Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing

@article{Krahmer2013SigmaDeltaQO,
title={Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing},
author={Felix Krahmer and Rayan Saab and {\"O}zg{\"u}r Yilmaz},
journal={CoRR},
year={2013},
volume={abs/1306.4549}
}

Suppose that the collection {ei}i=1 forms a frame for R, where each entry of the vector ei is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We show that an arbitrary signal in R can be recovered from its quantized frame coefficients up to an error which decays root-exponentially in the oversampling rate m/k. Here the quantization scheme is assumed to be chosen appropriately depending on the oversampling rate and the… CONTINUE READING