Two-Channel Filter Banks on Joint Time-Vertex Graphs with Oversampled Graph Laplacian Matrix

TL;DR

This paper introduces a novel oversampled joint time-vertex graph Laplacian matrix that enables more effective multiresolution filtering and denoising of graph signals and images, surpassing traditional critically sampled methods.

Contribution

The paper proposes a new joint time-vertex oversampled graph Laplacian matrix and two-channel filter banks that fully utilize all edges and support redundant multiresolution analysis.

Findings

Improved signal decomposition and reconstruction quality.

Enhanced denoising performance on graph signals and images.

Outperforms existing critically sampled and other methods in experiments.

Abstract

To address the limitations of conventional critically sampled graph filter banks in joint time-vertex signal processing, which require decomposing the joint graph into bipartite subgraphs and thus cannot fully exploit all temporal and spatial edges in a single-stage transform, we introduce the joint time-vertex oversampled graph Laplacian matrix. This operator enables the construction of bipartite extensions that preserve all edges of the original joint graph and supports redundant multiresolution representations. Based on this operator, we design two-channel joint time-vertex oversampled graph filter banks and develop efficient oversampling extensions using a $K$-coloring strategy. The proposed framework is applied to both graph signal and image/video denoising, modeling images as graph signals to leverage structural relationships. Extensive experiments demonstrate its effectiveness in decomposition, reconstruction, and denoising, achieving notable performance improvements over critically sampled and existing methods.