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- Title
Singular value decomposition for the 2D fan-beam Radon transform of tensor fields.
- Authors
Kazantsev, S. G.; Bukhgeim, A. A.
- Abstract
In this article we study the fan-beam Radon transform Dm of symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc D as the operator, acting from the object space L2(D; Sm) to the data space L2 ([0, 2π) × [0, 2π)). The orthogonal polynomial basis sn,k(± m) of solenoidal tensor fields on the disc D was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator Dm was obtained. The inversion formula for the fan-beam tensor transform Dm follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented.
- Subjects
RADON transforms; RADON integrals; RADON measures; TENSOR algebra; INTEGRAL transforms; INTEGRAL geometry
- Publication
Journal of Inverse & Ill-Posed Problems, 2004, Vol 12, Issue 3, p245
- ISSN
0928-0219
- Publication type
Article
- DOI
10.1515/1569394042215865