scholarly journals Adaptively Constrained Convex Optimization for Accurate Fiber Orientation Estimation with High Order Spherical Harmonics

2013 ◽  
pp. 485-492 ◽  
Author(s):  
Giang Tran ◽  
Yonggang Shi
Keyword(s):  
Convex Optimization ◽  
Spherical Harmonics ◽  
Fiber Orientation ◽  
High Order ◽  
Orientation Estimation ◽  
Constrained Convex Optimization

Reachability of Optimal Convergence Rate Estimates for High-Order Numerical Convex Optimization Methods

2019 ◽  
Vol 99 (1) ◽  
pp. 91-94
Author(s):  
A. V. Gasnikov ◽  
E. A. Gorbunov ◽  
D. A. Kovalev ◽  
A. A. M. Mokhammed ◽  
E. O. Chernousova
Keyword(s):  
Convex Optimization ◽  
Convergence Rate ◽  
Optimization Methods ◽  
High Order ◽  
Optimal Convergence Rate ◽  
Optimal Convergence

An efficient routine for computing symmetric real spherical harmonics for high orders of expansion

2005 ◽  
Vol 38 (3) ◽  
pp. 501-504 ◽  
Author(s):  
Andrzej Kudlicki ◽  
Małgorzata Rowicka ◽  
Mirosław Gilski ◽  
Zbyszek Otwinowski
Keyword(s):  
Electron Microscopy ◽  
Spherical Harmonics ◽  
Efficient Method ◽  
Protein Crystallography ◽  
High Order ◽  
Linear Combinations ◽  
Crystallographic Symmetry ◽  
Stable Computation ◽  
Very High

A numerically efficient method of constructing symmetric real spherical harmonics is presented. Symmetric spherical harmonics are real spherical harmonics with built-in invariance with respect to rotations or inversions. Such symmetry-invariant spherical harmonics are linear combinations of non-symmetric ones. They are obtained as eigenvectors of an appropriate operator, depending on symmetry. This approach allows for fast and stable computation up to very high order symmetric harmonic bases, which can be used in e.g. averaging of non-crystallographic symmetry in protein crystallography or refinement of large viruses in electron microscopy.

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