Regularizing filtrating of projections for two-dimensional tomography algorithms
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 2, pp. 187-200.

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The regularizing filters for tomography algorithms are proposed and investigated. The method for regularization parameter determination was developed on the basis of a discrepancy criterion. The numerical simulations were carried out. In particular, the proposed filtration of projections was compared to be Shepp–Logan one.
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A. V. Likhachev. Regularizing filtrating of projections for two-dimensional tomography algorithms. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 2, pp. 187-200. http://geodesic.mathdoc.fr/item/SJVM_2008_11_2_a5/

[1] Herman G. T., Image Reconstruction from Projections: The Fundamentals of Computerised Tomography, Academic Press, New York, 1980 | MR

[2] Natterer F., The Mathematics of Computerized Tomography, John Wiley Sons, New York, 1986 | MR | Zbl

[3] Tikhonov A. N., Arsenin V. Ya., Timonov A. A., Matematicheskie zadachi kompyuternoi tomografii, Nauka, M., 1987 | MR

[4] Pikalov V. V., Melnikova T. S., Tomografiya plazmy, Nauka. Sib. izdat. firma, Novosibirsk, 1995

[5] Lavrentev M. M., Zerkal S. M., Trofimov O. E., Chislennoe modelirovanie v tomografii i uslovno-korrektnye zadachi, Izd-vo IDMI NGU, Novosibirsk, 1999

[6] Shepp L. A. and Logan B. F., “The Fourier reconstruction of a head section”, IEEE Trans. Nucl. Sci., 21:3 (1974), 21–43 | MR

[7] Ramachandran G. N., Lakshminarayanan A. V., “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms”, Proc. Nat. Acad. Sci. US., 68 (1971), 2236–2240 | DOI | MR

[8] Herman G. T., Rowland S. W., “Three methods for reconstructing objects from $x$-rays: a comparative study”, Cumput. Graph. Img. Proc., 2 (1973), 151–178 | DOI | MR

[9] Likhachev A. V., “Issledovanie $1/z^2$-filtratsii v algoritmakh tomografii”, Avtometriya, 43:3 (2007), 57–64 | MR

[10] Likhachov A. V., Pickalov V. V., Ewert U., Redmer B., “Resolution enhancement in computerized tomography by deconvolution methods”, Proc. 2nd Workshop “NDT in Progress”. Int. Meeting of NDT Experts (October 6–8, 2003, Prague), Brno Univ. Technol., Brno, 2003, 137–150

[11] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1986 | MR | Zbl