Subband splitting: Simple, efficient and effective technique for solving block permutation problem in determined blind source separation

Solving the permutation problem is essential for determined blind source separation (BSS). Existing methods, such as independent vector analysis (IVA) and independent low-rank matrix analysis (ILRMA), tackle the permutation problem by modeling the co-occurrence of the frequency components of source signals. One of the remaining challenges in these methods is the block permutation problem, which may cause severe performance degradation. In this paper, we propose a simple and effective technique for solving the block permutation problem. The proposed technique splits the entire frequency bands into several overlapping subbands and sequentially applies BSS methods (e.g., IVA, ILRMA, or any other method) to each subband. Since the splitting reduces the size of the problem, the BSS methods can effectively work in each subband. Then, the permutations among the subbands are aligned by using the separation result in one subband as the initial values for the other subbands. Additionally, we propose SS-IVA and SS-ILRMA by combining subband splitting (SS) with IVA and ILRMA. Experimental results demonstrated that our technique remarkably improves the separation performance without increasing computational cost. In particular, our SS-ILRMA achieved the separation performance comparable to the oracle method (frequency-domain independent component analysis with the ideal permutation solver). Moreover, SS-ILRMA converged faster than conventional IVA and ILRMA.