Nonlinear Multilayered Representation of Graph-Signals
Résumé
We propose a nonlinear multiscale decomposition of signals defined on the vertex set of a general weighted graph. This decomposition is inspired by the hierarchical multiscale (BV,L2) decomposition of Tadmor, Nezzar, and Vese (Multiscale Model. Simul. 2(4):554-579, 2004). We find the decomposition by iterative regularization using a graph variant of the classical total variation regularization (Rudin et al, Physica D 60(1-4):259-268, 1992). Using tools from convex analysis, and in particular Moreau's identity, we carry out the mathematical study of the proposed method, proving the convergence of the representation and providing an energy decomposition result. The choice of the sequence of scales is also addressed.
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