Title :
A link between the decomposition of a third-order tensor in rank-(L,L,1) terms and Joint Block Diagonalization
Author :
Nion, Dimitri ; De Lathauwer, Lieven
Author_Institution :
Group Sci., Eng. & Technol., K.U. Leuven, Leuven, Belgium
Abstract :
In this paper, we show that the block component decomposition in rank-(L,L,1) terms of a third-order tensor, referred to as BCD-(L,L,1), can be reformulated as a joint block diagonalization (JBD) problem, provided that certain assumptions on the dimensions are satisfied. This JBD-based reformulation leads to a new uniqueness bound for the BCD-(L,L,1). We also propose a closed-form solution to solve exact JBD problems. For approximate JBD problems, this closed-form solution yields a good starting value for iterative optimization algorithms. The performance of our technique is illustrated by its application to blind CDMA signal separation.
Keywords :
blind source separation; code division multiple access; iterative methods; optimisation; tensors; blind CDMA signal separation; component decomposition; iterative optimization algorithms; joint block diagonalization; third-order tensor; Argon; Closed-form solution; Conferences; Convergence; Iterative algorithms; Least squares approximation; Matrix decomposition; Multiaccess communication; Source separation; Tensile stress;
Conference_Titel :
Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2009 3rd IEEE International Workshop on
Conference_Location :
Aruba, Dutch Antilles
Print_ISBN :
978-1-4244-5179-1
Electronic_ISBN :
978-1-4244-5180-7
DOI :
10.1109/CAMSAP.2009.5413231