A hierarchical approach for sparse source Blind Signal Separation problem

Mujahid N. Syed; Pando G. Georgiev; Panos M. Pardalos

doi:10.1016/j.cor.2012.12.002

A hierarchical approach for sparse source Blind Signal Separation problem

Mujahid N. Syed, Pando G. Georgiev^*, Panos M. Pardalos

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper, a Blind Signal Separation (BSS) problem is considered: given Xâ̂̂Rm×^N, BSS problem is to find Aâ̂̂Rm×ⁿ and Sâ̂̂Rn× ^N, where the matrices are related as X=AS. We have reviewed the sufficient conditions on the structure of X, A and S in terms of sparseness conditions on S, such that the equation X=AS can be solved uniquely (up to permutation and scalability). A hierarchical 0-1 MIP is proposed to solve the problem. Probabilistically, we have shown that every subsequent level of hierarchical MIP will be easier to solve than the precedent level of MIP. Moreover, we have presented case studies that illustrate the performance of proposed solution approach for correlated sparse sources.

Original language	English
Pages (from-to)	386-398
Number of pages	13
Journal	Computers and Operations Research
Volume	41
Issue number	1
DOIs	https://doi.org/10.1016/j.cor.2012.12.002
State	Published - 2014
Externally published	Yes

Keywords

Blind source separation
Hierarchical optimization
Sparse Component Analysis
Underdetermined mixtures

ASJC Scopus subject areas

General Computer Science
Modeling and Simulation
Management Science and Operations Research

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10.1016/j.cor.2012.12.002

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title = "A hierarchical approach for sparse source Blind Signal Separation problem",

abstract = "In this paper, a Blind Signal Separation (BSS) problem is considered: given X{\^a}{\^̂}Rm×N, BSS problem is to find A{\^a}{\^̂}Rm×n and S{\^a}{\^̂}Rn× N, where the matrices are related as X=AS. We have reviewed the sufficient conditions on the structure of X, A and S in terms of sparseness conditions on S, such that the equation X=AS can be solved uniquely (up to permutation and scalability). A hierarchical 0-1 MIP is proposed to solve the problem. Probabilistically, we have shown that every subsequent level of hierarchical MIP will be easier to solve than the precedent level of MIP. Moreover, we have presented case studies that illustrate the performance of proposed solution approach for correlated sparse sources.",

keywords = "Blind source separation, Hierarchical optimization, Sparse Component Analysis, Underdetermined mixtures",

author = "Syed, \{Mujahid N.\} and Georgiev, \{Pando G.\} and Pardalos, \{Panos M.\}",

year = "2014",

doi = "10.1016/j.cor.2012.12.002",

language = "English",

volume = "41",

pages = "386--398",

journal = "Computers and Operations Research",

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number = "1",

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TY - JOUR

T1 - A hierarchical approach for sparse source Blind Signal Separation problem

AU - Syed, Mujahid N.

AU - Georgiev, Pando G.

AU - Pardalos, Panos M.

PY - 2014

Y1 - 2014

N2 - In this paper, a Blind Signal Separation (BSS) problem is considered: given Xâ̂̂Rm×N, BSS problem is to find Aâ̂̂Rm×n and Sâ̂̂Rn× N, where the matrices are related as X=AS. We have reviewed the sufficient conditions on the structure of X, A and S in terms of sparseness conditions on S, such that the equation X=AS can be solved uniquely (up to permutation and scalability). A hierarchical 0-1 MIP is proposed to solve the problem. Probabilistically, we have shown that every subsequent level of hierarchical MIP will be easier to solve than the precedent level of MIP. Moreover, we have presented case studies that illustrate the performance of proposed solution approach for correlated sparse sources.

AB - In this paper, a Blind Signal Separation (BSS) problem is considered: given Xâ̂̂Rm×N, BSS problem is to find Aâ̂̂Rm×n and Sâ̂̂Rn× N, where the matrices are related as X=AS. We have reviewed the sufficient conditions on the structure of X, A and S in terms of sparseness conditions on S, such that the equation X=AS can be solved uniquely (up to permutation and scalability). A hierarchical 0-1 MIP is proposed to solve the problem. Probabilistically, we have shown that every subsequent level of hierarchical MIP will be easier to solve than the precedent level of MIP. Moreover, we have presented case studies that illustrate the performance of proposed solution approach for correlated sparse sources.

KW - Blind source separation

KW - Hierarchical optimization

KW - Sparse Component Analysis

KW - Underdetermined mixtures

UR - https://www.scopus.com/pages/publications/84885956985

U2 - 10.1016/j.cor.2012.12.002

DO - 10.1016/j.cor.2012.12.002

M3 - Article

AN - SCOPUS:84885956985

SN - 0305-0548

VL - 41

SP - 386

EP - 398

JO - Computers and Operations Research

JF - Computers and Operations Research

IS - 1

ER -

A hierarchical approach for sparse source Blind Signal Separation problem

Abstract

Keywords

ASJC Scopus subject areas

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