On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds

TL;DR

This paper introduces a convex recovery method for one-bit compressed sensing signals on low-dimensional manifolds, providing near-optimal guarantees and demonstrating effectiveness through numerical experiments.

Contribution

It presents the first tractable algorithm with recovery guarantees for one-bit compressed sensing on manifolds, leveraging Geometric Multi-Resolution Analysis.

Findings

Recovery guarantees with near-optimal scaling in manifold dimension

Convex method based on Geometric Multi-Resolution Analysis

Numerical experiments confirm approach validity

Abstract

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.