Robust Sparse Bayesian Learning for Sparse Signal Recovery Under Unknown Noise Distributions

This paper considers the robust recovery problem of sparse signal with sparse Bayesian learning (SBL) in noisy environments. Most of the current SBL algorithms are constructed on the optimization problem using the square loss, which mainly deals with Gaussian noise. However, real measurements are often contaminated by an unknown distributed noise that is unlikely to be Gaussian. To prevent performance degradation of SBL in such cases, we propose a robust sparse Bayesian learning method with a simple but effective hierarchical noise model. Using this model, the resultant loss is made up of a weighted error measure and a priori-dependent constraint on the weight, and then provides the flexibility for resisting the outliers and adapting to the real noise. A type-II Bayesian estimate is performed to infer the related model parameter and the unknown sparse signal. The advantage of our method is demonstrated by extensive experiments on synthetic data and real radio tomographic imaging data.