# Spline-Like Wavelet Filterbanks with Perfect Reconstruction on Arbitrary Graphs

arXiv: https://arxiv.org/abs/2209.06385 · HTML: https://mlsanity.com/paper/2209.06385/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2022.

## Built on by (most cited first, 1 of 1)

- [Data-Adaptive Graph Framelets with Generalized Vanishing Moments for Graph Machine Learning](https://mlsanity.com/paper/2309.03537/) (2023)

## Abstract (arXiv)

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.