G. Mixon. 2012-02-21. Numerically erasure-robust frames. https://arxiv.org/abs/1202.4525

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