Enhance Speech with Temporal Sparse Noise by Robust Kalman Filter

Single channel speech enhancement is an important problem in practice. One of the well used single channel speech enhancement method, spectral subtraction, can only work for stationary noise. Another method based on Kalman filtering is able to work with non-stationary signals. However, it can only produce optimal estimation of speech signal which is corrupted by Gaussian noise. In practice, speech acquisition also suffers from non-stationary temporal sparse noise. In this paper, we propose a method based on robust Kalman filter to remove not only the stationary noise but also such kind of temporal sparse noise. Formulated as a convex optimization problem, the robust Kalman filtering based method can be solved efficiently by Interior Point Method (IPM). Numerical results show that the proposed method is robust against temporal sparse noises.