Learning Ancestral Atom via Sparse Coding

Sparse signal models have been the focus of recent research. In sparse coding, signals are represented with a linear combination of a small number of elementary signals called atoms, and the collection of atoms is called a dictionary. Design of the dictionary has strong influence on the signal approximation performance. Recently, to put prior information into dictionary learning, several methods imposing a certain kind of structure on the dictionary are proposed. In this paper, like wavelet analysis, a dictionary for sparse signal representation is assumed to be generated from an ancestral atom, and a method for learning the ancestral atom is proposed. The proposed algorithm updates the ancestral atom by iterating dictionary update in unstructured dictionary space and projection of the updated dictionary onto the structured dictionary space. The algorithm allows a simple differential geometric interpretation. Numerical experiments are performed to show the characteristics and advantages of the proposed algorithm.