Time-dependent recursive regularization for sound source separation

Real world music pieces often present time-varying spectral shapes that normally lead to time, amplitude or frequency modulations in a phrase. Whereasthe standard Non-negative Matrix Factorization (NMF) assumes fixed spectral bases, an extension is proposed where the temporalactivations, the coefficients of the decomposition on the spectralatom basis, become frequency dependent In this paper, a frame-based recursive regularization method is proposed for sound source separation applications. System of equations evolves when a new frame is added and an old frame is dropped in order to track varying characteristics of some instruments. The amount of required matrix inversions is greatly reduced with the proposed work. This work is also compared with a time-dependent NMF method to show the superior performance on the signals with glissando and vibrato effects. Objective measure is applied as well.