DocumentCode
1134917
Title
An Algorithm to Compute Averages on Matrix Lie Groups
Author
Fiori, Simone ; Tanaka, Toshihisa
Author_Institution
Dipt. di Ing. Biomedica, Elettron. e Telecomun. (DiBET), Univ. Politec. delle Marche, Ancona, Italy
Volume
57
Issue
12
fYear
2009
Firstpage
4734
Lastpage
4743
Abstract
Averaging is a common way to alleviate errors and random fluctuations in measurements and to smooth out data. Averaging also provides a way to merge structured data in a smooth manner. The present paper describes an algorithm to compute averages on matrix Lie groups. In particular, we discuss the case of averaging over the special orthogonal group of matrices, the unitary group of matrices and the group of symmetric positive-definite matrices.
Keywords
Lie groups; matrix algebra; merging; random processes; matrix lie group; orthogonal group; random fluctuation; structured data merging; symmetric positive-definite matrices; unitary group; Averaging on curved spaces; complex-valued independent component analysis; matrix Lie groups; orthogonal group; positive-definite matrices; unitary group;
fLanguage
English
Journal_Title
Signal Processing, IEEE Transactions on
Publisher
ieee
ISSN
1053-587X
Type
jour
DOI
10.1109/TSP.2009.2027754
Filename
5165044
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