通过学习窄带频谱核，提升复杂图信号的重建精度。
Graph Signal Inference by Learning Narrowband Spectral Kernels
- 用窄带频谱核组合建模图信号频域特性。
- 联合优化核参数与信号系数，实现高精度插值。
- 适用于多图数据联合学习，适合图信号处理研究者。
图信号分析中常假设信号平滑或频谱带限，但实际图数据频谱可能集中在多个频段，包含中高频成分。本文提出一种新图信号模型，用图频率域的窄带核组合表示信号频谱，并设计算法联合优化核参数与信号表示系数。该方法可融合不同图上采集的信号进行联合学习。理论分析表明，多图联合学习在特定条件下优于单图独立建模。在多个图数据集上的实验显示，该方法相比现有多种基准方法，在信号插值精度上表现优异。
原文摘要 · Abstract (English)
While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum, possibly including mid-to-high-frequency components. In this work, we propose a novel graph signal model where the signal spectrum is represented through the combination of narrowband kernels in the graph frequency domain. We then present an algorithm that jointly learns the model by optimizing the kernel parameters and the signal representation coefficients from a collection of graph signals. Our problem formulation has the flexibility of permitting the incorporation of signals possibly acquired on different graphs into the learning algorithm. We then theoretically study the signal reconstruction performance of the proposed method, by also elaborating on when joint learning on multiple graphs is preferable to learning an individual model on each graph. Experimental results on several graph data sets shows that the proposed method offers quite satisfactory signal interpolation accuracy in comparison with a variety of reference approaches in the literature.
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