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Practical and mathematical aspects of the problem of reconstructing objects from radiographs. (English) Zbl 0521.65090

MSC:
65R10 Numerical methods for integral transforms
45H05 Integral equations with miscellaneous special kernels
92F05 Other natural sciences (mathematical treatment)
58C99 Calculus on manifolds; nonlinear operators
43A85 Harmonic analysis on homogeneous spaces
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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[1] I. Amemiya and T. Andô, Convergence of random products of contractions in Hilbert space, Acta Sci. Math. (Szeged) 26 (1965), 239 – 244. · Zbl 0143.16202
[2] W. F. Donoghue, Distributions and Fourier transforms, Academic Press, New York and London, 1969. · Zbl 0188.18102
[3] Émile Durand, Calcul par paires des valeurs propres d’une matrice réelle, Chiffres 3 (1960), 229 – 236 (French, with English, German, and Russian summaries). · Zbl 0099.24705
[4] R. Gordon, R. Bender and G. T. Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography, J. Theoret. Biol. 29 (1970), 471-481.
[5] R. B. Guenther, C. W. Kerber, E. K. Killian, K. T. Smith, and S. L. Wagner, Reconstruction of objects from radiographs and the location of brain tumors, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 4884 – 4886.
[6] C. Hamaker and D. C. Solmon, The angles between the null spaces of Xrays, J. Math. Anal. Appl. 62 (1978), no. 1, 1 – 23. · Zbl 0437.45025 · doi:10.1016/0022-247X(78)90214-7 · doi.org
[7] G. N. Hounsfield, Computerized transverse axial scanning (tomography) I: Description of system, Brit. J. Radiol. 46 (1973), 1016-1022.
[8] Peter D. Lax and Ralph S. Phillips, The Paley-Wiener theorem for the Radon transform, Comm. Pure Appl. Math. 23 (1970), 409 – 424. · Zbl 0189.14803 · doi:10.1002/cpa.3160230311 · doi.org
[9] Donald Ludwig, The Radon transform on euclidean space, Comm. Pure Appl. Math. 19 (1966), 49 – 81. · Zbl 0134.11305 · doi:10.1002/cpa.3160190207 · doi.org
[10] Bernard Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier, Grenoble 6 (1955 – 1956), 271 – 355 (French). · Zbl 0071.09002
[11] R. M. Mersereau and A. V. Oppenheim, Digital reconstruction of multidimensional signals from their projections, Proc. IEEE 62 (1974), 1319-1338.
[12] P. F. J. New and W. R. Scott, Computed tomography of the brain and orbit, Williams and Wilkins, Baltimore, Maryland, 1975.
[13] Kennan T. Smith and Donald C. Solmon, Lower dimensional integrability of \?² functions, J. Math. Anal. Appl. 51 (1975), no. 3, 539 – 549. · Zbl 0308.28004 · doi:10.1016/0022-247X(75)90105-5 · doi.org
[14] K. T. Smith, S. L. Wagner, R. B. Guenther and D. C. Solmon, The diagnosis of breast cancer in mammograms by the evaluation of density patterns, Radiology (to appear).
[15] Donald C. Solmon, The \?-ray transform, J. Math. Anal. Appl. 56 (1976), no. 1, 61 – 83. · Zbl 0334.44007 · doi:10.1016/0022-247X(76)90008-1 · doi.org
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