Abstract
We have seen that, when complete continuous X-ray data are available, then an attenuation-coefficient function f(x, y) can be reconstructed exactly using the filtered back-projection formula, Theorem 6.2.
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Bibliography
Cierniak, R.: X-Ray Computed Tomography in Biomedical Engineering. Springer, New York (2011)
Cooley, T.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)
Kuchment, P.: The Radon Transform and Medical Imaging. CBMS, vol. 85. SIAM, Philadelphia (2014)
Rowland, S.W.: Computer implementation of image reconstruction formulas. In: Herman, G.T. (ed.) Image Reconstruction from Projections: Implementation and Applications. Topics in Applied Physics, vol. 32. Springer, Berlin (1979)
Shepp, L.A., Kruskal, J.B.: Computerized tomography: the new medical X-ray technology. Am. Math. Mon. 34, 35–44 (1978)
Wang, L.: Cross-section reconstruction with a fan-beam scanning geometry. IEEE Trans. Comput. C-26, 264–268 (1977)
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Feeman, T.G. (2015). Discrete Image Reconstruction. In: The Mathematics of Medical Imaging. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-22665-1_8
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DOI: https://doi.org/10.1007/978-3-319-22665-1_8
Publisher Name: Springer, Cham
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