  This paper studies the problem of recovering a signal from one-bit compressed
sensing measurements under a manifold model; that is, assuming that the signal
lies on or near a manifold of low intrinsic dimension. We provide a convex
recovery method based on the Geometric Multi-Resolution Analysis and prove
recovery guarantees with a near-optimal scaling in the intrinsic manifold
dimension. Our method is the first tractable algorithm with such guarantees for
this setting. The results are complemented by numerical experiments confirming
the validity of our approach.
