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

Blind separation of underdetermined mixtures with additive white and pink noises

This paper presents an approach for underdetermined blind source separation in the case of additive Gaussian white noise and pink noise. Likewise, the proposed approach is applicable in the case of separating I + 3 sources from I mixtures with additive two kinds of noises. This situation is more challenging and suitable to practical real world problems. Moreover, unlike to some conventional approaches, the sparsity conditions are not imposed. Firstly, the mixing matrix is estimated based on an algorithm that combines short time Fourier transform and rough-fuzzy clustering. Then, the mixed signals are normalized and the source signals are recovered using modified Gradient descent Local Hierarchical Alternating Least Squares Algorithm exploiting the mixing matrix obtained from the previous step as an input and initialized by multiplicative algorithm for matrix factorization based on alpha divergence. The experiments and simulation results show that the proposed approach can separate I + 3 source signals from I mixed signals, and it has superior evaluation performance compared to some conventional approaches

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

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

Underdetermined Separation of Speech Mixture Based on Sparse Bayesian Learning

This paper describes a novel algorithm for underdetermined speech separation problem based on compressed sensing which is an emerging technique for efficient data reconstruction. The proposed algorithm consists of two steps. The unknown mixing matrix is firstly estimated from the speech mixtures in the transform domain by using K-means clustering algorithm. In the second step, the speech sources are recovered based on an autocalibration sparse Bayesian learning algorithm for speech signal. Numerical experiments including the comparison with other sparse representation approaches are provided to show the achieved performance improvement

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

Single-Channel Signal Separation Using Spectral Basis Correlation with Sparse Nonnegative Tensor Factorization

A novel approach for solving the single-channel signal separation is presented the proposed sparse nonnegative tensor factorization under the framework of maximum a posteriori probability and adaptively fine-tuned using the hierarchical Bayesian approach with a new mixing mixture model. The mixing mixture is an analogy of a stereo signal concept given by one real and the other virtual microphones. An “imitated-stereo” mixture model is thus developed by weighting and time-shifting the original single-channel mixture. This leads to an artificial mixing system of dual channels which gives rise to a new form of spectral basis correlation diversity of the sources. Underlying all factorization algorithms is the principal difficulty in estimating the adequate number of latent components for each signal. This paper addresses these issues by developing a framework for pruning unnecessary components and incorporating a modified multivariate rectified Gaussian prior information into the spectral basis features. The parameters of the imitated-stereo model are estimated via the proposed sparse nonnegative tensor factorization with Itakura–Saito divergence. In addition, the separability conditions of the proposed mixture model are derived and demonstrated that the proposed method can separate real-time captured mixtures. Experimental testing on real audio sources has been conducted to verify the capability of the proposed method