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