Analysis of Hard-Thresholding for Distributed Compressed Sensing with One-Bit Measurements

Abstract

A simple hard-thresholding operation is shown to be able to recover $L$ signals ${\mathbf{x}}_1,...,{\mathbf{x}}_L\in {\mathbb{R}}^n$ that share a common support of size $s$ from $m=\mathcal{O}(s)$ one-bit measurements per signal if $L\ge \log (en/s)$. This result improves the single signal recovery bounds with $m=\mathcal{O}(s\log (en/s))$ measurements in the sense that asymptotically fewer measurements per non-zero entry are needed. Numerical evidence supports the theoretical considerations.

17 pages, 2 figures