Abstract

In this talk we preset a novel multi-phase dictionary learning algorithm that addresses the complexity by clustering and reducing the dictionary, enhancing the resolution power of the method by accounting for the representation error introduced by the dictionary reduction. The problem is set up and solved in the Bayesian framework, and all steps involving sparse coding are performed by using sparsity promoting Bayesian hypermodels and a priorconditioning techniques that are demonstrated earlier to provide a computationally efficient way to find compressible solutions to linear inverse problems. As a novelty, in the cluster identification problem, we introduce a new and data-informed way to implement group sparsity in order to identify as few clusters as possible to explain the data. Moreover, ideas from the previous works on Bayesian modeling error analysis are modefied and extended to quantify the modeling error introduced when passing from the full dictionary cluster to the reduced one.  This works has been done in collaboration with Alberto Bocchinfuso and Erkki Somersalo.