Relevance of H∞ filtering for speech enhancement

Among parametric methods for speech enhancement, one consists in combining an autoregressive model for speech and a Kalman filter. This filtering is optimal in the H₂ sense providing the initial state vector, the input and the observation vectors in the state space representation of the system are independent, white and Gaussian. However, these assumptions do not necessarily hold when processing speech. In this paper, we propose to investigate an alternative approach, which is based on H_∞ filtering and hence does not depend on these restrictive assumptions. In that setting, the purpose is to minimize the worst possible effects of the noises and system uncertainties on the estimation error. A comparative study between Kalman and H_∞ filtering is carried out, when the additive colored noise can be modeled by a moving average (MA) process.