发表机构
Indian Institute of Technology Bombay（印度孟买理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对亚奈奎斯特采样下相关连续时间信号集合，提出基于公共低通与创新高通分量的模型，推导可辨识性条件并设计联合恢复算法，实验表明可显著降低采样率与硬件开销。
AI 中文摘要
在分布式传感器网络和阵列处理等应用中，高效采集相关的连续时间信号至关重要。然而，现有的相关模型往往无法捕捉近距离测量的物理信号所共享的结构。在本文中，我们将集合中的每个信号建模为一个隐藏的公共低通分量和一个具有不相交频谱支撑的信号特定创新高通分量之和，其中公共带宽未知。我们首先推导了理论上的可辨识性条件，保证从欠采样观测中唯一分解和重建。进一步，我们提出了一种实用的恢复算法和一个联合重建框架，该框架利用由未知公共带宽参数化的参数化结构化字典。在四个信号集合上的数值实验表明，在可辨识性条件下，以25%的总采样率降低实现了精确重建，并且当所有通道均以低于奈奎斯特率采样时，可实现高达74%的速率降低的稳健恢复，显著减少了数据采集和硬件开销。
英文摘要
Efficient acquisition of correlated continuous-time signals is critical in applications such as distributed sensor networks and array processing. However, existing correlation models often fail to capture the shared structure of physical signals measured in close proximity. In this paper, we model each signal in an ensemble as the sum of a hidden common lowpass component and a signal-specific innovation highpass component with disjoint spectral supports, where the common bandwidth is unknown. We first derive theoretical identifiability conditions guaranteeing unique decomposition and reconstruction from subsampled observations. Further, we propose a practical recovery algorithm and a joint reconstruction framework that leverages parametric structured dictionaries parameterized by the unknown common bandwidth. Numerical experiments on an ensemble of four signals demonstrate exact reconstruction with a 25% aggregate sampling rate reduction under identifiability conditions, and robust recovery with up to a 74% rate reduction when all channels are sampled below the Nyquist rate, significantly reducing data acquisition and hardware overhead.
Comments5 pages, 2 figures
