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

2025-02-25

AI Summary

Conventional blind source separation (BSS) methods, such as independent vector analysis (IVA) and independent low-rank matrix analysis (ILRMA), suffer from insufficient modeling of inter-frequency-band structural dependencies, leading to mismatches between assumed source distributions and estimated results—particularly due to their rigid reliance on second-order statistics and strict source independence assumptions. Method: This paper proposes a Sinkhorn-divergence-based optimal source power reallocation method that integrates optimal transport theory into the IVA/ILRMA framework for the first time. It adaptively calibrates source variances across frequency bands while preserving statistical independence modeling and explicitly capturing inter-band dependencies. Contribution/Results: The method is fully compatible with existing BSS pipelines, requires no additional labels or priors, and significantly improves separation performance and robustness. Extensive simulations demonstrate average signal-to-distortion ratio (SDR) gains of 2.1–3.8 dB over baseline methods.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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.

Problem

• Blind source separation (BSS) recovery
• Sinkhorn divergence optimization
• Source power allocation across bands

Innovation

• Sinkhorn divergence optimizes source power
• Optimal transport corrects source variance estimates
• Enhanced algorithms integrate Sinkhorn iterative scheme