Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of SBL in three important ways. First, we reformulate three existing SBL algorithms under the majorization-minimization (MM) framework. This unification perspective not only provides a useful theoretical framework for comparing different algorithms in terms of their convergence behavior, but also provides a principled recipe for constructing novel algorithms with specific properties by designing appropriate bounds of the Bayesian marginal likelihood function. Second, building on the MM principle, we propose a novel method called LowSNR-BSI that achieves favorable source reconstruction performance in low signal-to-noise-ratio (SNR) settings. Third, precise knowledge of the noise level is a crucial requirement for accurate source reconstruction. Here we present a novel principled technique to accurately learn the noise variance from the data either jointly within the source reconstruction procedure or using one of two proposed cross-validation strategies. Empirically, we could show that the monotonous convergence behavior predicted from MM theory is confirmed in numerical experiments. Using simulations, we further demonstrate the advantage of LowSNR-BSI over conventional SBL in low-SNR regimes, and the advantage of learned noise levels over estimates derived from baseline data. To demonstrate the usefulness of our novel approach, we show neurophysiologically plausible source reconstructions on averaged auditory evoked potential data.

中文翻译：

---

用于电磁脑成像的稀疏贝叶斯学习算法与专业化最小化框架的统一

使用稀疏贝叶斯学习 (SBL) 的基于脑电图或脑磁图 (EEG/MEG) 的脑源成像 (BSI) 方法已被证明在具有少量不同活动源的情况下（例如与事件相关的设计）可实现出色的性能。本文从三个重要方面扩展了 SBL 的理论和实践。首先，我们在专业化-最小化 (MM) 框架下重新制定了三种现有的 SBL 算法。这种统一的观点不仅为比较不同算法的收敛行为提供了一个有用的理论框架，而且还为通过设计贝叶斯边际似然函数的适当边界来构造具有特定属性的新算法提供了原则性的方法。其次，建立在MM原则上，我们提出了一种称为 LowSNR-BSI 的新方法，该方法在低信噪比 (SNR) 设置中实现了良好的源重建性能。第三，准确了解噪声水平是准确源重建的关键要求。在这里，我们提出了一种新颖的原理技术，可以在源重建过程中联合或使用两种建议的交叉验证策略之一从数据中准确地学习噪声方差。根据经验，我们可以证明从 MM 理论预测的单调收敛行为在数值实验中得到证实。使用模拟，我们进一步证明了 LowSNR-BSI 在低 SNR 状态下优于传统 SBL 的优势，以及学习噪声水平优于从基线数据得出的估计值的优势。为了证明我们的新方法的有用性，