A dictionary-learning algorithm for the analysis sparse model with a determinant-type of sparsity measure

Dictionary learning for sparse representation of signals has been successfully applied in signal processing. Most the existing methods are based on the synthesis model, in which the dictionary is overcomplete. This paper addresses the dictionary learning and sparse representation with the so-called analysis model. In this new model, the analysis dictionary multiplying the signal can lead to a sparse outcome. Though it has been studied in the literature, there is still not an investigation in the context of nonnegative signal representation, which should not be a trivial problem. In this paper, moreover, we propose to learn an analysis dictionary from signals using a determinant-type of sparsity measure. In the formulation, we adopt the Euclidean distance as the error measure. Based on these, we present a new algorithm for the dictionary learning and sparse representation. Numerical experiments on recovery of analysis dictionary show the effectiveness of the proposed method.