Journal
IEEE SIGNAL PROCESSING LETTERS
Volume 18, Issue 1, Pages 47-50Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LSP.2010.2091126
Keywords
Conjugate gradient; HRcalculus; quaternion gradient; quaternion LMS (QLMS); quaternion Wiener filter
Categories
Funding
- EPSRC [EP/H026266/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/H026266/1] Funding Source: researchfish
Ask authors/readers for more resources
Real functions of quaternion variables are typical cost functions in quaternion valued statistical signal processing, however, standard differentiability conditions in the quaternion domain do not permit direct calculation of their gradients. To this end, based on the isomorphism with real vectors and the use of quaternion involutions, we introduce the calculus as a convenient way to calculate derivatives of such functions. It is shown that the maximum change of the gradient is in the direction of the conjugate gradient, which conforms with the corresponding solution in the complex domain. Examples in some typical gradient based optimization settings support the result.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available