Fast and Stable Block Majorization-Minimization Algorithms for Independent Vector Analysis With Scale-Consistent Spatial Regularization

Independent vector analysis (IVA), a fundamental source separation technique, can be extended by incorporating prior knowledge of the sources and their spatial characteristics. When pre-estimated relative transfer functions (RTFs) are available for one or more sources, spatially-regularized IVA (SR-IVA) leverages this information as spatial regularization to enhance IVA. However, SR-IVA suffers from a fundamental scale inconsistency: the optimal scaling of each separation filter differs between the IVA cost function and the spatial regularization term, which calls the validity of the SR-IVA formulation into question. Scale-consistent SR-IVA (SSR-IVA) was proposed to address this limitation. While it retains the IVA cost function for optimizing the separation matrix, it applies spatial regularization only to its scale-consistent part, specifically, the inverse of the RTF matrix, each column of which models the RTF of a source. This formulation effectively resolves the scale inconsistency inherent in SR-IVA. Despite this modeling advantage, the existing optimization algorithm for SSR-IVA suffers from slow convergence, which limits its practical applicability. In this paper, we propose two block majorization-minimization algorithms for SSR-IVA that sequentially update each RTF in a computationally efficient manner. These algorithms can be regarded as extensions of the conventional iterative source steering (ISS) algorithm for IVA and achieve theoretically minimal per-iteration complexity. As a key technique, we introduce an RTF-structure-preserving multiplicative update to ensure that the RTF matrix remains composed of the RTFs throughout the optimization. Experimental results demonstrate that SSR-IVA using the proposed ISS-type algorithms achieves higher source separation accuracy than both SR-IVA and SSR-IVA using the conventional algorithm, while also converging significantly faster than the latter.