Spectral Domain Spline Graph Filter Bank

TL;DR

This paper introduces a spectral domain spline graph filter bank with perfect reconstruction and spectral sampling, enabling efficient multi-scale analysis of graph signals on arbitrary undirected graphs.

Contribution

It proposes a novel two-channel spline graph filter bank with spectral sampling that offers perfect reconstruction, spectral domain critical sampling, and low complexity implementation, adaptable to any undirected graph.

Findings

Demonstrates superior nonlinear approximation performance.

Shows improved denoising results over existing methods.

Validates effectiveness through simulations on various graph signals.

Abstract

In this paper, we present a structure for two-channel spline graph filter bank with spectral sampling (SGFBSS) on arbitrary undirected graphs. Our proposed structure has many desirable properties; namely, perfect reconstruction, critical sampling in spectral domain, flexibility in choice of shape and cut-off frequency of the filters, and low complexity implementation of the synthesis section, thanks to our closed-form derivation of the synthesis filter and its sparse structure. These properties play a pivotal role in multi-scale transforms of graph signals. Additionally, this framework can use both normalized and non-normalized Laplacian of any undirected graph. We evaluate the performance of our proposed SGFBSS structure in nonlinear approximation and denoising applications through simulations. We also compare our method with the existing graph filter bank structures and show its superior performance.