Underdetermined Reverberant Blind Source Separation: Sparse Approaches for Multiplicative and Convolutive Narrowband Approximation

TL;DR: The separation problem in an optimization framework is formulated based on the multiplicative narrowband approximation in the time-frequency domain with the help of the short-time-Fourier-transform and the sparse representation of the source signals to solve the blind source separation problem.

Abstract: We consider the problem of blind source separation for underdetermined convolutive mixtures. Based on the multiplicative narrowband approximation in the time-frequency domain with the help of the short-time-Fourier-transform STFT and the sparse representation of the source signals, we formulate the separation problem in an optimization framework. This framework is then generalized based on the recently investigated convolutive narrowband approximation and the statistics of the room impulse response. Algorithms with convergence proof are then employed to solve the proposed optimization problems. The evaluation of the proposed frameworks and algorithms for synthesized and live recorded mixtures are illustrated. The proposed approaches are also tested for mixtures with input noise. Numerical evaluations show the advantages of the proposed methods.