@article{Xiang:2018:10.1016/j.sigpro.2018.02.018,
author = {Xiang, M and Enshaeifar, S and Stott, AE and Took, CC and Xia, Y and Kanna, S and Mandic, DP},
doi = {10.1016/j.sigpro.2018.02.018},
journal = {Signal Processing},
pages = {193--204},
title = {Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing},
url = {http://dx.doi.org/10.1016/j.sigpro.2018.02.018},
volume = {148},
year = {2018}
}

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TY  - JOUR
AB  - 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.
AU  - Xiang,M
AU  - Enshaeifar,S
AU  - Stott,AE
AU  - Took,CC
AU  - Xia,Y
AU  - Kanna,S
AU  - Mandic,DP
DO  - 10.1016/j.sigpro.2018.02.018
EP  - 204
PY  - 2018///
SN  - 0165-1684
SP  - 193
TI  - Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing
T2  - Signal Processing
UR  - http://dx.doi.org/10.1016/j.sigpro.2018.02.018
VL  - 148
ER  - 

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