Numerically Erasure-robust Frames
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.
Linear Algebra and its Applications
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