2010
DOI: 10.1007/s10092-010-0024-7
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Scattered data interpolation of Radon data

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Cited by 6 publications
(6 citation statements)
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“…Scattered data can then be interpolated using suitable methods. For example a radial functions method was recently introduced by Beatson and zu Castell [1] to obtain new values of the Radon transform. This technique can be combined with the methods introduced below to obtain a reconstruction using less initial data.…”
Section: Kernel Based Image Reconstructionmentioning
confidence: 99%
“…Scattered data can then be interpolated using suitable methods. For example a radial functions method was recently introduced by Beatson and zu Castell [1] to obtain new values of the Radon transform. This technique can be combined with the methods introduced below to obtain a reconstruction using less initial data.…”
Section: Kernel Based Image Reconstructionmentioning
confidence: 99%
“…In either case, robust numerical algorithms are required to reconstruct characteristic features of images at sufficiently high accuracy, on the one hand, and at sufficiently small computational costs, on the other hand. For details concerning the acquisition of X-ray scans, their underlying mathematical models, and standard computational methods for medical image reconstruction, we refer to the textbook [5] of Feeman. To describe the mathematical problem of image reconstruction from X-ray scans, we regard the Radon transform Rf of f ∈ L 1 (R 2 ), defined as Rf (t, θ) = R f (t cos θ − s sin θ, t sin θ + s cos θ) ds (1) for (t, θ) ∈ R × [0, π). Note that for any f ∈ L 1 (R 2 ) the stability estimate…”
Section: Introductionmentioning
confidence: 99%
“…c j g j of the basis functions. According to our problem formulation at the outset of this introduction, we require g j ∈ L 1 (R 2 ), for all 1 ≤ j ≤ n, so that the Radon transform Rg j , as in (1), is for any basis function g j well-defined. This then amounts to solving the linear system…”
Section: Introductionmentioning
confidence: 99%
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