Because of its self-regularizing nature and uncertainty estimation, the Bayesian approach has achieved excellent recovery performance across a wide range of sparse signal recovery applications. However, most methods are based on the real-value signal model, with the complex-value signal model rarely considered. Typically, the complex signal model is adopted so that phase information can be utilized. Therefore, it is non-trivial to develop Bayesian models for the complex-value signal model. Motivated by the adaptive least absolute shrinkage and selection operator (LASSO) and the sparse Bayesian learning (SBL) framework, a hierarchical model with adaptive Laplace priors is proposed for applications of complex sparse signal recovery in this paper. The proposed hierarchical Bayesian framework is easy to extend for the case of multiple measurement vectors. Moreover, the space alternating principle is integrated into the algorithm to avoid using the matrix inverse operation. In the experimental section of this work, the proposed algorithm is concerned with both complex Gaussian random dictionaries and directions of arrival (DOA) estimations. The experimental results show that the proposed algorithm offers better sparsity recovery performance than the state-of-the-art methods for different types of complex signals.
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