图形信号处理：顶点域和谱域中的双重GSP采样
Graph Signal Processing: Dualizing GSP Sampling in the Vertex and Spectral Domains
摘要：
基于顶点和基于谱的GSP采样最近已经被研究。文献认识到，一个领域的方法在另一个领域没有对应的方法。本文表明，事实上，人们可以开发一个统一的图形信号采样理论与类似的解释，在这两个领域就像在传统的DSP采样。为了实现这一点，我们引入了一个频谱移位$M$作用在频谱域，而不是移位$A$，作用在顶点域。这导致从谱域开始的GSP理论，例如，谱域中的线性移位不变（LSI）滤波是利用多项式$P(M)$。然后，我们开发的GSP顶点和频谱域双版本的四个标准采样步骤的子采样，抽取，上采样和插值。我们展示了如何GSP采样减少DSP采样时，图是有向时间周期图。简单的例子说明了普惠制抽样中可用的选择的影响。
英文摘要：
Vertex based and spectral based GSP sampling has been studied recently. The literature recognizes that methods in one domain do not have a counterpart in the other domain. This paper shows that in fact one can develop a unified graph signal sampling theory with analogous interpretations in both domains just like sampling in traditional DSP. To achieve it, we introduce a spectral shift $M$ acting in the spectral domain rather than shift $A$ that acts in the vertex domain. This leads to a GSP theory that starts from the spectral domain, for example, linear shift invariant (LSI) filtering in the spectral domain is with polynomials $P(M)$. We then develop GSP vertex and spectral domain dual versions for each of the four standard sampling steps of subsampling, decimation, upsampling, and interpolation. We show how GSP sampling reduces to DSP sampling when the graph is the directed time cycle graph. Simple examples illustrate the impact of choices that are available in GSP sampling.
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