Determined Blind Source Separation with Sinkhorn Divergence-based Optimal Allocation of the Source Power

Blind source separation (BSS) refers to the process of recovering multiple source signals from observations recorded by an array of sensors. Common approaches to BSS, including independent vector analysis (IVA), and independent low-rank matrix analysis (ILRMA), typically rely on second-order models to capture the statistical independence of source signals for separation. However, these methods generally do not account for the implicit structural information across frequency bands, which may lead to model mismatches between the assumed source distributions and the distributions of the separated source signals estimated from the observed mixtures. To tackle these limitations, this paper shows that conventional approaches such as IVA and ILRMA can easily be leveraged by the Sinkhorn divergence, incorporating an optimal transport (OT) framework to adaptively correct source variance estimates. This allows for the recovery of the source distribution while modeling the inter-band signal dependence and reallocating source power across bands. As a result, enhanced versions of these algorithms are developed, integrating a Sinkhorn iterative scheme into their standard implementations. Extensive simulations demonstrate that the proposed methods consistently enhance BSS performance.