Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry Property
Classical Analysis and ODEs
2016-04-13 v1 Information Theory
math.IT
Abstract
We investigate the sign-linear embeddings of 1-bit compressed sensing given by Gaussian measurements. One can give short arguments concerning a Restricted Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse hemispheres. This approach has a natural extension to the presence of additive white noise prior to quantization. Noisy one-bit mappings are shown to satisfy an RIP when the metric on the sphere is given by the noise.
Cite
@article{arxiv.1604.03499,
title = {Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry Property},
author = {Scott Spencer},
journal= {arXiv preprint arXiv:1604.03499},
year = {2016}
}
Comments
10 pages