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
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;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2009.2027754
