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.
Categories: cs.IT math.IT