Smith, Kennan T.; Solmon, Donald C.; Wagner, Sheldon L. Practical and mathematical aspects of the problem of reconstructing objects from radiographs. (English) Zbl 0521.65090 Bull. Am. Math. Soc. 83, 1227-1270 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 91 Documents 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.) Keywords:computerized tomography; mathematical models; CT scanner; Radon transform; line integrals; reconstruction; convergence rates; iterative algorithm; original density; error bounds; noise instability; analytic continuation Citations:Zbl 0381.68079 PDF BibTeX XML Cite \textit{K. T. Smith} et al., Bull. Am. Math. Soc. 83, 1227--1270 (1977; Zbl 0521.65090) Full Text: DOI OpenURL References: [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 [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 [9] Donald Ludwig, The Radon transform on euclidean space, Comm. Pure Appl. Math. 19 (1966), 49 – 81. · Zbl 0134.11305 [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 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.