Regularized dictionary learning for sparse approximation

Sparse signal models approximate signals using a small number of elements from a large set of vectors, called a dictionary. The success of such methods relies on the dictionary fitting the signal structure. Therefore, the dictionary has to be designed to fit the signal class of interest. This paper uses a general formulation that allows the dictionary to be learned form the data with some a priori information about the dictionary. In this formulation a universal cost function is proposed and practical algorithms are presented to minimize this cost under different constraints on the dictionary. The proposed methods are compared with previous approaches using synthetic and real data. Simulations highlight the advantages of the proposed methods over other currently available dictionary learning strategies.