  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 a highly developed source model can solve the permutation problem
of the frequency-domain BSS to a large extent, which is the reason for the
excellence of ILRMA. In this paper, we further improve the separation
performance of ILRMA by additionally considering the general structure of
spectrograms, which is 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 to each other via the uncertainty
principle. Such co-occurrence among the spectral components can function as an
assistant for solving the permutation problem, which has been demonstrated by a
recent study. On the basis of these facts, we propose an algorithm for
realizing Consistent ILRMA by slightly modifying the original algorithm. Its
performance was extensively evaluated through experiments performed with
various window lengths and shift lengths. The results indicated several
tendencies of the original and proposed ILRMA that include some topics not
fully discussed 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.
