Harmonicity based dereverberation with maximum a posteriori estimation

A harmonicity based dereverberation (HERB) scheme has recently been proposed for single channel speech dereverberation. HERB was shown to work effectively for modest reverberation times of up to 1.0 sec when a sufficiently large amount of observed signals are available. The conventional formulation of HERB makes intuitive use of the stronger components of the speech signal, namely the pitch harmonics, when obtaining the dereverberation filter; however, it does not provide an analytical framework within which the dereverberation performance can be optimized. In this paper, we reformulate HERB as a maximum a posteriori (MAP) estimation problem, in which the dereverberation filter is determined as one that maximizes the a posteriori probability given the observed signals. We derive a closed form solution to this problem by assuming that the a posteriori probability is given by means of a Gaussian probability distribution function (PDF) under a harmonicity constraint. A preliminary experiment shows that we can further improve the performance of HERB by carefully choosing the PDF when the amount of observed signals is small.