Kernel-based methods for inversion of the Radon transform on SO(3) and their applications to texture analysis

DOI10.1016/j.cam.2005.12.003zbMath1102.65134OpenAlexW2112623636MaRDI QIDQ849615

Helmut Schaeben, Ralf Hielscher, Jürgen Prestin, Karl Gerald van den Boogaart

Publication date: 31 October 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.12.003

zbMATH Keywords

numerical resultsnumerical inversionzonal basis functionscrystallographic preferred orientation

Mathematics Subject Classification ID

Radon transform (44A12) Numerical methods for integral transforms (65R10)

Related Items (14)

Approximation by Positive Definite Functions on Compact Groups ⋮ Probabilistic Marcinkiewicz-Zygmund inequalities on the rotation group ⋮ Fast summation of functions on the rotation group ⋮ Scattered data approximation on the bisphere and application to texture analysis ⋮ Semiparametric estimation of shifts on compact Lie groups for image registration ⋮ Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles ⋮ Marcinkiewicz–Zygmund Inequalities and Polynomial Approximation from Scattered Data onSO(3) ⋮ Generalized splines for Radon transform on compact Lie groups with applications to crystallography ⋮ Stability results for approximation by positive definite functions on \(SO(3)\) ⋮ Orientation distribution within a single hematite crystal ⋮ Surface spline approximation on \(SO(3)\) ⋮ The generalized totally geodesic Radon transform and its application to texture analysis ⋮ Sampling, splines and frames on compact manifolds ⋮ Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries

Cites Work

• The Radon transform.
• Interpolation by positive definite functions on locally compact groups with application to \(\text{SO} (3)\)
• Spherical harmonics
• Orthonormal Ridgelets and Linear Singularities
• A concise quaternion geometry of rotations
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