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Non-negative blind source separation (non-negative BSS), which is alsoreferred to as non-negative matrix factorization (NMF), is a very active fieldin domains as different as astrophysics, audio processing or biomedical signalprocessing. In this context, the efficient retrieval of the sources requiresthe use of signal priors such as sparsity. If NMF has now been well studiedwith sparse constraints in the direct domain, only very few algorithms canencompass non-negativity together with sparsity in a transformed domain sincesimultaneously dealing with two priors in two different domains is challenging.In this article, we show how a sparse NMF algorithm coined non-negativegeneralized morphological component analysis (nGMCA) can be extended to imposenon-negativity in the direct domain along with sparsity in a transformeddomain, with both analysis and synthesis formulations. To our knowledge, thiswork presents the first comparison of analysis and synthesis priors ---as wellas their reweighted versions--- in the context of blind source separation.Comparisons with state-of-the-art NMF algorithms on realistic data show theefficiency as well as the robustness of the proposed algorithms.

NMF with Sparse Regularizations in Transformed Domains