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


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.)


Zbl 0381.68079
Full Text: DOI


[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
[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
[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
[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
[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
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