循环图上稀疏信号的采样与重构-Graph-FRI简介
Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI
摘要：
采用图的目标是更广义的信号处理理论，我们提出了一种新的采样框架（小波）稀疏信号定义在循环图上的有限创新率（FRI）理论的基本属性扩展到图域，并可以适用于任意图形通过适当的近似方案。在其核心，引入的Graph-FRI框架指出，循环图顶点上的任何K-稀疏信号都可以从其在图谱域中的降维表示（图傅里叶变换（GFT））中完美重建，最小尺寸为2K。利用最近发展起来的e样条和e样条小波理论，可以将这种图谱变换分解为利用图e样条滤波器的多分辨率低通滤波操作，以及随后的到谱图域的变换;这允许推断不同的采样模式，并且最终推断相关联的粗化图的结构，其保留了原始图的基本属性，包括圆性以及在适用的情况下的图形生成集。
英文摘要：
With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-framework states that any K-sparse signal on the vertices of a circulant graph can be perfectly reconstructed from its dimensionality-reduced representation in the graph spectral domain, the Graph Fourier Transform (GFT), of minimum size 2K. By leveraging the recently developed theory of e-splines and e-spline wavelets on graphs, one can decompose this graph spectral transformation into the multiresolution low-pass filtering operation with a graph e-spline filter, and subsequent transformation to the spectral graph domain; this allows to infer a distinct sampling pattern, and, ultimately, the structure of an associated coarsened graph, which preserves essential properties of the original, including circularity and, where applicable, the graph generating set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
