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doi:10.1016/j.sigpro.2004.05.015 
Copyright © 2004 Elsevier B.V. All rights reserved.
A study on IMM with NPHMM and an application to speech enhancement
Received 31 May 2002;
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Abstract
The nonlinear speech enhancement method with interactive parallel-extended Kalman filter is applied to speech contaminated by additive white noise. To represent the nonlinear and nonstationary nature of speech, we assume that speech is the output of a nonlinear prediction hidden Markov models (NPHMM) combining both neural network and HMM. The NPHMM is a nonlinear autoregressive process whose time-varying parameters are controlled by a hidden Markov chain. The simulation results shows that the proposed method offers better performance gains relative to the previous results (Signal Process 65 (1998) 373) with slightly increased complexity.
Author Keywords: Nonlinear speech enhancement; Parallel-extended Kalman filter; Nonlinear prediction HMM; Neural network
Nomenclature
Nomenclature- A=[aij]
- state transition matrix
- hs(t)=i(·)
- neural network based predictor at time t conditioned on state i
- X(t−1)=[x(t−1)…x(t−p)]T
- sequence of past p observations of speech data
- es(t)=i(t)
- driving sequence
- wk|i
- weight vector between output unit and hidden layer
- wk,j|i
- weight matrix between hidden layer and input layer
- g(.)
- differential nonlinear function
- S={s(1),s(2),…,s(T)}
- state sequence
- γij(t)
- a posterior probability of the transition from state i to state j
- z(t)
- white noise contaminated speech
- v(t)
- additive white Gaussian noise with zero mean and variance R(t)
- minimum mean square error estimator of x(t) under the noisy speech
- Hist(t,k)≡{s(0)=k0,s(1)=k1,…,s(t)=kt},
- where k=(k0,k1,…,kt) is the specific sequence of models from the space of all possible sequences
