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Approximate inverse meets local tomography. (English) Zbl 0966.65109
Design reconstruction filters for the filtered backprojection algorithm (FBA) are presented. The convergence and convergence rates for the FBA as the discretization step size goes to zero is proved. The FBA is also expressed by the approximate inverse. A scheme which yields a proper scaling of the reconstruction filters is proposed. The analytical theory is supported by numerical experiments.

65R20 Numerical methods for integral equations
44A12 Radon transform
92C55 Biomedical imaging and signal processing
Full Text: DOI
[1] Local inversion of the Radon transform in even dimensions using wavelets. In 75 Years of Radon Transform, (eds). International Press: Cambridge, MA, 1994; 45-69. · Zbl 0823.44003
[2] Wavelets and local tomography. In Wavelets in Medicine and Biology, (eds). CRC Press: Boca Raton, FL, 1996; 231-261.
[3] Faridani, Z. Angew. Math. Mech. 70 pp t530– (1990)
[4] Results, old and new, in computed tomography. In Inverse Problems in Wave Propagation, (eds). The IMA Volumes in Mathematics and its Applications, vol. 90. Springer: New York, 1997; 167-193. · doi:10.1007/978-1-4612-1878-4_8
[5] Faridani, SIAM J. Appl. Math. 57 pp 1095– (1997)
[6] Faridani, SIAM J. Appl. Math. 52 pp 459– (1992)
[7] Holschneider, Inverse Problems 7 pp 853– (1991) · Zbl 0751.35049
[8] Katsevich, Inverse Problems 11 pp 1005– (1995)
[9] Non-Homogeneous Boundary Value Problems and Applications, Vol. 1. Springer: New York, 1972.
[10] Louis, Inverse Problems 12 pp 175– (1996) · Zbl 0851.65036
[11] Louis, Inverse Problems 15 pp 489– (1999)
[12] Louis, Inverse Problems 6 pp 427– (1990)
[13] Wavelets: theory and applications. Pure and Applied Mathematics. Wiley: Chichester, 1997.
[14] The Mathematics of Computerized Tomography. Wiley: Chichester, 1986. · Zbl 0617.92001
[15] Rashid-Farrokhi, IEEE Trans. Image Proc. 6 pp 1412– (1997)
[16] Rieder, SIAM J. Numer. Anal.
[17] Shepp, IEEE Trans. Nucl. Sci. 21 pp 21– (1974)
[18] Smith, Applied Optics 24 pp 3950– (1985)
[19] Introduction to Numerical Analysis. Springer: New York, 1996.
[20] Increasing the spatial resolution in computerized tomography. In Problems in Tomographic Reconstruction, (eds). Siberian Branch of the Academy of Science. USSR: Novosibirsk, 1985; 28-35.
[21] Partial Differential Equations. Cambridge University Press: Cambridge, U. K., 1987. · doi:10.1017/CBO9781139171755
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