Analysis dictionary learning based on summation of blocked determinants measure of sparseness

This paper addresses the dictionary learning and sparse representation with the analysis model. Though it has been studied in the literature, there is still not an investigation in the context of dictionary learning for nonnegative signal representation. For measuring the sparseness, in this paper, we propose a measure that is so called the summation of blocked determinants. Based on this measure, a new analysis sparse model is derived, and an iterative sparseness maximization approach is proposed to solve this model. In the approach, the nonnegative sparse representation problem can be cast into row-to-row optimizations with respect to the dictionary, and then the quadratic programming (QP) technique is used to optimize each row. Numerical experiments on recovery of analysis dictionary show the effectiveness of the proposed algorithm.