Time-Deconvolutive CNMF for Multichannel Blind Source Separation

Abstract

This paper tackles multichannel separation of convolutive mixtures of audio sources by using complex-valued nonnegative matrix factorization (CNMF). We extend models proposed by previous works and show that one may tailor advanced single-channel NMF techniques, such as the deconvolutive NMF, to the multichannel factorization scheme. Additionally, we propose a regularized cost function that enables the user to control the distribution of the estimated parameters without significantly increasing the underlying computational cost. We also develop an optimization framework compatible with previous related works. Our simulations show that the proposed deconvolutive model offers advantages when compared to the simple NMF, and that the regularization is able to steer the parameters towards a solution with desirable properties.

Multichannel Source Separation Using Time-Deconvolutive CNMF

“…We proposed an extended version [1] of the CNMF algorithm [11], leveraging the efficient representation from the deconvolutive NMF model. We also provided the user with control over the distribution of the extracted signatures through regularization, which steers the method toward a sparse solution.…”

“…where v H is the Hermitian of v andz is the complex conjugate of z. Additionally, assuming that different sources q and q are orthogonal, and then transposing the correlation property to the 1 A subset C of a given vector space is a cone if αx ∈ C for any x ∈ C and any α ≥ 0. It is a convex cone when it is closed for conical combinations, i.e., when α 1 x 1 + α 2 x 2 ∈ C for any x 1 , x 2 ∈ C and any α 1 , α 2 ≥ 0.…”