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Hamaker, C.; Solmon, D. C.

The angles between the null spaces of X rays. (English) Zbl 0437.45025

J. Math. Anal. Appl. 62, 1-23 (1978).
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Cited in 36 Documents

MSC:

45L05 Theoretical approximation of solutions to integral equations
45G05 Singular nonlinear integral equations
65R20 Numerical methods for integral equations
65D99 Numerical approximation and computational geometry (primarily algorithms)

Keywords:

reconstructing two-dimensional cross sections; electron micrographs; reconstruction problem; angles between the null spaces of X rays; estimating the internal structures of the human body from multiple radiographs; numerical results
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References:

[1] Amemiya, I.; Ando, T., Convergence of random products of contractions in Hilbert space, Acta Sci. Math. (Szeged), 26, 239-244 (1965) · Zbl 0143.16202
[2] Crowther, R. A.; DeRosier, D. J.; Klug, A., The reconstruction of a three dimensional structure from projections and its applications to electron microscopy, (Proc. Roy. Soc. London A, 317 (1970)), 319-340
[3] Dixmier, J., Étude sur les variétés et les opérateurs de Julia, avec quelques application, Bull. Soc. Math. France, 77, 11-101 (1949) · Zbl 0045.39102
[4] Durand, E., (Solutions Numériques des Équations Algébriques, Tome II (1960), Masson: Masson Paris), 120 · Zbl 0099.10801
[5] Gordon, R.; Bender, R.; Herman, G. T., Algebraic reconstruction techniques (ART) for three dimensional electron microscopy and x-ray photography, J. Theor. Biol., 29, 471-481 (1970)
[6] Hounsfield, G. N., Computerized transverse axial scanning (tomography): Part I Description of system, British J. Radiol., 46, 1016-1022 (1973)
[7] Isaacson, E.; Keller, H. B., Analysis of Numerical Methods (1966), Wiley: Wiley New York · Zbl 0168.13101
[8] Logan, B. F.; Shepp, L. A., Optimal reconstruction of a function from its projections, Duke Math. J., 645-659 (Dec. 1975) · Zbl 0343.41020
[9] Luenberger, D. G., Optimization by Vector Space Methods, ((1969), Wiley: Wiley New York), 57 · Zbl 0176.12701
[10] Ramachandran, N.; Lakshminarayanan, A. V., Three-dimensional reconstruction from radiographs and electron micrographs: Application of convolutions instead of Fourier transforms, (Proc. Nat. Acad. Sci. USA, 68 (1971)), 2236-2240
[11] Smith, K. T.; Solmon, D. C.; Wagner, S. L., Practical and mathematical aspects of the problem of reconstructing objects from radiographs, Bull. Amer. Math. Soc. (Nov. 1977) · Zbl 0521.65090
[12] Solmon, D. C., The x-ray transform, J. Math. Anal. Appl., 56, 61-83 (1976) · Zbl 0334.44007
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