GSP = DSP + 边界条件——图信号处理伴随模型
GSP = DSP + Boundary Conditions -- The Graph Signal Processing Companion Model
AI总结：
本文提出图信号处理伴随模型，证明GSP等价于DSP加边界条件，并展示其卷积可用FFT实现、调制可产生平移效应以实现多路复用，从而扩展了GSP理论。
摘要：
本文提出了图信号处理（GSP）伴随模型，该模型自然地复现了经典信号处理（DSP）的基本原理，并将其应用于GSP。伴随模型表明，GSP可以等价于DSP“加上”适当的边界条件（bc）——这一结论在广泛条件下成立，并且适用于任意无向或有向图。这种等价性为如何扩展GSP提供了思路：将DSP概念自然地推广到GSP伴随模型，然后将其迁移回常见的图顶点域和图傅里叶域。本文表明，GSP展开为两个在DSP中重合的不同模型：基于我们即将引入的谱频率向量$λ$的（Hadamard或逐点）幂的伴随模型，以及基于邻接矩阵及其特征向量的传统图顶点模型。本文在多个方向上扩展了GSP，包括证明在图伴随模型中卷积可以通过FFT实现，以及通过适当选择载波的GSP调制展现出DSP平移效应，从而能够通过对图信号进行调制来实现多路复用。
英文摘要：
The paper presents the graph signal processing (GSP) companion model that naturally replicates the basic tenets of classical signal processing (DSP) for GSP. The companion model shows that GSP can be made equivalent to DSP 'plus' appropriate boundary conditions (bc) - this is shown under broad conditions and holds for arbitrary undirected or directed graphs. This equivalence suggests how to broaden GSP - extend naturally a DSP concept to the GSP companion model and then transfer it back to the common graph vertex and graph Fourier domains. The paper shows that GSP unrolls as two distinct models that coincide in DSP, the companion model based on (Hadamard or pointwise) powers of what we will introduce as the spectral frequency vector $λ$, and the traditional graph vertex model, based on the adjacency matrix and its eigenvectors. The paper expands GSP in several directions, including showing that convolution in the graph companion model can be achieved with the FFT and that GSP modulation with appropriate choice of carriers exhibits the DSP translation effect that enables multiplexing by modulation of graph signals.
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