Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
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| 024 | 7 | 0 | |a 10.1515/1569394042215865 |2 doi |
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| 245 | 0 | 0 | |a Singular value decomposition for the 2D fan-beam Radon transform of tensor fields |h [Elektronische Daten] |c [S. G. Kazantsev, A. A. Bukhgeim] |
| 520 | 3 | |a 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 L 2(; S m ) to the data space L 2([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. | |
| 540 | |a Copyright 2004, Walter de Gruyter | ||
| 700 | 1 | |a Kazantsev |D S. G. |u Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mails: kazan@math.nsc.ru, bukhgeim@math.nsc.ru |4 aut | |
| 700 | 1 | |a Bukhgeim |D A. A. |u Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mails: kazan@math.nsc.ru, bukhgeim@math.nsc.ru |4 aut | |
| 773 | 0 | |t Journal of Inverse and Ill-posed Problems |d Walter de Gruyter |g 12/3(2004-06-01), 245-278 |x 0928-0219 |q 12:3<245 |1 2004 |2 12 |o jiip | |
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| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/1569394042215865 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Kazantsev |D S. G. |u Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mails: kazan@math.nsc.ru, bukhgeim@math.nsc.ru |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bukhgeim |D A. A. |u Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mails: kazan@math.nsc.ru, bukhgeim@math.nsc.ru |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Inverse and Ill-posed Problems |d Walter de Gruyter |g 12/3(2004-06-01), 245-278 |x 0928-0219 |q 12:3<245 |1 2004 |2 12 |o jiip | ||
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