Probabilistic Modeling Paradigms for Audio Source Separation

This is the author's final version of the article, first published as E. Vincent, M. G. Jafari, S. A. Abdallah, M. D. Plumbley, M. E. Davies. Probabilistic Modeling Paradigms for Audio Source Separation. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 7, pp. 162-185. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch007file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04Most sound scenes result from the superposition of several sources, which can be separately perceived and analyzed by human listeners. Source separation aims to provide machine listeners with similar skills by extracting the sounds of individual sources from a given scene. Existing separation systems operate either by emulating the human auditory system or by inferring the parameters of probabilistic sound models. In this chapter, the authors focus on the latter approach and provide a joint overview of established and recent models, including independent component analysis, local time-frequency models and spectral template-based models. They show that most models are instances of one of the following two general paradigms: linear modeling or variance modeling. They compare the merits of either paradigm and report objective performance figures. They also,conclude by discussing promising combinations of probabilistic priors and inference algorithms that could form the basis of future state-of-the-art systems

Audio Source Separation Using Sparse Representations

This is the author's final version of the article, first published as A. Nesbit, M. G. Jafari, E. Vincent and M. D. Plumbley. Audio Source Separation Using Sparse Representations. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 10, pp. 246-264. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch010file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04The authors address the problem of audio source separation, namely, the recovery of audio signals from recordings of mixtures of those signals. The sparse component analysis framework is a powerful method for achieving this. Sparse orthogonal transforms, in which only few transform coefficients differ significantly from zero, are developed; once the signal has been transformed, energy is apportioned from each transform coefficient to each estimated source, and, finally, the signal is reconstructed using the inverse transform. The overriding aim of this chapter is to demonstrate how this framework, as exemplified here by two different decomposition methods which adapt to the signal to represent it sparsely, can be used to solve different problems in different mixing scenarios. To address the instantaneous (neither delays nor echoes) and underdetermined (more sources than mixtures) mixing model, a lapped orthogonal transform is adapted to the signal by selecting a basis from a library of predetermined bases. This method is highly related to the windowing methods used in the MPEG audio coding framework. In considering the anechoic (delays but no echoes) and determined (equal number of sources and mixtures) mixing case, a greedy adaptive transform is used based on orthogonal basis functions that are learned from the observed data, instead of being selected from a predetermined library of bases. This is found to encode the signal characteristics, by introducing a feedback system between the bases and the observed data. Experiments on mixtures of speech and music signals demonstrate that these methods give good signal approximations and separation performance, and indicate promising directions for future research

Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation

This paper concerns underdetermined linear instantaneous and convolutive blind source separation (BSS), i.e., the case when the number of observed mixed signals is lower than the number of sources.We propose partial BSS methods, which separate supposedly nonstationary sources of interest (while keeping residual components for the other, supposedly stationary, "noise" sources). These methods are based on the general differential BSS concept that we introduced before. In the instantaneous case, the approach proposed in this paper consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures). In the convolutive case, we extend our recent time-domain fast fixed-point C-FICA algorithm to underdetermined mixtures. Both proposed approaches thus keep the attractive features of the FastICA and C-FICA methods. Our approaches are based on differential sphering processes, followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper. Experimental tests show that these differential algorithms are much more robust to noise sources than the standard FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for linear instantaneous and convolutive underdetermined mixture

Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings

We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for characterizing the room acoustic from the unknown competing speech sources relying on localization of the early images of the speakers by sparse approximation of the spatial spectra of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings demonstrate the effectiveness of the proposed approach for multi-party speech recovery and recognition.Comment: 31 page

Underdetermined convolutive source separation using two dimensional non-negative factorization techniques

PhD ThesisIn this thesis the underdetermined audio source separation has been considered, that is, estimating the original audio sources from the observed mixture when the number of audio sources is greater than the number of channels. The separation has been carried out using two approaches; the blind audio source separation and the informed audio source separation. The blind audio source separation approach depends on the mixture signal only and it assumes that the separation has been accomplished without any prior information (or as little as possible) about the sources. The informed audio source separation uses the exemplar in addition to the mixture signal to emulate the targeted speech signal to be separated. Both approaches are based on the two dimensional factorization techniques that decompose the signal into two tensors that are convolved in both the temporal and spectral directions. Both approaches are applied on the convolutive mixture and the high-reverberant convolutive mixture which are more realistic than the instantaneous mixture. In this work a novel algorithm based on the nonnegative matrix factor two dimensional deconvolution (NMF2D) with adaptive sparsity has been proposed to separate the audio sources that have been mixed in an underdetermined convolutive mixture. Additionally, a novel Gamma Exponential Process has been proposed for estimating the convolutive parameters and number of components of the NMF2D/ NTF2D, and to initialize the NMF2D parameters. In addition, the effects of different window length have been investigated to determine the best fit model that suit the characteristics of the audio signal. Furthermore, a novel algorithm, namely the fusion K models of full-rank weighted nonnegative tensor factor two dimensional deconvolution (K-wNTF2D) has been proposed. The K-wNTF2D is developed for its ability in modelling both the spectral and temporal changes, and the spatial covariance matrix that addresses the high reverberation problem. Variable sparsity that derived from the Gibbs distribution is optimized under the Itakura-Saito divergence and adapted into the K-wNTF2D model. The tensors of this algorithm have been initialized by a novel initialization method, namely the SVD two-dimensional deconvolution (SVD2D). Finally, two novel informed source separation algorithms, namely, the semi-exemplar based algorithm and the exemplar-based algorithm, have been proposed. These algorithms based on the NMF2D model and the proposed two dimensional nonnegative matrix partial co-factorization (2DNMPCF) model. The idea of incorporating the exemplar is to inform the proposed separation algorithms about the targeted signal to be separated by initializing its parameters and guide the proposed separation algorithms. The adaptive sparsity is derived for both ii of the proposed algorithms. Also, a multistage of the proposed exemplar based algorithm has been proposed in order to further enhance the separation performance. Results have shown that the proposed separation algorithms are very promising, more flexible, and offer an alternative model to the conventional methods

Reverberant Audio Source Separation via Sparse and Low-Rank Modeling

The performance of audio source separation from underdetermined convolutive mixture assuming known mixing filters can be significantly improved by using an analysis sparse prior optimized by a reweighting l1 scheme and a wideband datafidelity term, as demonstrated by a recent article. In this letter, we show that the performance can be improved even more significantly by exploiting a low-rank prior on the source spectrograms.We present a new algorithm to estimate the sources based on i) an analysis sparse prior, ii) a reweighting scheme so as to increase the sparsity, iii) a wideband data-fidelity term in a constrained form, and iv) a low-rank constraint on the source spectrograms. Evaluation on reverberant music mixtures shows that the resulting algorithm improves state-of-the-art methods by more than 2 dB of signal-to-distortion ratio