基于自适应LASSO先验的稀疏贝叶斯学习算法

To improve the recovery accuracy of sparse signal, we study on sparse Bayesian learning (SBL) algorithm using adaptive least absolute shrinkage and selection operator (LASSO) priors. First, a hierarchical Bayesian framework is built for Bayesian model. Each elements of the weights is assigned with hierarchical priors, resulting in adaptive LASSO priors. Compared with other priors, the proposed adaptive LASSO priors encourage sparsity more efficiently and all the variables in the proposed model can be updated using close form solution. Thus, a SBL algorithm using adaptive LASSO priors is proposed. Second, the space alternating approach is integrated into the proposed algorithm to reduce the computational complexity by avoiding matrix inverse operation. In this way, the parameters can be updated efficiently and a fast SBL algorithm using adaptive LASSO priors is proposed. The accuracy performance of the proposed algorithms are verified using numerical simulations versus different size of measurement matrix and single snapshot direction-of-arrival (DOA) estimation, respectively. The experiments show that the root mean square error (RMSE) of the proposed adaptive LASSO priors based SBL method is lower than state-of-the-art methods. Besides, the RMSE of proposed fast algorithm is slightly lower than the proposed adaptive LASSO priors based SBL method but achieves lower computational complexity performance.