Year: 2022
Type: article
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 can stably 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.
Authors: Zhongxing Sun, Wei Cui, Yulong Liu
Institution: Beijing Institute of Technology
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: 干扰下的结构信号重建理论及应用研究, G7578982776
OpenAlex ID: W3136527576