Introducing fast multichannel nonnegative matrix factorization for underdetermined blind audio source separation

In blind audio source separation (BSS), when the number of sources does not exceed the number of microphones (i.e., the determined case), efficient methods such as independent low-rank matrix analysis can be applied. However, these methods are generally inapplicable to the underdetermined case, where there are more sources than microphones. An alternative is the multichannel Wiener filter framework, which remains applicable even in underdetermined settings. Within this framework, multichannel nonnegative matrix factorization (MNMF) is a widely used technique, but it suffers from high computational cost due to repeated matrix inversions. In this talk, I introduce FastMNMF, a recent algorithm that accelerates MNMF by several orders of magnitude through joint diagonalization. FastMNMF constrains the spatial covariance matrices of all sources to be jointly diagonalizable, enabling efficient computation by reducing matrix inversion to simple inversion of diagonal elements. I will also briefly review the evolution of BSS techniques and discuss future research directions.