Love the abstract, a real blast from the past. The wavelet transform is a truly beautiful idea, with compact wavelets first identified by Duabechies in the 90s. They were revolutionary for, among other things, being a truly unique class of function with fascinating properties (fractal, compact analogues of the Fourier transform).

They have applications in image and video processing, though IMO they aren’t used as often as they should be (they are default in JPEG2000 IIRC, but that’s not commonly used).

There have definitely been attempts to do graph based wavelets before; tbh I’m not familiar enough with the literature to comment on the novelty of this work, but it looks solid on a quick inspection.