发表机构
Università di Torino; FCEyN-University of Buenos Aires; IMAS-CONICET; Università di Napoli Parthenope（都灵大学; 布宜诺斯艾利斯大学物理与天文学院; 阿根廷国家科学研究委员会马德普拉塔数学研究所; 帕提诺佩那不勒斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用归一化图拉普拉斯的谱理论，在格图和有限图上研究图信号的动态采样，构造动态框架并推导重构公式，并分析迭代次数与采样分布对框架条件数的影响。
AI 中文摘要
我们利用归一化图拉普拉斯算子的谱理论研究图信号的动态采样。图Paley-Wiener空间GPW_w被定义为与带宽参数w相关的谱子空间，并研究由保持这些空间不变的有界算子的迭代生成的测量值的重构问题。对于格图Z，我们给出了归一化拉普拉斯算子的显式谱分解，将相应的图Paley-Wiener空间与环面上的经典带限空间等同起来，并在此设置中恢复了经典采样定理。利用算子轨道的框架，我们为GPW_w(Z)构造了动态框架并推导了重构公式。我们还讨论了向Z^n的扩展，其中带宽区域由拉普拉斯符号的下水平集描述。最后，对于有限图，我们根据图算子迭代生成的有限框架来表述GPW_w(G)中的动态恢复。使用路径图P_N作为数值模型，我们研究了迭代次数和采样顶点的空间分布如何影响最优框架界以及所得动态框架的条件数。
英文摘要
We study dynamical sampling for graph signals using the spectral theory of the normalized graph Laplacian. Graph Paley-Wiener spaces GPW_w are defined as spectral subspaces associated with a bandwidth parameter w, and reconstruction is studied from measurements generated by iterates of bounded operators leaving these spaces invariant. For the lattice graph Z, we give an explicit spectral decomposition of the normalized Laplacian, identify the corresponding Graph Paley--Wiener spaces with classical bandlimited spaces on the torus, and recover the classical sampling theorem in this setting. Using frames of operator orbits, we construct dynamical frames for GPW_w(Z) and derive reconstruction formulas. We also discuss the extension to Z^n, where the bandwidth region is described by a sublevel set of the Laplacian symbol. Finally, for finite graphs, we formulate dynamical recovery in GPW_w(G)\) in terms of finite frames generated by iterates of the graph operator. Using the path graph P_N as a numerical model, we study how the number of iterates and the spatial distribution of the sampled vertices affect the optimal frame bounds and the conditioning of the resulting dynamical frame.
Comments31 pages, 5 figures
