Mathematical analysis of speech dereverberation based on time-varying Gaussian source model: Its solution and convergence characteristics

This paper presents an overview of a speech dereverberation method based on the time-varying nature of speech, and provides new mathematical analysis results on the characteristics of its solution and convergence. This method models the speech signal with a time-varying Gaussian source model and models the observation process with a multi-channel autoregressive model. The speech dereverberation is accomplished by maximizing a likelihood function that is determined based on the above two models. This method has been experimentally confirmed to work effectively even for relatively short observations of the order of a few seconds. In this paper, we provide a mathematical analysis of the solution and the convergence behavior of the method. First, we show that the solution maximizing the expectation of the likelihood function strictly coincides with the true solution under a condition where solution ambiguities are appropriately excluded. In addition, we show that the solution obtained from an actual observation is expected to converge with one that is close to the true solution as the observation time increases.