1. A speech processing device comprising: a reverberation characteristic selection unit configured to correlate correction data indicating a contribution of a reverberation component based on a corresponding reverberation characteristic with an adaptive acoustic model which is trained using reverbed speech to which a reverberation based on the corresponding reverberation characteristic is added for each of reverberation characteristics, to calculate likelihoods based on the adaptive acoustic models for a recorded speech, and to select correction data corresponding to the adaptive acoustic model having the calculated highest likelihood; a dereverberation unit configured to remove the reverberation component from the speech based on the correction data, wherein the reverberation characteristics differ in the contribution of a component which is inversely proportional to a distance between a sound collection unit configured to record speech from a sound source and the sound source, and wherein the reverberation characteristic selection unit correlates distance data indicating the distances corresponding to the reverberation characteristics with the correction data and the adaptive acoustic models and selects the distance data corresponding to the adaptive acoustic model having the calculated highest likelihood; an acoustic model prediction unit configured to predict an acoustic model corresponding to the distance indicated by the distance data selected by the reverberation characteristic selection unit from a first acoustic model trained using reverbed speech to which a reverberation corresponding to the reverberation characteristic based on a predetermined distance is added and a second acoustic model trained using speech in an environment in which reverberations are negligible; and a speech recognition unit configured to perform a speech recognizing process on the speech using the acoustic model predicted by the acoustic model prediction unit.