Bayesian decomposition trees with application to signal denoising

Tree-structured dictionaries of orthonormal bases (wavelet packet/Malvar\´s wavelets) provide a natural framework to answer the problem of finding a "best representation" of both deterministic and stochastic signals. In this paper, we reformulate the "best basis" search as a model selection problem and present a Bayesian approach where the decomposition operators themselves are considered as model parameters. Denoising applications are subsequently presented to substantiate the proposed methodology.