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.

翻译：在线性测量中,各种曲线编程程序(例如,普遍Lasso及其变体)的恢复性能在文献中已经确立,然而,在数字信号处理的实际应用中,量化过程是不可避免的,往往导致非线性测量。本文专门研究在定量测量下进行的腐败感测。具体地说,我们证明,在统一拼凑的帮助下,受限制和未受限制的拉索能够在测量矩阵为亚加苏西时从定量样本中恢复信号和腐败。我们的理论结果揭示了量化解析在拉索斯的恢复性能中的作用。提供了数值实验,以证实我们的理论结果。