论文标题
多维无限抽样和鲁棒重建
Multi-Dimensional Unlimited Sampling and Robust Reconstruction
论文作者
论文摘要
在本文中，我们引入了一种新的采样和重建方法，以用于多维模拟信号。在无限传感框架（USF）的基础上，我们提出了一个新的折叠采样操作员，称为多维模量离疗程，该操作员也与现有的一维模量运算符兼容。与以前的方法不同，所提出的模型是专门针对多维信号量身定制的。特别是，该模型在维度2及更高版本中使用某些冗余，并利用稳健性进行输入恢复。我们证明了新运算符定义明确，并且其输出具有有限的动态范围。对于无声的情况，我们得出了一种理论上保证的输入重建方法。当输入被高斯噪声损坏时，我们利用较高维度的冗余来提供误差概率的界限，并显示出足够高的采样率的误差，从而降至0，从而为嘈杂情况提供了新的理论保证。我们的数值示例证实了理论结果，并表明与USF相比，所提出的方法可以处理明显更大的噪声。
In this paper we introduce a new sampling and reconstruction approach for multi-dimensional analog signals. Building on top of the Unlimited Sensing Framework (USF), we present a new folded sampling operator called the multi-dimensional modulo-hysteresis that is also backwards compatible with the existing one-dimensional modulo operator. Unlike previous approaches, the proposed model is specifically tailored to multi-dimensional signals. In particular, the model uses certain redundancy in dimensions 2 and above, which is exploited for input recovery with robustness. We prove that the new operator is well-defined and its outputs have a bounded dynamic range. For the noiseless case, we derive a theoretically guaranteed input reconstruction approach. When the input is corrupted by Gaussian noise, we exploit redundancy in higher dimensions to provide a bound on the error probability and show this drops to 0 for high enough sampling rates leading to new theoretical guarantees for the noisy case. Our numerical examples corroborate the theoretical results and show that the proposed approach can handle a significantly larger amount of noise compared to USF.
