In this paper, we propose a supervised single-channel speech enhancement method that combines Kullback-Leibler (KL) divergence-based non-negative matrix factorization (NMF) and a hidden Markov model (NMF-HMM). With the integration of the HMM, the temporal dynamics information of speech signals can be taken into account. This method includes a training stage and an enhancement stage. In the training stage, the sum of the Poisson distribution, leading to the KL divergence measure, is used as the observation model for each state of the HMM. This ensures that a computationally efficient multiplicative update can be used for the parameter update of this model. In the online enhancement stage, a novel minimum mean square error estimator is proposed for the NMF-HMM. This estimator can be implemented using parallel computing, reducing the time complexity. Moreover, compared to the traditional NMF-based speech enhancement methods, the experimental results show that our proposed algorithm improved the short-time objective intelligibility and perceptual evaluation of speech quality by 5% and 0.18, respectively.

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In this paper, we present a novel supervised Non-negative Matrix Factorization (NMF) speech enhancement method, which is based on Hidden Markov Model (HMM) and Kullback-Leibler (KL) divergence (NMF-HMM). Our algorithm applies the HMM to capture the timing information, so the temporal dynamics of speech signal can be considered by comparing with the traditional NMF-based speech enhancement method. More specifically, the sum of Poisson, leading to the KL divergence measure, is used as the observation model for each state of HMM. This ensures that the parameter update rule of the proposed algorithm is identical to the multiplicative update rule, which is quick and efficient. In the training stage, this update rule is applied to train the NMF-HMM model. In the online enhancement stage, a novel minimum mean-square error (MMSE) estimator that combines the NMF-HMM is proposed to conduct speech enhancement. The performance of the proposed algorithm is evaluated by perceptual evaluation of speech quality (PESQ) and short-timeobjective intelligibility (STOI). The experimental results indicate that the STOI score of proposed strategy is able to outperform 7% than current state-of-the-art NMF-based speech enhancement methods.

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In this paper, we propose a novel non-negative matrix factorization (NMF) and hidden Markov model (NMF-HMM) based speech enhancement algorithm, which employs a Poisson mixture model (PMM). Compared to the previously proposed NMF-HMM method, the new algorithm, termed PMM-NMF-HMM, uses the Poisson mixture distribution for the state conditional likelihood function for a HMM rather than the single Poisson distribution. This means that there are the more basis matrices that can be used to model the speech and noise signals, so more signal information can be captured by the resulting model. The proposed method is supervised and thus includes a training and an enhancement stage. It is shown that, in the training stage, the proposed method can be implemented efficiently using multiplicative update (MU) for the model parameters, much like the NMF-HMM algorithm. In the speech enhancement stage, which can be performed online, a novel PMM-NMF-HMM minimum mean-square error (MMSE) estimator is developed. The experimental results indicate that the PMM-NMF-HMM method can obtain higher short-time objective intelligibility (STOI) and perceptual evaluation of speech quality (PESQ) score than NMF-HMM. Additionally, the method also outperforms other state-of-the-art NMFbased supervised speech enhancement algorithms.