The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for such a system can exist, based on the theory of polytopes. Furthermore, we develop the paradigm of combined sparse representations, where only a part of the...

We investigate the use of sparse priors to regularize nonnegative blind source separation (BSS) problems. Dealing with the nonnegativity constraint in the direct/sample domain, and at the same time sparsity in some other signal representation, raises algorithmic issues. We show how such sparse non-negative BSS problems can be tackled with the help of proximal splitting methods. We present a pre...

This paper presents a statistical model for textures that uses a non-negative decomposition on a set of local atoms learned from an exemplar. This model is described by the variances and kurtosis of the marginals of the decomposition of patches in the learned dictionary. A fast sampling algorithm allows to draw a typical image from this model. The resulting texture synthesis captures the geomet...