caa a22 4500 378920146 CHVBK 20180305123603.0 cr unu---uuuuu 161128e20040601xx s 000 0 eng 10.1515/1569394042215865 doi (NATIONALLICENCE)gruyter-10.1515/1569394042215865 Singular value decomposition for the 2D fan-beam Radon transform of tensor fields [Elektronische Daten] [S. G. Kazantsev, A. A. Bukhgeim] 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. Copyright 2004, Walter de Gruyter Kazantsev S. G. 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 aut Bukhgeim A. A. 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 aut Journal of Inverse and Ill-posed Problems Walter de Gruyter 12/3(2004-06-01), 245-278 0928-0219 12:3<245 2004 12 jiip https://doi.org/10.1515/1569394042215865 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569394042215865 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kazantsev S. G. 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 aut NATIONALLICENCE 700 1- Bukhgeim A. A. 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 aut NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 12/3(2004-06-01), 245-278 0928-0219 12:3<245 2004 12 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter