Practical and mathematical aspects of the problem of reconstructing objects from radiographs

Smith, Kennan T.; Solmon, Donald C.; Wagner, Sheldon L.

doi:10.1090/S0002-9904-1977-14406-6

Authors: Kennan T. Smith, Donald C. Solmon and Sheldon L. Wagner
Journal: Bull. Amer. Math. Soc. 83 (1977), 1227-1270
MSC (1970): Primary 92A05, 78A55; Secondary 44A15
DOI: https://doi.org/10.1090/S0002-9904-1977-14406-6
Addendum: Bull. Amer. Math. Soc., Volume 84, Number 4 (1978), 691--691
MathSciNet review: 0490032
Full-text PDF Free Access

1. I. Amemiya and T. Andô, Convergence of random products of contractions in Hilbert space, Acta Sci. Math. (Szeged) 26 (1965), 239–244. MR 187116
2. W. F. Donoghue, Distributions and Fourier transforms, Academic Press, New York and London, 1969.
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). MR 137722
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. MR 354065, https://doi.org/10.1073/pnas.71.12.4884
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. MR 463859, https://doi.org/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. MR 273309, https://doi.org/10.1002/cpa.3160230311
9. Donald Ludwig, The Radon transform on euclidean space, Comm. Pure Appl. Math. 19 (1966), 49–81. MR 190652, https://doi.org/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). MR 0086990
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 𝐿² functions, J. Math. Anal. Appl. 51 (1975), no. 3, 539–549. MR 377496, https://doi.org/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 𝑋-ray transform, J. Math. Anal. Appl. 56 (1976), no. 1, 61–83. MR 481961, https://doi.org/10.1016/0022-247X(76)90008-1