caa a22 4500 445862009 CHVBK 20180317145446.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s10092-010-0024-7 doi (NATIONALLICENCE)springer-10.1007/s10092-010-0024-7 Scattered data interpolation of Radon data [Elektronische Daten] [R. Beatson, W. zu Castell] Linear combinations of translates of a given basis function have long been successfully used to solve scattered data interpolation and approximation problems. We demonstrate how the classical basis function approach can be transferred to the projective space ℙd−1. To be precise, we use concepts from harmonic analysis to identify positive definite and strictly positive definite zonal functions on ℙd−1. These can then be applied to solve problems arising in tomography since the data given there consists of integrals over lines. Here, enhancing known reconstruction techniques with the use of a scattered data interpolant in the "space of lines”, naturally leads to reconstruction algorithms well suited to limited angle and limited range tomography. In the medical setting algorithms for such incomplete data problems are desirable as using them can limit radiation dosage. Springer-Verlag, 2010 Basis function methods nationallicence Computer tomography nationallicence Positive definite functions nationallicence Real Projective space nationallicence Beatson R. Department of Mathematics and Statistics, University of Canterbury, 8020, Christchurch, New Zealand aut zu Castell W. Department of Scientific Computing, Helmholtz Zentrum München, German Research Center for Environmental Health, Ingolstaedter Landstrasse 1, 85764, Neuherberg, Germany aut Calcolo Springer Milan 48/1(2011-03-01), 5-19 0008-0624 48:1<5 2011 48 10092 https://doi.org/10.1007/s10092-010-0024-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10092-010-0024-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Beatson R. Department of Mathematics and Statistics, University of Canterbury, 8020, Christchurch, New Zealand aut NATIONALLICENCE 700 1- zu Castell W. Department of Scientific Computing, Helmholtz Zentrum München, German Research Center for Environmental Health, Ingolstaedter Landstrasse 1, 85764, Neuherberg, Germany aut NATIONALLICENCE 773 0- Calcolo Springer Milan 48/1(2011-03-01), 5-19 0008-0624 48:1<5 2011 48 10092 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer