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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 65D32, 44A15
Retrieve articles in all journals with MSC: 65D32, 44A15
Additional Information
Article copyright:
© Copyright 1985
American Mathematical Society