扩散图信号的盲分离
Blind Demixing of Diffused Graph Signals
AI总结：
本文针对扩散图信号混合场景，提出联合识别图滤波器并分离稀疏输入信号的盲分离方法，推导不同支撑图下的分离可行性与恢复概率界，分析单图退化情形，并通过实验验证理论结果。
摘要：
利用图对不规则信息域进行建模是处理当代（网络）数据部分复杂特性的有效方法。其核心问题之一是以图信号形式表示的数据如何依赖于图的拓扑结构。广泛使用的方法假设观测信号可被视为图滤波器（即图的矩阵表示的多项式）的输出，且这些滤波器的输入具有特定结构。扩散图信号——对应于最初稀疏的（节点局部化的）信号通过滤波在图中扩散形成的信号——就属于这一类别。在此背景下，本文研究从扩散图信号的混合体中联合识别图滤波器并分离其（稀疏）输入信号的问题，从而将时域和空域信号的经典盲分离（盲源分离）推广到图信号处理框架。我们首先考虑不同信号的支撑图互不相同的场景，给出了分离可行性定理以及成功恢复的概率界。此外，还分析了单图下分离的退化问题。论文最后通过合成图和真实世界图的数值实验，从经验上验证了主要理论发现。
英文摘要：
Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the graph. Widely-used approaches assume that the observed signals can be viewed as outputs of graph filters (i.e., polynomials of a matrix representation of the graph) whose inputs have a particular structure. Diffused graph signals, which correspond to an originally sparse (node-localized) signal percolated through the graph via filtering, fall into this class. In that context, this paper deals with the problem of jointly identifying graph filters and separating their (sparse) input signals from a mixture of diffused graph signals, thus generalizing to the graph signal processing framework the classical blind demixing (blind source separation) of temporal and spatial signals. We first consider the scenario where the supporting graphs are different across the signals, providing a theorem for demixing feasibility along with probabilistic bounds on successful recovery. Additionally, an analysis of the degenerate problem of demixing with a single graph is also presented. Numerical experiments with synthetic and real-world graphs empirically illustrating the main theoretical findings close the paper.
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。
