Robust decomposition of inverse filter of channel and prediction error filter of speech signal for dereverberation

This paper estimates the inverse filter of a signal transmission channel of a room driven by a speech signal. Speech signals are often modeled as piecewise stationary autoregressive (AR) processes. The most fundamental issue is how to estimate a channel's inverse filter separately from the inverse filter of the speech generating AR system, or the prediction error filter (PEF). We first point out that by jointly estimating the channel's inverse filter and the PEF, the channel's inverse is identifiable due to the time varying nature of the PEF. Then, we develop an algorithm that achieves this joint estimation. The notable property of the proposed method is its robustness against deviation from the linear convolutive model of an observed signal caused by, for example, observation noise. Experimental results with simulated and real recorded reverberant signals showed the effectiveness of the proposed method.