Polynomial graph filter of multiple shifts and distributed implementation of inverse filtering
arXiv:2003.11152
Abstract
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.
References in corpus (14)
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
- Discrete Signal Processing on Graphs
- Perfect Reconstruction Two-Channel Wavelet Filter-Banks for Graph Structured Data
- Signal Recovery on Graphs: Variation Minimization
- GSPBOX: A toolbox for signal processing on graphs
- Autoregressive Moving Average Graph Filtering
- Deep Graph-Convolutional Image Denoising
- Forecasting Time Series with VARMA Recursions on Graphs
- Advances in Distributed Graph Filtering
- Two-Channel Critically-Sampled Graph Filter Banks With Spectral Domain Sampling
- Splines and Wavelets on Circulant Graphs
- Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI
- Multi-dimensional Graph Fourier Transform
- Preconditioned Gradient Descent Algorithm for Inverse Filtering on Spatially Distributed Networks