Bayesian Sparse Reconstruction Method of Compressed Sensing in the Presence of Impulsive Noise

The majority of existing recovery algorithms in the framework of compressed sensing are not robust to the impulsive noise. However, the impulsive noise is always present in the actual communication and signal processing system. In this paper, we propose a method named ‘Bayesian sparse reconstruction’ to recover the sparse signal from the measurement vector which is corrupted by the impulsive noise. The Bayesian sparse reconstruction method is composed of five parts, which are the preliminary detection of the location set of impulses, the impulsive noise fast relevance vector machine algorithm, the step of pruning, Bayesian impulse detection algorithm and the maximum a posteriori estimate of the sparse vector. The Bayesian sparse reconstruction method can achieve effective signal recovery in the presence of impulsive noise, depending on the mutual influence of the impulsive noise fast relevance vector machine algorithm, the step of pruning and the Bayesian impulse detection algorithm. Experimental results show that the Bayesian sparse reconstruction method is robust to the impulsive noise and effective in the additive white Gaussian noise environment.