Quantized compressed sensing: a survey

Abstract

The field of quantized compressed sensing investigates how to jointly design a measurement matrix, quantizer, and reconstruction algorithm in order to accurately reconstruct low-complexity signals from a minimal number of measurements that are quantized to a finite number of bits. In this short survey, we give an overview of the state-of-the-art rigorous reconstruction results that have been obtained for three popular quantization models: one-bit quantization, uniform scalar quantization, and noise-shaping methods.