Speech dereverberation is desirable with a view to achieving, for example, robust speech recognition in the real world. However, it is still a challenging problem, especially when using a single microphone. Although blind equalization techniques have been exploited, they cannot deal with speech signals appropriately because their assumptions are not satisfied by speech signals. We propose new dereverberation principles based on an inherent property of speech signals, namely quasi-periodicity. The present methods learn the dereverberation filter from a lot of speech data with no prior knowledge of the data, and can achieve high quality speech dereverberation especially when the reverberation time is long.