This paper proposes a method to recover missing data during observation by factorial hidden Markov models (FHMMs). The fundamental idea of the proposed method originates from the mimesis model, inspired by the mirror neuron system. By combining the motion recognition from partial observation algorithm and the proto-symbol based duplication of observed motion algorithm, whole body motion imitation from partial observation can be achieved. The algorithm for missing data recovery uses the same basic strategy as the whole body motion imitation from partial observation, but requires more accurate spatial representability. FHMMs allow for more efficient representation of a continuous data sequence by distributed state representation compared to hidden Markov models (HMMs). The proposed algorithm is tested with human motion data and the experimental results show improved representability compared to the conventional HMMs.