This paper addresses the problem of blind speech dereverberation by inverse filtering of a room acoustic system. Since a speech signal can be modeled as being generated by a speech production system driven by an innovations process, a reverberant signal is the output of a composite system consisting of the speech production and room acoustic systems. Therefore, we need to extract only the part corresponding to the room acoustic system (or its inverse filter) from the composite system (or its inverse filter). The time-variant nature of the speech production system can be exploited for this purpose. In order to realize the time-variance-based inverse filter estimation, we introduce a joint estimation of the inverse filters of both the time-invariant room acoustic and the time-variant speech production systems, and present two estimation algorithms with distinct properties.