The generalized Haar-Walsh transform (with J. Irion), Proc. 2014 IEEE Workshop on Statistical Signal Processing, pp.472-475, 2014.


We introduce a novel multiscale transform for signals on graphs which is a generalization of the classical Haar and Walsh-Hadamard Transforms. Using a recursive partitioning of the graph and successive averaging and differencing operations, our transform generates an overcomplete dictionary of orthonormal bases. We describe how to adapt the classical best-basis search algorithm to this setting, and show results from preliminary denoising experiments.

Keywords: Fiedler vectors, spectral graph partitioning, multiscale baiss dictionaries, wavelets on graphs

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