Frequency-domain Convolutive Blind Source Separation with Minimum Volume Constraint

‍ ‍Most frequency-domain blind source separation algorithms are based on the narrow-band assumption， which is no longer applicable in the long reverberation environment. The convolutive transfer function-based multichannel nonnegative matrix factorization （CTF-MNMF） does not rely on the narrow-band assumption， and the separation performance in the long reverberation environment is significantly improved compared with other traditional methods. However， the nonnegative matrix factorization （NMF） approximates the power spectrum of source signal， which is ill-posed in most cases， and the optimal solution is non-unique. In this paper， a frequency-domain blind source separation method with minimum volume constraint is proposed. Minimum volume constraint of the NMF basis matrix is added into the objective function of CTF-MNMF， aiming at improve the fitness of the problem and the discriminability of the estimated parameters. Majorization-Minimization （MM） optimization method is used to solve the objective function with the minimum volume constraint， and the closed-form solution of the estimated parameters is derived. Simulation experiments show that the separation performance of the method is significantly improved compared with the CTF-MNMF method in a long reverberation environment.