Analysis of hard-thresholding for distributed compressed sensing with one-bit measurements

Abstract

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