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 ℓ⁰-sparsity constraint. This constraint makes each input vector representable by a limited combination of atoms. The proposed method consists of two steps which are alternatively iterated: 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 outperform other methods in the literature that address the same learning problem, in different applications, and both with synthetic and “real” data, i.e. coming from natural images.