Design of new auxiliary function for fully blind spatially regularized independent low-rank matrix analysis

A representative method for blind source separation (BSS) is independent low-rank matrix analysis (ILRMA). Spatially regularized ILRMA (SR-ILRMA) utilizes prior information about the acoustic transfer system, such as steering vectors (SVs) for each source, as a regularizer in ILRMA. Although it has been reported that SR-ILRMA achieved higher separation performance than ILRMA in an experiment, SR-ILRMA is not a fully blind method; i.e., SVs should be known in advance. In our previous study, we proposed a fully blind SR-ILRMA that simultaneously estimates SVs and other parameters in SR-ILRMA on the basis of the majorization–minimization (MM) algorithm. Since an auxiliary function is not unique in the MM algorithm, it may be possible to design a better auxiliary function that achieves faster convergence. In this paper, we design a new auxiliary function for deriving the update rule of SVs, motivated by the conjecture that an auxiliary function that better approximates the cost function would lead to faster convergence. In a numerical experiment, we confirm that the update rule based on the new auxiliary function achieves faster convergence than that based on the conventional one.