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Some contributions to joint optimal filtering and parameter estimation with application to monaural speech separation

Abstract : The thesis is composed of two parts. In the first part, we deal with the monaural speech separation problem. We propose two algorithms. In the first algorithm, we exploit the joint autoregressive model that models short and long (periodic) correlations of Gaussian speech signals to formulate a state space model with unknown parameters. The EM-Kalman algorithm is then used to estimate jointly the sources (involved in the state vector) and the parameters of the model. In the second algorithm, we use the same speech model but this time in the frequency domain (quasi-periodic Gaussian sources with AR spectral envelope). Observation data is sliced using a well-designed window. Parameters are estimated separately from the sources by optimizing the Gaussian ML criterion expressed using the sample and parameterized covariance matrices. Classical frequency domain asymptotic methods replace linear convolution by circulant convolution leading to approximation errors. We show how the introduction of windows can lead to slightly more complex frequency domain techniques, replacing diagonal covariance matrices by banded covariance matrices, but with controlled approximation error. The sources are then estimated using the Wiener filtering. The second part is about the relative performance of joint vs. marginalized parameter estimation. We consider jointly Gaussian latent data and observations. We provide contributions to Cramer-Rao bounds, then, we investigate three iterative joint estimation approaches: Alternating MAP/ML which suffers from inconsistent parameter bias, EM which converges to ML and VB that we prove converges asymptotically to the ML solution for parameter estimation.
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Siouar Bensaid. Some contributions to joint optimal filtering and parameter estimation with application to monaural speech separation. Other. Université Nice Sophia Antipolis, 2014. English. ⟨NNT : 2014NICE4025⟩. ⟨tel-01063397⟩

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