Title :
On gradient calculation in quaternion adaptive filtering
Author :
Jahanchahi, Cyrus ; Took, Clive Cheong ; Mandic, Danilo P.
Author_Institution :
Electr. & Electron. Eng. Dept., Imperial Coll. London, London, UK
Abstract :
A novel way to calculate the gradient of real functions of quaternion variables, typical cost functions in quaternion signal processing, is proposed. This is achieved by revisiting quaternion involutions and by simplifying the existing HR derivatives. This has allowed us to express the class of quaternion least mean square (QLMS) algorithms in a more compact form while keeping the same generic form of LMS. Simulations in the prediction setting support the approach.
Keywords :
adaptive filters; adaptive signal processing; conjugate gradient methods; least mean squares methods; HR derivatives; QLMS algorithms; conjugate gradient method; cost functions; gradient calculation; quaternion adaptive filtering; quaternion involutions; quaternion least mean square algorithm; quaternion signal processing; quaternion variables; real functions; Adaptation models; Calculus; Least squares approximation; Quaternions; Signal processing; Signal processing algorithms; Standards; HR calculus; Quaternion LMS (QLMS); Quaternion gradient; conjugate gradient; involutions;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on
Conference_Location :
Kyoto
Print_ISBN :
978-1-4673-0045-2
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2012.6288738
