Robust one-bit compressed sensing with partial circulant matrices
Information Theory
2018-12-18 v1 Signal Processing
math.IT
Probability
Abstract
We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly sub-sampled circulant matrix) and is robust to analog pre-quantization noise as well as to adversarial bit corruptions in the quantization process. Our results imply that quantization is not a statistically expensive procedure in the presence of nontrivial analog noise: recovery requires the same sample size one would have needed had the measurement matrix been Gaussian and the noisy analog measurements been given as data.
Cite
@article{arxiv.1812.06719,
title = {Robust one-bit compressed sensing with partial circulant matrices},
author = {Sjoerd Dirksen and Shahar Mendelson},
journal= {arXiv preprint arXiv:1812.06719},
year = {2018}
}