Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs

Abstract

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.

arXiv comment33 pages,11 figures. This manuscript has been submitted to ScienceDirect Applied and Computational Harmonic Analysis (ACHA) on Jan 27,2022

References in corpus (7)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Perfect Reconstruction Two-Channel Wavelet Filter-Banks for Graph Structured Data
• Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs
• Sparse Representation on Graphs by Tight Wavelet Frames and Applications
• Spectral Projector-Based Graph Fourier Transforms
• Splines and Wavelets on Circulant Graphs
• Graph Fourier Transform Based on ${\ell }_1$ Norm Variation Minimization