Two-Channel Critically-Sampled Graph Filter Banks With Spectral Domain Sampling

TL;DR

This paper introduces two-channel critically-sampled graph filter banks using spectral domain sampling, achieving perfect reconstruction and symmetry, with proven criteria and demonstrated effectiveness in approximation and denoising tasks.

Contribution

It presents a novel spectral domain sampling method for graph filter banks that guarantees perfect reconstruction and symmetric structure, unlike traditional vertex domain approaches.

Findings

Achieves perfect reconstruction regardless of graph characteristics

Demonstrates superior performance in denoising tasks

Proves spectral and vertex domain sampling coincide in a special case

Abstract

We propose two-channel critically-sampled filter banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable properties: 1) perfect reconstruction regardless of the characteristics of the underlying graphs and graph variation operators and 2) a symmetric structure; i.e., both analysis and synthesis filter banks are built using similar building blocks. Along with the structure of the filter banks, this paper also proves the general criterion for perfect reconstruction and theoretically shows that the vertex and spectral domain sampling coincide for a special case. The effectiveness of our approach is evaluated by comparing its performance in nonlinear approximation and denoising with various conventional graph transforms.