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

SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets

We present new clean maps of the CMB temperature anisotropies (as measured by Planck) constructed with a novel internal linear combination (ILC) algorithm using directional, scale-discretised wavelets --- Scale-discretised, directional wavelet ILC or SILC. Directional wavelets, when convolved with signals on the sphere, can separate the anisotropic filamentary structures which are characteristic of both the CMB and foregrounds. Extending previous component separation methods, which use the frequency, spatial and harmonic signatures of foregrounds to separate them from the cosmological background signal, SILC can additionally use morphological information in the foregrounds and CMB to better localise the cleaning algorithm. We test the method on Planck data and simulations, demonstrating consistency with existing component separation algorithms, and discuss how to optimise the use of morphological information by varying the number of directional wavelets as a function of spatial scale. We find that combining the use of directional and axisymmetric wavelets depending on scale could yield higher quality CMB temperature maps. Our results set the stage for the application of SILC to polarisation anisotropies through an extension to spin wavelets.Comment: 15 pages, 13 figures. Minor changes to match version published in MNRAS. Map products available at http://www.silc-cmb.or

An adaptive stereo basis method for convolutive blind audio source separation

NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in PUBLICATION, [71, 10-12, June 2008] DOI:neucom.2007.08.02

Foreground removal for Square Kilometre Array observations of the Epoch of Reionization with the Correlated Component Analysis

We apply the Correlated Component Analysis (CCA) method on simulated data of the Square Kilometre Array, with the aim of accurately cleaning the 21 cm reionization signal from diffuse foreground contamination. The CCA has been developed for the Cosmic Microwave Background, but the application of the Fourier-domain implementation of this method to the reionization signal is straightforward. The CCA is a parametric method to estimate the frequency behaviour of the foregrounds from the data by using second-order statistics. We test its performance on foreground simulations of increasing complexity, designed to challenge the parametric models adopted. We also drop the assumption of spectral smoothness that most of the methods rely upon. We are able to clean effectively the simulated data across the explored frequency range (100-200 MHz) for all the foreground simulations. This shows that the CCA method is very promising for EoR component separation.Comment: 12 pages, 15 figures, accepted by MNRA

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