Spectral graph transforms: wavelets, frames, and open problems
Sandra Saliani (Università degli Studi della Basilicata)
Abstract: Classical transforms, as Fourier, wavelet, wavelet packets and time-frequency dictionaries have been generalized to functions defined on finite, undirected graphs, where the connections between vertices are encoded by the Laplacian matrix.
Despite working in a finite and discrete environment, many problems arise in applications where the graph is very large, as it is not possible to determine all the eigenvectors of the Laplacian explicitly. For example, in the case of our interest: a voxel-wise brain graph $\mathcal{G}$ with $900760$ nodes (representing the brain voxels), and signals given by the fRMI (functional magnetic resonance imaging).
After an overview of the methods and of the open problems, we present a new method to generate frames of wavelet packets defined in the graph spectral domain to represent signals on finite graphs.
Joint work with Iulia Martina Bulai.
classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory
Audience: researchers in the topic
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| Organizers: | Alessandro Monguzzi*, Valentina Casarino, Bianca M. Gariboldi, Stefano Meda |
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