Robust sparse Bayesian learning based on the Bernoulli-Gaussian model of impulsive noise

Abstract

Traditional sparse reconstruction methods suffer from performance degradation in the presence of impulsive noise. In this paper, we adopt the Bernoulli-Gaussian distribution to model the impulsive noise and introduce the hidden state variables to indicate the state of the noise. Based on the new hierarchical Bayesian model, a robust sparse reconstruction algorithm called Bernoulli-Gaussian robust sparse Bayesian learning (BG-RSBL) is developed through the variational Bayesian inference framework. Different from existing robust reconstruction methods, BG-RSBL does not make sparse assumptions about the impulses and outliers. The employment of the Bernoulli-Gaussian model enables BG-RSBL to adapt to environments with a wider range of impulse densities. Comparative analysis shows that the reconstruction performance can be improved by including the outliers in posterior inference with appropriate weightings. Simulations performed under both Bernoulli-Gaussian and symmetric α-stable distributed impulsive noise demonstrate the robust and outstanding reconstruction performance of the proposed algorithm.