Bayesian Distributed Speech Enhancement With Adaptive Stein Variational Gradient Descent for Non-Ideal Wireless Acoustic Sensor Networks

Distributed speech enhancement in wireless acoustic sensor networks (WASNs) remains challenging under practical, non-ideal network conditions, such as packet loss, clock asynchrony, and dynamic topologies, which significantly degrade the performance of existing deterministic approaches. To address this, this paper proposes a novel Bayesian framework for distributed speech enhancement that systematically incorporates network uncertainties. The core of our method is an adaptive, distributed Stein Variational Gradient Descent (SVGD) algorithm. Unlike traditional point-estimate filtering, it enables efficient collaborative inference by approximating the full posterior distribution of the optimal speech filter weights. Specifically, we first formulate a comprehensive state-space model that jointly characterizes the speech signals and the network imperfections. We then develop a diffusion-based distributed SVGD algorithm where each node maintains a local particle set, updated via a topology-aware adaptive kernel function that fuses information from neighbors in a communication-efficient manner. Furthermore, we derive rigorous theoretical guarantees on the convergence and consensus properties of the proposed algorithm, even in the presence of packet loss and link failures. Theoretical analysis proves that the proposed algorithm achieves consensus and stability even with a packet loss rate up to 30%. Extensive simulations and real-world experiments also demonstrate that our method consistently outperforms state-of-the-art distributed speech enhancement techniques even under challenging non-ideal network scenarios.