基于自适应LASSO先验的稀疏贝叶斯学习算法

为了提高稀疏信号恢复的准确性, 开展了基于自适应套索算子(Least absolute shrinkage and selection operator, LASSO)先验的稀疏贝叶斯学习(Sparse Bayesian learning, SBL)算法研究. 1) 在稀疏贝叶斯模型构建阶段, 构造了一种新的多层贝叶斯框架, 赋予信号中元素独立的LASSO先验. 该先验比现有稀疏先验更有效地鼓励稀疏并且该模型中所有参数更新存在闭合解. 然后在该多层贝叶斯框架的基础上提出了一种基于自适应LASSO先验的SBL算法. 2) 为降低提出的算法的计算复杂度, 在贝叶斯推断阶段利用空间轮换变元方法对提出的算法进行改进, 避免了矩阵求逆运算, 使参数更新快速高效, 从而提出了一种基于自适应LASSO先验的快速SBL算法. 本文提出的算法的稀疏恢复性能通过实验进行了验证, 分别针对不同大小测量矩阵的稀疏信号恢复以及单快拍波达方向(Direction of arrival, DOA)估计开展了实验. 实验结果表明: 提出基于自适应LASSO先验的SBL算法比现有算法具有更高的稀疏恢复准确度; 提出的快速算法的准确度略低于提出的基于自适应LASSO先验的SBL算法, 但计算复杂度明显降低.

Sparse Bayesian Learning Using Adaptive LASSO Priors

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.