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This paper describes a versatile method that accelerates multichannel sourceseparation methods based on full-rank spatial modeling. A popular approach tomultichannel source separation is to integrate a spatial model with a sourcemodel for estimating the spatial covariance matrices (SCMs) and power spectraldensities (PSDs) of each sound source in the time-frequency domain. One of themost successful examples of this approach is multichannel nonnegative matrixfactorization (MNMF) based on a full-rank spatial model and a low-rank sourcemodel. MNMF, however, is computationally expensive and often works poorly dueto the difficulty of estimating the unconstrained full-rank SCMs. Instead ofrestricting the SCMs to rank-1 matrices with the severe loss of the spatialmodeling ability as in independent low-rank matrix analysis (ILRMA), werestrict the SCMs of each frequency bin to jointly-diagonalizable but stillfull-rank matrices. For such a fast version of MNMF, we propose acomputationally-efficient and convergence-guaranteed algorithm that is similarin form to that of ILRMA. Similarly, we propose a fast version of astate-of-the-art speech enhancement method based on a deep speech model and alow-rank noise model. Experimental results showed that the fast versions ofMNMF and the deep speech enhancement method were several times faster andperformed even better than the original versions of those methods,respectively.

Fast Multichannel Source Separation Based on Jointly Diagonalizable Spatial Covariance Matrices