Matrix computations (3rd ed.)
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
Journal of Mathematical Imaging and Vision
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
On the Geometry of Rolling and Interpolation Curves on Sn, SOn, and Grassmann Manifolds
Journal of Dynamical and Control Systems
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Handbook of Blind Source Separation: Independent Component Analysis and Applications
Handbook of Blind Source Separation: Independent Component Analysis and Applications
Complex blind source separation via simultaneous strong uncorrelating transform
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Conjugate gradient on Grassmann manifolds for robust subspace estimation
Image and Vision Computing
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We propose a conjugate gradient type optimization technique for the computation of the Karcher mean on the set of complex linear subspaces of fixed dimension, modeled by the so-called Grassmannian. The identification of the Grassmannian with Hermitian projection matrices allows an accessible introduction of the geometric concepts required for an intrinsic conjugate gradient method. In particular, proper definitions of geodesics, parallel transport, and the Riemannian gradient of the Karcher mean function are presented. We provide an efficient step-size selection for the special case of one dimensional complex subspaces and illustrate how the method can be employed for blind identification via numerical experiments.