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

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dc.creatorKazantsev, Sergey G.
dc.creatorBukhgeim, Alexandre A.
dc.date2004-04-24
dc.date.accessioned2026-07-07T05:07:42Z
dc.date.available2026-07-07T05:07:42Z
dc.descriptionIn this article we study the fan-beam Radon transform ${\cal D}_m $ of symmetrical solenoidal 2D tensor fields of arbitrary rank $m$ in a unit disc $\mathbb D$ as the operator, acting from the object space ${\mathbf L}_{2}(\mathbb D; {\bf S}_m)$ to the data space $L_2([0,2π)\times[0,2π)).$ The orthogonal polynomial basis ${\bf s}^{(\pm m)}_{n,k}$ of solenoidal tensor fields on the disc $\mathbb D$ was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator ${\cal D}_m $ was obtained. The inversion formula for the fan-beam tensor transform ${\cal D}_m $ 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.
dc.descriptionLaTeX, 37 pages with 5 figures
dc.identifierhttps://arxiv.org/abs/math/0404442
dc.identifierhttp://arxiv.org/abs/math/0404442
dc.identifierJournal of Inverse and Ill-Posed Problems, 2004, Vol. 12, No.3, pp. 245-278.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70959
dc.subjectComplex Variables
dc.subjectMathematical Physics
dc.subject44A12 (Primary); 53A45, 42C05 (Secondary)
dc.titleSingular value decomposition for the 2D fan-beam Radon transform of tensor fields
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