Variational Bayesian learning for removal of sparse impulsive noise from speech signals

In this paper, a new variational Bayesian (VB) learning algorithm is proposed to remove sparse impulsive noise from speech signals. The clean signal is modeled using an autoregressive (AR) model on frame basis. The contaminated signal is modeled as the sum of the AR model of the clean speech signal, a sparse noise term and a dense Gaussian noise term. The sparse noise and the dense Gaussian noise terms model the large additive values caused by the impulsive noise and the small additive values or Gaussian noise, respectively. A hierarchical Bayesian model is constructed for the contaminated signal and a VB framework is used to estimate the parameters of the model. The AR model parameter estimation, the speech signal recovery and the sparse impulsive noise removal are carried out simultaneously. The proposed algorithm starts from random initial values and it does not require training and a threshold as compared to other methods. Experiments are performed using a standard speech database and impulsive noise generated from a probabilistic impulsive noise model and real impulsive noise. The comparison of obtained results with other methods demonstrates the performance of the proposed method.