Spectral graph wavelet packets frames

Classical wavelet, wavelet packets and time-frequency dictionaries have been generalized to the graph setting, the main goal being to obtain atoms which are jointly localized both in the vertex and the graph spectral domain. We present a new method to generate a whole dictionary of frames of wavelet packets defined in the graph spectral domain to represent signals on weighted graphs. We will give some concrete examples on how the spectral graph wavelet packets can be used for compressing, denoising and reconstruction by considering a signal, given by the fRMI (functional magnetic resonance imaging) data, on the nodes of voxel-wise brain graph with 900760 nodes, representing the brain voxels.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This study extends classical wavelet, wavelet packets, and time-frequency dictionaries to the graph setting, aiming to obtain atoms that are jointly localized in both the vertex and graph spectral domain. A new method is proposed to generate a complete dictionary of wavelet packet frames defined in the graph spectral domain for representing signals on weighted graphs.