Sublinear-time Support Recovery in One-bit Compressed Sensing

THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD.” 1-bit compressed sensing (1bCS) is a quantized signal acquisition technique to compress highdimensional sparse signals. The goal in 1bCS is to design sensing matrices $A \in \mathbb{R}^{m \times n}$ with the fewest possible rows that enable efficient and accurate recovery of sparse signals $x \in \mathbb{R}^{n}$ from 1-bit measurements of the form $sign (A x)$. In this work, we focus on designing sensing matrices $A$ that enable super-efficient recovery of the support set of sparse signals. Our results prove that with a slight increase in the number of measurements, we can in fact obtain sublinear-time (in $n$) algorithms for support recovery. Furthermore, we also show that the proposed techniques can be modified to achieve resilience against bounded number of adversarial errors.