A Bayesian non parametric approach to learn dictionaries with adapted numbers of atoms

Learning redundant dictionaries for sparse representation from sets of patches has proven its efficiency in solving inverse problems. In many methods, the size of the dictionary is fixed in advance. Moreover the optimization process often calls for the prior knowledge of the noise level to tune parameters. We propose a Bayesian non parametric approach which is able to learn a dictionary of adapted size : the adequate number of atoms is inferred thanks to an Indian Buffet Process prior. The noise level is also accurately estimated so that nearly no parameter tuning is needed. Numerical experiments illustrate the relevance of the resulting dictionaries.