具有不规则性的图傅里叶变换
Irregularity-Aware Graph Fourier Transforms
摘要：
在本文中，我们提出了一种新的推广的图形傅里叶变换（GFT）。我们的方法是基于分别考虑信号能量和信号变化的定义，导致几种可能的正交GFT。我们的方法包括传统的GFT定义的特殊情况下，同时也导致新的GFT设计，更好地考虑到不规则的性质的图形。作为一个例子，在传感器网络的背景下，我们使用的Voronoi细胞面积的顶点在我们的GFT定义，表明它导致一个更合理的定义图信号能量，即使采样是非常不规则的。
英文摘要：
In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our approach includes traditional definitions of the GFT as special cases, while also leading to new GFT designs that are better at taking into account the irregular nature of the graph. As an illustration, in the context of sensor networks we use the Voronoi cell area of vertices in our GFT definition, showing that it leads to a more sensible definition of graph signal energy even when sampling is highly irregular.
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