  Sparse Bayesian learning (SBL) can be implemented with low complexity based
on the approximate message passing (AMP) algorithm. However, it is vulnerable
to 'difficult' measurement matrices, which may cause AMP to diverge. Damped AMP
has been used for SBL to alleviate the problem 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
(UAMP). 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 UAMPSBL is more robust and efficient, leading to
remarkably better performance.
