Blind Separation of Exponential Polynomials and the Decomposition of a Tensor in Rank-$(L_r,L_r,1)$ Terms

We present a new necessary and sufficient condition for essential uniqueness of the decomposition of a third-order tensor in rank-$(L_r,L_r,1)$ terms. We derive a new deterministic technique for blind signal separation that relies on this decomposition. The method assumes that the signals can be mod...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications Vol. 32; no. 4; pp. 1451 - 1474
Main Author: De Lathauwer, Lieven
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.10.2011
Subjects:
Algebra
Decomposition
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Polynomials
Sciences and techniques of general use
Signal processing
System theory
Polynomial
Tensor
blind signal separation
Necessary and sufficient condition
Decomposition method
Rank
multilinear algebra
15A69
Linear model
15A18
Numerical analysis
exponential polynomial
Linear algebra
canonical polyadic decomposition
higher-order tensor
block term decomposition
Singular value decomposition
ISSN:0895-4798, 1095-7162
Online Access:Get full text
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Summary:We present a new necessary and sufficient condition for essential uniqueness of the decomposition of a third-order tensor in rank-$(L_r,L_r,1)$ terms. We derive a new deterministic technique for blind signal separation that relies on this decomposition. The method assumes that the signals can be modeled as linear combinations of exponentials or, more generally, as exponential polynomials. The results are illustrated by means of numerical experiments.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0895-4798
1095-7162
DOI:10.1137/100805510