Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it does not work well for a generic measurement matrix, which may cause AMP to diverge. Damped AMP has been used for SBL to alleviate divergence issues at the cost of reducing convergence speed. In this work, we propose a new SBL algorithm based on structured variational inference, leveraging AMP with a unitary transformation. Both single measurement vector and multiple measurement vector problems are investigated. It is shown that, compared to state-of-the-art AMP-based SBL algorithms, the proposed UAMP-SBL is more robust and efficient, leading to remarkably better performance.

中文翻译：

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稀疏贝叶斯学习的统一近似消息传递

可以基于近似消息传递 (AMP) 算法以低复杂度实现稀疏贝叶斯学习 (SBL)。但是，它不适用于通用测量矩阵，这可能会导致 AMP 发散。阻尼 AMP 已用于 SBL，以降低收敛速度为代价来缓解发散问题。在这项工作中，我们提出了一种基于结构化变分推理的新 SBL 算法，利用具有酉变换的 AMP。研究了单测量向量和多测量向量问题。结果表明，与最先进的基于 AMP 的 SBL 算法相比，所提出的 UAMP-SBL 更加健壮和高效，从而显着提高了性能。