Document Zbl 0521.65090

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).

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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

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Full Text: DOI

References:

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[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.
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[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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