The inverse Radon transform that does not contain the singular filtration
Keywords:
Radon transform, central cross-section theorem, reverse projection, ramp filter, Gaussian low-pass filter
Abstract
The paper presents the results of a study in the field of computed tomography, on the basis of which the method for reconstructing the internal structure of a studied object has been proposed. The idea is to use the inverse Radon transform, which does not lead to the emergence of a singular nucleus. In this work, this method has been tested and compared with the existing methods.
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References
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Durrani, T. S. and Bisset, D. Erratum to: The Radon Transform and Its Properties. // Geophys. – 1985. – V. 50. – P. 884-886.
Hungerbühler, N. Singular Filters for the Radon Backprojection. // J. Appl. Analysis. – V. 5. – P. 17-33.
Kunyansky, L. A. Generalized and Attenuated Radon Transforms: Restorative Approach to the Numerical Inversion // Inverse Problems. – V. 8. – P. 809-819.
Zalcman, L. Uniqueness and Nonuniqueness for the Radon Transform // Bull. London Math. Soc. – V. 14. – P. 241-245.
Deans, S. R. The Radon Transform and Some of Its Applications. – New York: Wiley, 1983. – 462 p.
Kak, A. C. and Slaney, M. Principles of Computerized Tomographic Imaging. – IEEE Press, 1988. – 323 p.
Esser, P. D. (Ed.). Emission Computed Tomography: Current Trends. – New York: Society of Nuclear Medicine, 1983. – 249 p.
Shepp, L. A. and Kruskal, J. B. Computerized Tomography: The New Medical X-Ray Technology // Amer. Math. Monthly. – 1978. – V. 85. – P. 420-439.
Nievergelt, Y. Elementary Inversion of Radon's Transform. // SIAM Rev. – 1986. – V. 28. – P. 79-84.
Durrani, T. S. and Bisset, D. Erratum to: The Radon Transform and Its Properties. // Geophys. – 1985. – V. 50. – P. 884-886.
Hungerbühler, N. Singular Filters for the Radon Backprojection. // J. Appl. Analysis. – V. 5. – P. 17-33.
Kunyansky, L. A. Generalized and Attenuated Radon Transforms: Restorative Approach to the Numerical Inversion // Inverse Problems. – V. 8. – P. 809-819.
Zalcman, L. Uniqueness and Nonuniqueness for the Radon Transform // Bull. London Math. Soc. – V. 14. – P. 241-245.
Published
2017-12-22
How to Cite
Вайсбурд, А. И., Вихтинская, Т. Г., & Немченко, К. Э. (2017). The inverse Radon transform that does not contain the singular filtration. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 36, 38-43. Retrieved from https://periodicals.karazin.ua/mia/article/view/10090
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