A Strategy for Residual Component-Based Multiple Structured Dictionary Learning

A new strategy for multiple structured dictionary learning is proposed. It is motivated by the fact that a signal and its residual after sparse approximation do not necessarily possess the same geometric structure. Based on the geometric structure of each residual component, the most appropriate dictionary is selected. A single-atom sparse representation vector of this residual is calculated and the chosen dictionary is updated. For a given training signal, the process of model (dictionary) selection and one-atom representation is repeated until the desired sparsity or approximation error is reached. Thus, the proposed strategy provides a mechanism whereby each signal can update the most relevant dictionaries based on the structure of its residuals. Simulations conducted over natural images show that, in comparison to standard single or multiple dictionary learning and sparse representation approaches, the proposed strategy significantly improves the representation quality.