Matúš, František The \(L^ 2\)-optimal convolving functions in reconstruction convolution algorithms. (English) Zbl 0638.65093 Kybernetika 23, 294-304 (1987). The paper is concerned with the choice of the convolving function in the filtered backprojection algorithm of computerized tomography. This algorithm computes an approximation to Radon’s integral equation \(g=Rf\) in the form \(f=R^*(v*g)\) where \(R^*\) is a discrete backprojection and v*g is a discrete convolution. The criterion for choosing v is to minimize \(\| f_ 0-R^*(v*Rf_ 0)\|\) for a certain function \(f_ 0\). Numerical results for v are given. Reviewer: F.Natterer MSC: 65R10 Numerical methods for integral transforms 65R20 Numerical methods for integral equations 45H05 Integral equations with miscellaneous special kernels 44A15 Special integral transforms (Legendre, Hilbert, etc.) Keywords:Radon transform; filtered backprojection algorithm; computerized tomography; Radon’s integral equation; discrete backprojection; discrete convolution; Numerical results PDFBibTeX XMLCite \textit{F. Matúš}, Kybernetika 23, 294--304 (1987; Zbl 0638.65093) Full Text: EuDML References: [1] И. М. Гельфаид М. И. Грасв Н. Я. Виленкин: Интегральная геометрия и связаные с ней вопросы теории представленуй. Физматгиз, Москва 1962. · Zbl 1226.30001 [2] G. T. Herman: Image Reconstruction from Projection: Implementation and Applications. Springer-Verlag, Berlin 1979. [3] K. Rektorys: Variational Methods in Mathematics, Science and Engineering (in Czech). Second Edition. SNTL, Prague 1977. [4] D. H. Griffel: Applied Functional Analysis. Ellis Horwood Limited, New York 1981. · Zbl 0461.46001 [5] A. E. Taylor: Introduction to Functional Analysis (in Czech). Academia, Prague 1973. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.