Quantized Corrupted Sensing with Random Dithering

TL;DR

This paper investigates the problem of recovering structured signals from quantized measurements contaminated by corruption, demonstrating that uniform dithering enables effective recovery using convex programming methods like Lasso.

Contribution

It introduces a theoretical framework showing that uniform dithering allows Lasso-based methods to recover signals from quantized corrupted measurements with sub-Gaussian matrices.

Findings

Uniform dithering improves recovery performance in quantized corrupted sensing.

Lasso methods can recover signals and corruption from quantized samples under certain conditions.

Quantization resolution significantly impacts the effectiveness of the recovery process.

Abstract

Corrupted sensing concerns the problem of recovering a high-dimensional structured signal from a collection of measurements that are contaminated by unknown structured corruption and unstructured noise. In the case of linear measurements, the recovery performance of different convex programming procedures (e.g., generalized Lasso and its variants) is well established in the literature. However, in practical applications of digital signal processing, the quantization process is inevitable, which often leads to non-linear measurements. This paper is devoted to studying corrupted sensing under quantized measurements. Specifically, we demonstrate that, with the aid of uniform dithering, both constrained and unconstrained Lassos are able to recover signal and corruption from the quantized samples when the measurement matrix is sub-Gaussian. Our theoretical results reveal the role of quantization resolution in the recovery performance of Lassos. Numerical experiments are provided to confirm our theoretical results.