Fast Independent Component Analysis Algorithm for Quaternion Valued Signals

Authors:
Soroush Javidi;Clive Cheong Took;Danilo P. Mandic
Affiliations:
Department of Electrical and Electronic Engineering, Imperial College London, London, U.K.;Department of Electrical and Electronic Engineering, Imperial College London, London, U.K.;Department of Electrical and Electronic Engineering, Imperial College London, London, U.K.
Venue:
IEEE Transactions on Neural Networks - Part 1
Year:
2011

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Abstract

An extension of the fast independent component analysis algorithm is proposed for the blind separation of both ${\BBQ}$-proper and ${\BBQ}$-improper quaternion-valued signals. This is achieved by maximizing a negentropy-based cost function, and is derived rigorously using the recently developed ${\mbi{\BBH\BBR}}$ calculus in order to implement Newton optimization in the augmented quaternion statistics framework. It is shown that the use of augmented statistics and the associated widely linear modeling provides theoretical and practical advantages when dealing with general quaternion signals with noncircular (rotation-dependent) distributions. Simulations using both benchmark and real-world quaternion-valued signals support the approach.