K-WEB: NONNEGATIVE DICTIONARY LEARNING FOR SPARSE IMAGE REPRESENTATIONS

This paper presents a new nonnegative dictionary learning method, to decompose an input data matrix into a dictionary of nonnegative atoms, and a representation matrix with a strict `0-sparsity constraint. This constraint makes each input vec-tor representable by a limited combination of atoms. The pro-posed method consists of two steps which are alternatively it-erated: a sparse coding and a dictionary update stage. As for the dictionary update, an original method is proposed, which we call K-WEB, as it involves the computation of k WEighted Barycenters. The so designed algorithm is shown to outper-form other methods in the literature that address the same learning problem, in different applications, and both with syn-thetic and “real ” data, i.e. coming from natural images. Index Terms — Dictionary learning, sparse representa-tions, K-SVD, NM