Fast algorithm for complex-NMF with application to source separation

In this paper we consider a Nonnegative Matrix Factorization (NMF) model on complex numbers, in particular, we propose a group complex-NMF (cNMF) model that subsumes the phase-consistency complex NMF for the audio Blind Source Separation (aBSS). Using Wirtinger calculus, we propose a gradient-based algorithm to solve cNMF. The algorithm is then further accelerated using a heuristic extrapolation scheme. Numerical results show that the accelerated algorithm has significantly faster convergence.