Non-negative source separation using the maximum likelihood approach

This papers addresses the problem of non-negative source separation using the maximum likelihood approach. It is shown that this approach can be effective by considering that the sources are distributed according to a density having a non-negative support from which an adequate nonlinear separating function can be derived. In the particular of spectroscopic data which is our main concern, a good candidate is the Gamma distribution which allows to encode both non-negativity and sparsity of the source signals. Numerical experiments are used to assess the performances of the method.