Majorization-minimization algorithm for smooth Itakura-Saito nonnegative matrix factorization

Nonnegative matrix factorization (NMF) with the Itakura-Saito divergence has proven efficient for audio source separation and music transcription, where the signal power spectrogram is factored into a "dictionary" matrix times an "activation" matrix. Given the nature of audio signals it is expected that the activation coefficients exhibit smoothness along time frames. This may be enforced by penalizing the NMF objective function with an extra term reflecting smoothness of the activation coefficients. We propose a novel regularization term that solves some deficiencies of our previous work and leads to an efficient implementation using a majorization-minimization procedure.