  Due to its self-regularizing nature and its ability to quantify uncertainty,
the Bayesian approach has achieved excellent recovery performance across a wide
range of sparse signal recovery applications. However, most existing methods
are based on the real-value signal model, with the complex-value signal model
rarely considered. 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 in this paper for
recovery of complex sparse signals. Moreover, the space alternating approach is
integrated into the algorithm to reduce the computational complexity of the
proposed method. In experiments, the proposed algorithm is studied for complex
Gaussian random dictionaries and different types of complex signals. These
experiments show that the proposed algorithm offers better recovery performance
for different types of complex signals than state-of-the-art methods.
