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Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

Xiang, Min, Enshaeifar, Shirin, Stott, Alexander E., Cheong Took, Clive, Xia, Yili, Kanna, Sithan and Mandic, Danilo P. (2018) Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing Signal Processing, 148. pp. 193-204.

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Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing - AAM.pdf - Accepted version Manuscript
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Abstract

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Computing Science
Authors :
NameEmailORCID
Xiang, Min
Enshaeifar, Shirins.enshaeifar@surrey.ac.uk
Stott, Alexander E.
Cheong Took, Clivec.cheongtook@surrey.ac.uk
Xia, Yili
Kanna, Sithan
Mandic, Danilo P.
Date : 13 February 2018
Identification Number : 10.1016/j.sigpro.2018.02.018
Copyright Disclaimer : © 2018 Elsevier B.V. All rights reserved.
Uncontrolled Keywords : Quaternion matrix diagonalisation; Complementary covariance; Pseudo-covariance; Widely linear processing; Quaternion non-circularity; Improperness
Depositing User : Clive Harris
Date Deposited : 20 Feb 2018 15:31
Last Modified : 15 May 2018 08:02
URI: http://epubs.surrey.ac.uk/id/eprint/845871

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