English

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

R2 v1 2026-06-22T13:30:40.053Z