A Variational EM Algorithm for the Separation of Moving Sound Sources

International audienceThis paper addresses the problem of separation of moving sound sources. We propose a probabilistic framework based on the complex Gaussian model combined with non-negative matrix factorization. The properties associated with moving sources are modeled using time-varying mixing filters described by a stochastic temporal process. We present a variational expectation-maximization (VEM) algorithm that employs a Kalman smoother to estimate the mixing filters. The sound sources are separated by means of Wiener filters, built from the estimators provided by the proposed VEM algorithm. Preliminary experiments with simulated data show that, while for static sources we obtain results comparable with the base-line method of Ozerov et al., in the case of moving source our method outperforms a piece-wise version of the baseline method

A harmonic excitation state-space approach to blind separation of speech

We discuss an identification framework for noisy speech mixtures. A block-based generative model is formulated that explicitly incorporates the time-varying harmonic plus noise (H+N) model for a number of latent sources observed through noisy convolutive mixtures. All parameters including the pitches of the source signals, the amplitudes and phases of the sources, the mixing filters and the noise statistics are estimated by maximum likelihood, using an EM-algorithm. Exact averaging over the hidden sources is obtained using the Kalman smoother. We show that pitch estimation and source separation can be performed simultaneously. The pitch estimates are compared to laryngograph (EGG) measurements. Artificial and real room mixtures are used to demonstrate the viability of the approach. Intelligible speech signals are re-synthesized from the estimated H+N models

Convolutive Blind Source Separation Methods

In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks

Multichannel Speech Separation and Enhancement Using the Convolutive Transfer Function

This paper addresses the problem of speech separation and enhancement from multichannel convolutive and noisy mixtures, \emph{assuming known mixing filters}. We propose to perform the speech separation and enhancement task in the short-time Fourier transform domain, using the convolutive transfer function (CTF) approximation. Compared to time-domain filters, CTF has much less taps, consequently it has less near-common zeros among channels and less computational complexity. The work proposes three speech-source recovery methods, namely: i) the multichannel inverse filtering method, i.e. the multiple input/output inverse theorem (MINT), is exploited in the CTF domain, and for the multi-source case, ii) a beamforming-like multichannel inverse filtering method applying single source MINT and using power minimization, which is suitable whenever the source CTFs are not all known, and iii) a constrained Lasso method, where the sources are recovered by minimizing the $\ell_1$-norm to impose their spectral sparsity, with the constraint that the $\ell_2$-norm fitting cost, between the microphone signals and the mixing model involving the unknown source signals, is less than a tolerance. The noise can be reduced by setting a tolerance onto the noise power. Experiments under various acoustic conditions are carried out to evaluate the three proposed methods. The comparison between them as well as with the baseline methods is presented.Comment: Submitted to IEEE/ACM Transactions on Audio, Speech and Language Processin

Multichannel high resolution NMF for modelling convolutive mixtures of non-stationary signals in the time-frequency domain

Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies

Multimodal methods for blind source separation of audio sources

The enhancement of the performance of frequency domain convolutive blind source separation (FDCBSS) techniques when applied to the problem of separating audio sources recorded in a room environment is the focus of this thesis. This challenging application is termed the cocktail party problem and the ultimate aim would be to build a machine which matches the ability of a human being to solve this task. Human beings exploit both their eyes and their ears in solving this task and hence they adopt a multimodal approach, i.e. they exploit both audio and video modalities. New multimodal methods for blind source separation of audio sources are therefore proposed in this work as a step towards realizing such a machine. The geometry of the room environment is initially exploited to improve the separation performance of a FDCBSS algorithm. The positions of the human speakers are monitored by video cameras and this information is incorporated within the FDCBSS algorithm in the form of constraints added to the underlying cross-power spectral density matrix-based cost function which measures separation performance. [Continues.

Dirichlet latent variable model : a dynamic model based on Dirichlet prior for audio processing

We propose a dynamic latent variable model for learning latent bases from time varying, non-negative data. We take a probabilistic approach to modeling the temporal dependence in data by introducing a dynamic Dirichlet prior – a Dirichlet distribution with dynamic parameters. This new distribution allows us to assure non-negativity and avoid intractability when sequential updates are performed (otherwise encountered in using Dirichlet prior). We refer to the proposed model as the Dirichlet latent variable model (DLVM). We develop an expectation maximization algorithm for the proposed model, and also derive a maximum a posteriori estimate of the parameters. Furthermore, we connect the proposed DLVM to two popular latent basis learning methods - probabilistic latent component analysis (PLCA) and non-negative matrix factorization (NMF).We show that (i) PLCA is a special case of our DLVM, and (ii) DLVM can be interpreted as a dynamic version of NMF. The usefulness of DLVM is demonstrated for three audio processing applications - speaker source separation, denoising, and bandwidth expansion. To this end, a new algorithm for source separation is also proposed. Through extensive experiments on benchmark databases, we show that the proposed model out performs several relevant existing methods in all three applications