Deep Unrolled Architecture for Fast and Accurate Gaussian Independent Vector Analysis

Abstract

Joint blind source separation (JBSS) is an inverse problem arising in engineering, particularly in medical imaging, where multiple signal datasets must be factorized simultaneously. A powerful approach to JBSS is Gaussian independent vector analysis (IVA-G), which models source datasets as independent Gaussian vectors and estimates both precision and demixing matrices. Recently, we introduced PALM-IVA-G, an iterative algorithm derived from the proximal alternating linearized minimization (PALM) framework, to solve IVA-G by minimizing a cost function derived from a maximum-likelihood estimator with provable convergence. However, its computational cost increases with the number of datasets and sources, and it requires careful hyperparameter tuning. To address these challenges, we propose U-PALM-IVA-G, an unrolled version of PALM-IVA-G that leverages deep unfolding to enhance efficiency. Experiments on six synthetic datasets of varying size and complexity demonstrate that U-PALM-IVA-G achieves significant speed improvements and enhanced solution quality compared to PALM-IVA-G.