The hidden Markov model (HMM) inversion algorithm, based on either the gradient search or the Baum-Welch reestimation of input speech features, is proposed and applied to the robust speech recognition tasks under general types of mismatch conditions. This algorithm stems from the gradient-based inversion algorithm of an artificial neural network (ANN) by viewing an HMM as a special type of ANN. Given input speech features s, the forward training of an HMM finds the model parameters lambda subject to an optimization criterion. On the other hand, the inversion of an HMM finds speech features, s, subject to an optimization criterion with given model parameters lambda. The gradient-based HMM inversion and the Baum-Welch HMM inversion algorithms can be successfully integrated with the model space optimization techniques, such as the robust MINIMAX technique, to compensate the mismatch in the joint model and feature space. The joint space mismatch compensation technique achieves better performance than the single space, i.e. either the model space or the feature space alone, mismatch compensation techniques. It is also demonstrated that approximately 10-dB signal-to-noise ratio (SNR) gain is obtained in the low SNR environments when the joint model and feature space mismatch compensation technique is used.
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