Low-rank Matrix Sensing With Dithered One-Bit Quantization

TL;DR

This paper investigates low-rank matrix sensing using dithered one-bit quantization, proposing an enhanced randomized Kaczmarz algorithm with theoretical guarantees and demonstrating its effectiveness through numerical experiments.

Contribution

It introduces a novel approach combining dithered one-bit sampling with an improved randomized Kaczmarz algorithm for low-rank matrix recovery, along with theoretical analysis.

Findings

Algorithm converges efficiently under certain conditions

The method requires a feasible number of samples for accurate recovery

Numerical results confirm the effectiveness of the proposed approach

Abstract

We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the low-rank matrix of interest from the highly-quantized collected data, we offer an enhanced randomized Kaczmarz algorithm that efficiently solves the emerging highly-overdetermined feasibility problem. Additionally, we provide theoretical guarantees in terms of the convergence and sample size requirements. Our numerical results demonstrate the effectiveness of the proposed methodology.