Sparse Bayesian learning for sparse signal recovery using l1/2-norm

Sparse signal recovery is an important technique for acoustic direction-of-arrival (DOA) estimation which is widely used in applications such as humanoid robots and voice control loudspeakers. However, the estimation accuracy performance is limited by the size of platform and the sound wavelength. To improve the accuracy performance, we propose a sparse signal recovery approach for acoustic DOA estimation based on a hierarchical formulation of the generalized Gaussian prior with a shape parameter q = 1/2. Specifically, a sparse Bayesian learning (SBL) framework is built using l(1/2)-norm priors to efficiently utilize the space sparsity nature of acoustic sources. The priors, built primarily based on a hierarchical structure with a couple of layers, are used for modeling the sparse signals. Then, an expectation-maximization algorithm is proposed for inference and parameter learning. The estimation accuracy performance of the proposed approach is verified in terms of sparse signal recovery and acoustic DOA estimation. The experimental results exhibit that the proposed method achieves the highest recovery accuracy performance and has the lowest root mean square error (RMSE) in contrast with the state-of-the-art sparse signal recovery methods.