NMF with Sparse Regularizations in Transformed Domains
Nonnegative blind source separation, which is also referred to as nonnegative matrix factorization (NMF), is a very active field in domains as different as astrophysics, audio processing, and biomedical signal processing. In this context, the efficient retrieval of the sources requires the use of signal priors such as sparsity. Although NMF has been well studied with sparse constraints in the direct domain, only very few algorithms can encompass nonnegativity together with sparsity in a transformed domain since simultaneously dealing with two priors in two different domains is challenging. In this paper, we show how a sparse NMF algorithm called nonnegative generalized morphological component analysis (nGMCA) can be extended to impose nonnegativity in the direct domain along with sparsity in a transformed domain, with both analysis and synthesis formulations. To the best of our knowledge, this work presents the first comparison of analysis and synthesis priors---as well as their reweighted versions---in t...