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Quantum-Source Independent Component Analysis and Related Statistical Blind Qubit Uncoupling Methods Read chapter Read first chapter

2014 | OriginalPaper | Chapter

7. Underdetermined Audio Source Separation Using Laplacian Mixture Modelling

Author : Nikolaos Mitianoudis

Published in: Blind Source Separation

Publisher: Springer Berlin Heidelberg

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Abstract

The problem of underdetermined audio source separation has been explored in the literature for many years. The instantaneous \(K\)-sensors, \(L\)-sources mixing scenario (where \(K<L\)) has been tackled by many different approaches, provided the sources remain quite distinct in the virtual positioning space spanned by the sensors. In this case, the source separation problem can be solved as a directional clustering problem along the source position angles in the mixture. The use of Laplacian Mixture Models in order to cluster and thus separate sparse sources in underdetermined mixtures will be explained in detail in this chapter. The novel Generalised Directional Laplacian Density will be derived in order to address the problem of modelling multidimensional angular data. The developed scheme demonstrates robust separation performance along with low processing time.

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previous chapter Sparse Component Analysis: A General Framework for Linear and Nonlinear Blind Source Separation and Mixture Identification
next chapter Itakura-Saito Nonnegative Matrix Two-Dimensional Factorizations for Blind Single Channel Audio Separation
Appendix
Available only for authorised users
Footnotes
1
A \(\pi \)-periodicity is valid for the observed phenomenon, since data in \((\pi /2,3\pi /2)\) are symmetrical to the ones in \((-\pi /2,\pi /2)\) (See Fig. 7.1b). Hence, the use of the atan function instead of the extended atan2 function is justified. For the rest of the analysis, we will assume that \(\theta _n\) takes values between \((0,\pi )\) rather than \((-\pi /2,\pi /2)\). This implies that data in the 4th quadrant \((-\pi /2,0)\) are mapped with odd symmetry to the 2nd quadrant (\(\pi /2,\pi \)). This is performed in order to facilate the derivations of the Generalised Directional Laplacian Distribution and does not alter anything in the actual data.
 
2
Note that for \(n\) positive integer, we have that \(\varGamma (n)=(n-1)!\)
 
3
MATLAB code for the “GaussSep” algorithm is available from http://​www.​irisa.​fr/​metiss/​members/​evincent/​software.
 
4
MATLAB code for the “DEMIX” algorithm is available from http://​infoscience.​epfl.​ch/​record/​165878/​files/​.
 
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Metadata
Title
Underdetermined Audio Source Separation Using Laplacian Mixture Modelling
Author
Nikolaos Mitianoudis
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
Book
Blind Source Separation

Print ISBN: 978-3-642-55015-7

Electronic ISBN: 978-3-642-55016-4

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-642-55016-4_7