Consistent independent low-rank matrix analysis for determined blind source separation

Independent low-rank matrix analysis (ILRMA) is the state-of-the-art algorithm for blind source separation (BSS) in the determined situation (the number of microphones is greater than or equal to that of source signals). ILRMA achieves a great separation performance by modeling the power spectrograms of the source signals via the nonnegative matrix factorization (NMF). Such highly developed source model can effectively solve the permutation problem of the frequency-domain BSS, which should be the reason of the excellence of ILRMA. In this paper, we further improve the separation performance of ILRMA by additionally considering the general structure of spectrogram called consistency, and hence we call the proposed method Consistent ILRMA. Since a spectrogram is calculated by an overlapping window (and a window function induces spectral smearing called main- and side-lobes), the time-frequency bins depend on each other. In other words, the time-frequency components are related each other via the uncertainty principle. Such co-occurrence among the spectral components can be an assistant for solving the permutation problem, which has been demonstrated by a recent study. Based on these facts, we propose an algorithm for realizing Consistent ILRMA by slightly modifying the original algorithm. Its performance was extensively studied through the experiments performed with various window lengths and shift lengths. The results indicated several tendencies of the original and proposed ILRMA which include some topics have not discussed well in the literature. For example, the proposed Consistent ILRMA tends to outperform the original ILRMA when the window length is sufficiently long compared to the reverberation time of the mixing system.