The \(L^ 2\)-optimal convolving functions in reconstruction convolution algorithms. (English) Zbl 0638.65093

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


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.)
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