Analysis of projection-back-free property in fully blind spatially regularized independent low-rank matrix analysis

Independent low-rank matrix analysis (ILRMA) is a representative method for blind source separation. Unfortunately, in ILRMA, there is scale ambiguity in separated signals for each frequency bin. To adjust the spectral scale of separated signals, a post-processing technique called projection back (PB) is commonly used. However, PB requires the calculation of the inverse of the demixing matrix, which often amplifies numerical errors when the demixing matrix is ill-conditioned. In our previous study, we proposed fully blind spatially regularized ILRMA (FB-SR-ILRMA), which is a blind method to simultaneously estimate the demixing matrices and the steering vectors of each source without knowing sensor positions, as with PB. In this paper, we focus on the potential ability of FB-SR-ILRMA to automatically adjust the scale of separated signals on the basis of distortionless response, which is a common principle in the field of beamforming. Thus, FB-SR-ILRMA can dismiss PB. In a numerical experiment, we investigated the difference in separation performance of FB-SR-ILRMA with and without PB. We confirmed that FB-SR-ILRMA without PB provides separated signals with sufficiently high quality, comparable to the oracle minimum variance distortionless response beamformer. We also confirmed that PB tends to degrade the source-to-interference ratio.