论文标题
多个偏移的多项式图滤波器和反向过滤的分布式实现
Polynomial graph filter of multiple shifts and distributed implementation of inverse filtering
论文作者
论文摘要
多项式图滤波器及其反向在图形信号处理中起重要作用。多项式图过滤器的一个优点是可以以分布式方式实现它们，这仅涉及相邻顶点之间的数据传输。反滤波中产生的挑战是直接实现可能会承受高计算负担，因为即使原始过滤器具有较小的带宽，反向图过滤器通常具有完整的带宽。在本文中，我们考虑了多个移位的多项式图滤波器的反过滤过程的分布式实现，我们提出了可以在分布式网络中实现的两种迭代近似算法，在分布式网络中，每个顶点都配备了有限的数据存储，计算功率和数据交换设施，以与其邻接的Vertices相邻的设施。我们还展示了提出的迭代近似算法的有效性，以实现反向过滤过程及其令人满意的性能，以在218个位置在218个位置进行变化的图形信号和美国每小时温度的数据集。
Polynomial graph filters and their inverses play important roles in graph signal processing. An advantage of polynomial graph filters is that they can be implemented in a distributed manner, which involves data transmission between adjacent vertices only. The challenge arisen in the inverse filtering is that a direct implementation may suffer from high computational burden, as the inverse graph filter usually has full bandwidth even if the original filter has small bandwidth. In this paper, we consider distributed implementation of the inverse filtering procedure for a polynomial graph filter of multiple shifts, and we propose two iterative approximation algorithms that can be implemented in a distributed network, where each vertex is equipped with systems for limited data storage, computation power and data exchanging facility to its adjacent vertices. We also demonstrate the effectiveness of the proposed iterative approximation algorithms to implement the inverse filtering procedure and their satisfactory performance to denoise time-varying graph signals and a data set of US hourly temperature at 218 locations.
