  Unlike compressive sensing where the measurement outputs are assumed to be
real-valued and have infinite precision, in "one-bit compressive sensing",
measurements are quantized to one bit, their signs. In this work, we show how
to recover the support of sparse high-dimensional vectors in the one-bit
compressive sensing framework with an asymptotically near-optimal number of
measurements. We also improve the bounds on the number of measurements for
approximately recovering vectors from one-bit compressive sensing measurements.
Our results are universal, namely the same measurement scheme works
simultaneously for all sparse vectors.
  Our proof of optimality for support recovery is obtained by showing an
equivalence between the task of support recovery using 1-bit compressive
sensing and a well-studied combinatorial object known as Union Free Families.
