  This paper concerns the problem of 1-bit compressed sensing, where the goal
is to estimate a sparse signal from a few of its binary measurements. We study
a non-convex sparsity-constrained program and present a novel and concise
analysis that moves away from the widely used notion of Gaussian width. We show
that with high probability a simple algorithm is guaranteed to produce an
accurate approximation to the normalized signal of interest under the
$\ell_2$-metric. On top of that, we establish an ensemble of new results that
address norm estimation, support recovery, and model misspecification. On the
computational side, it is shown that the non-convex program can be solved via
one-step hard thresholding which is dramatically efficient in terms of time
complexity and memory footprint. On the statistical side, it is shown that our
estimator enjoys a near-optimal error rate under standard conditions. The
theoretical results are substantiated by numerical experiments.
