具有随机抖动的量化破坏传感
Quantized Corrupted Sensing with Random Dithering
摘要：
受损传感涉及从被未知结构化损坏和非结构化噪声污染的测量集合中恢复高维结构化信号的问题。在线性测量的情况下，不同凸规划过程（例如，广义Lasso及其变体）在文献中得到了很好的建立。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，这往往会导致非线性测量。本文主要研究量化测量下的污染感知问题。具体来说，我们证明，在均匀抖动的帮助下，约束和无约束的Lassos都能够恢复信号和腐败的量化样本时，测量矩阵是亚高斯。我们的理论结果揭示了量子化分辨率在Lassos恢复性能中的作用。数值实验证实了我们的理论结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
