Spline-Like Wavelet Filterbanks with Perfect Reconstruction on Arbitrary Graphs

TL;DR

This paper introduces a new class of spline-like wavelet filterbanks for graph signals that achieve perfect reconstruction, are localized in the graph domain, and can be optimized for specific frequency responses, improving denoising performance.

Contribution

It proposes a novel spline-like wavelet filterbank framework for arbitrary graphs with perfect reconstruction and frequency annihilation capabilities, extending existing methods.

Findings

Filters are localized in the graph domain.

Filterbanks achieve perfect reconstruction.

Demonstrated effectiveness in denoising tasks.

Abstract

In this work, we propose a class of spline-like wavelet filterbanks for graph signals. These filterbanks possess the properties of critical sampling and perfect reconstruction. Besides, the analysis filters are localized in the graph domain because they are polynomials of the normalized adjacency matrix of the graph. We generalize the spline-like filters in the literature so that they have the ability to annihilate signals of some specified frequencies. Optimization problems are posed for the analysis filters to approximate desired responses. We conduct some experiments to demonstrate the good locality of the proposed filters and the good performance of the filterbank in the denoising task.