Speech Enhancement: Application of the Kalman Filter in the Estimate-Maximize (EM) Framework

The application of the Kalman filter to the single-microphone speech enhancement task is presented in this chapter. Among numerous published algorithms, an important sub-group employs the estimate-maximize (EM) procedure to iteratively estimate the spectral parameters of the speech and noise signals. We elaborate on a specific member of this sub-group. In the E-step, the Kalman smoother is applied and in the M-step, a non-standard Yule-Walker equation set is solved. An approximated EM algorithm is derived by applying the gradient-descent method to the likelihood function. We obtain a sequential, computationally efficient, algorithm. It is then shown, that the sequential parameter estimation can be replaced by a Kalman filter to obtain a dual speech and parameters Kalman filter. A natural generalization to the dual scheme is an estimation scheme in which both speech and parameters are jointly estimated by applying a nonlinear extension to the Kalman filter, namely the unscented Kalman filter. Extensive experimental study, using real speech and noise signals is provided to compare the proposed methods with alternative speech enhancement algorithms. Kalman filter based algorithms are shown to maintain the natural speech quality. However, their noise reduction ability is limited.