Spherical quadrature and inversion of Radon transforms

Madych, W. R.; Nelson, S. A.

doi:10.1090/S0002-9939-1985-0806086-6

Spherical quadrature and inversion of Radon transforms

Authors: W. R. Madych and S. A. Nelson
Journal: Proc. Amer. Math. Soc. 95 (1985), 453-457
MSC: Primary 65D32; Secondary 44A15
DOI: https://doi.org/10.1090/S0002-9939-1985-0806086-6
MathSciNet review: 806086
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Abstract: An equivalence is established between certain aspects of: (i) mechanical quadrature for integration on a sphere; (ii) a ridge function representation problem connected with inversion of Radon transform data.

A. Erdelyi (ed.), Tables of integral transforms, McGraw-Hill, New York, 1954.

F. Alberto Grünbaum, The limited angle reconstruction problem, Computed tomography (Cincinnati, Ohio, 1982) Proc. Sympos. Appl. Math., vol. 27, Amer. Math. Soc., Providence, R.I., 1982, pp. 43–61. MR 692053
B. F. Logan and L. A. Shepp, Optimal reconstruction of a function from its projections, Duke Math. J. 42 (1975), no. 4, 645–659. MR 397240
W. R. Madych and S. A. Nelson, Characterization of tomographic reconstructions which commute with rigid motions, J. Functional Analysis 46 (1982), no. 2, 258–263. MR 660190, DOI https://doi.org/10.1016/0022-1236%2882%2990039-8
W. R. Madych and S. A. Nelson, Polynomial based algorithms for computed tomography. II, SIAM J. Appl. Math. 44 (1984), no. 1, 193–208. MR 730010, DOI https://doi.org/10.1137/0144015
W. R. Madych and S. A. Nelson, Radial sums of ridge functions: a characterization, Math. Methods Appl. Sci. 7 (1985), no. 1, 90–100. MR 783388, DOI https://doi.org/10.1002/mma.1670070106
A. D. McLaren, Optimal numerical integration on a sphere, Math. Comp. 17 (1963), 361–383. MR 159418, DOI https://doi.org/10.1090/S0025-5718-1963-0159418-2
Kennan T. Smith, Reconstruction formulas in computed tomography, Computed tomography (Cincinnati, Ohio, 1982) Proc. Sympos. Appl. Math., vol. 27, Amer. Math. Soc., Providence, R.I., 1982, pp. 7–23. MR 692050
L. A. Shepp and J. B. Kruskal, Computerized Tomography: The New Medical X-Ray Technology, Amer. Math. Monthly 85 (1978), no. 6, 420–439. MR 1538734, DOI https://doi.org/10.2307/2320062
A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. Prentice-Hall Series in Automatic Computation. MR 0327006