We consider the combination of two approaches for modeling data admitting sparse representations: On the one hand, dictionary learning has proven very effective for various signal restoration and representation tasks. On the other hand, recent work on structured sparsity provides a natural framework for modeling dependencies between
dictionary elements. We propose to combine these approaches to learn dictionaries embedded in a hierarchy. Experiments show that for natural image patches, learned dictionary elements organize themselves naturally in such a hierarchical structure, leading
to an improved performance for restoration tasks. When applied to text documents, our
method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models. (Joint work with Rodolphe Jenatton, Julien Mairal and Guillaume Obozinski)