Robust One-bit Compressed Sensing With Manifold Data

Abstract

We study one-bit compressed sensing for signals on a low-dimensional manifold. We introduce two computationally efficient reconstruction algorithms that only require access to a geometric multi-resolution analysis approximation of the manifold. We derive rigorous reconstruction guarantees for these methods in the scenario that the measurements are subgaussian and show that they are robust with respect to both pre- and post-quantization noise. Our results substantially improve upon earlier work in this direction.