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

2014 | OriginalPaper | Chapter

2. Blind Source Separation Based on Dictionary Learning: A Singularity-Aware Approach

Authors : Xiaochen Zhao, Guangyu Zhou, Wei Dai, Wenwu Wang

Published in: Blind Source Separation

Publisher: Springer Berlin Heidelberg

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Abstract

This chapter surveys recent works in applying sparse signal processing techniques, in particular, dictionary learning algorithms to solve the blind source separation problem. For the proof of concepts, the focus is on the scenario where the number of mixtures is not less than that of the sources. Based on the assumption that the sources are sparsely represented by some dictionaries, we present a joint source separation and dictionary learning algorithm (SparseBSS) to separate the noise corrupted mixed sources with very little extra information. We also discuss the singularity issue in the dictionary learning process, which is one major reason for algorithm failure. Finally, two approaches are presented to address the singularity issue.

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previous chapter Quantum-Source Independent Component Analysis and Related Statistical Blind Qubit Uncoupling Methods
next chapter Performance Study for Complex Independent Component Analysis
Footnotes
1
Note that in this chapter \(\varvec{P}_{k}\) is defined as a patching operator for image sources. The patching operator for audio sources can be similarly defined as well.
 
2
An illustration: take \(\varvec{Y},\,\varvec{D},\,\varvec{X}\) as scalars. If \(\varvec{Y}\ne 0\), there exists a singular point at \(\varvec{D}=0\) on \(f\left( \varvec{D}\right) =\underset{\varvec{X}}{\mathrm{min}}\left\| \varvec{Y}-\varvec{D}\varvec{X}\right\| _{F}^{2}\), where \(\varvec{X}\) can be assigned as any real number.
 
3
For the BMMCA test, a better performance was demonstrated in [14]. We point out that here a different true mixing matrix is used. And furthermore, in our tests the patches are taken with a 50 % overlap (by shifting 4 pixels from the current patch to the next) while in [14] the patches are taken by shifting only one pixel from the current patch to the next.
 
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Metadata
Title
Blind Source Separation Based on Dictionary Learning: A Singularity-Aware Approach
Authors
Xiaochen Zhao
Guangyu Zhou
Wei Dai
Wenwu Wang
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_2