# Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs

arXiv: https://arxiv.org/abs/2210.02024 · HTML: https://mlsanity.com/paper/2210.02024/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 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)

This paper extends the existing theory of perfect reconstruction two-channel filter banks from bipartite graphs to non-bipartite graphs. By generalizing the concept of downsampling/upsampling we establish the frame of two-channel filter bank on arbitrary connected, undirected and weighted graphs. Then the equations for perfect reconstruction of the filter banks are presented and solved under proper conditions. Algorithms for designing orthogonal and biorthogonal banks are given and two typical orthogonal two-channel filter banks are calculated. The locality and approximation properties of such filter banks are discussed theoretically and experimentally.