期刊
IEEE SIGNAL PROCESSING LETTERS
卷 18, 期 1, 页码 47-50出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LSP.2010.2091126
关键词
Conjugate gradient; HRcalculus; quaternion gradient; quaternion LMS (QLMS); quaternion Wiener filter
资金
- EPSRC [EP/H026266/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/H026266/1] Funding Source: researchfish
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.
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