Singular value decomposition for the 2D fan-beam Radon transform of tensor fields

Singular value decomposition for the 2D fan-beam Radon transform of tensor fields Full article

Journal

Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945

Output data

Year: 2004, Volume: 12, Number: 3, Pages: 245-278 Pages count : 34 DOI: 10.1515/1569394042215865

Authors

Kazantsev S.G. ¹ , Bukhgeim A.A. ¹

Affiliations

1	Sobolev Institute of Mathematics

In this article we study the fan-beam Radon transform of symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc as the operator, acting from the object space L2(; Sm) to the data space L2([0, 2π) × [0, 2π)). The orthogonal polynomial basis of solenoidal tensor fields on the disc was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator was obtained. The inversion formula for the fan-beam tensor transform 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.

Kazantsev S.G. , Bukhgeim A.A.
Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
Journal of Inverse and Ill-Posed Problems. 2004. V.12. N3. P.245-278. DOI: 10.1515/1569394042215865 Scopus OpenAlex

Scopus:	2-s2.0-85047022473
OpenAlex:	W1979054340

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