An Extended Sparse Bayesian Learning for Recovery of High-Dimensional Sparse Vector

The sparse Bayesian learning (SBL) is an essential technique in sparse recovery problems but is subject to the cubic complexity of matrix inversion. Existing fast algorithms evaded this problem at the cost of rapid performance degrades with non-sparse sampling matrix or high-dimensional sparse vector. In this letter, an extended sparse Bayesian learning (E-SBL) algorithm was developed. Specifically, it further takes the sparse vector and sampling matrix into various groups and separately considers their corresponding posterior distributions by mean-field variational inference (MFVI). It is found that the E-SBL will be inverse-free if treating each sparse element as a group. As a result, it outperforms other state-of-the-art fast sparse recovery methods for high-dimensional sparse vector.