Discrete uncertainty principles on graphs
Discrete uncertainty principles on graphs
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图上的离散不确定性原理
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
P. Vaidyanathan
中科院分区：
文献类型：
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作者：
Oguzhan Teke;P. Vaidyanathan
本文提出了一种新的方法来制定的不确定性原则的图，通过使用非局部测度的概念的基础上稀疏。不确定性原理是基于信号中非零元素的总数及其相应的图形傅里叶变换（GFT）来制定的。通过提供一个下界，这个总数，它表明，一个非零的图形信号和它的GFT不能同时任意稀疏。总稀疏的理论界推导。对于几个真实世界的图，这个界限实际上可以通过选择图信号作为图的适当特征向量来实现。
This paper advances a new way to formulate the uncertainty principle for graphs, by using a non-local measure based on the notion of sparsity. The uncertainty principle is formulated based on the total number of nonzero elements in the signal and its corresponding graph Fourier transform (GFT). By providing a lower bound for this total number, it is shown that a nonzero graph signal and its GFT cannot be arbitrarily sparse simultaneously. The theoretical bound on total sparsity is derived. For several real-world graphs this bound can actually be achieved by choosing the graph signals to be appropriate eigenvectors of the graph.