New Algorithms and Improved Guarantees for One-Bit Compressed Sensing on Manifolds

• Published in: 2019 13th International conference on Sampling Theory and Applications (SampTA) pp. 1 - 4
• Main Authors: Iwen, Mark A., Lybrand, Eric, Nelson, Aaron A., Saab, Rayan
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-07-2019
• Subjects: Compressed sensing; manifold; Manifolds; Measurement uncertainty; Noise shaping; one-bit; quantization; Quantization (signal); rate-distortion; Reconstruction algorithms
• DOI: 10.1109/SampTA45681.2019.9030884

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 Σ∆ 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.