  We study the problem of approximately recovering signals on a manifold from
one-bit linear measurements drawn from either a Gaussian ensemble, partial
circulant ensemble, or bounded orthonormal ensemble and quantized using
Sigma-Delta or distributed noise shaping schemes. We assume we are given a
Geometric Multi-Resolution Analysis, which approximates the manifold, and we
propose a convex optimization algorithm for signal recovery. We prove an upper
bound on the recovery error which outperforms prior works that use memoryless
scalar quantization, requires a simpler analysis, and extends the class of
measurements beyond Gaussians. Finally, we illustrate our results with
numerical experiments.
