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Computed tomography and rockets

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Mathematical Methods in Tomography

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1497))

The author was partially supported by NSF grant MCS 8901203. The author is indebted to Paul Burstein of Skiametrics for much support and practical information including pointing out the application to large rocket motors, suggesting appropriate phantoms to test and appropriate amount of data to take, as well as useful comments to the manuscript. The author thanks Charles Dunkl for the suggestion to use Cesaro summability to help get rid of Gibbs phenomenon in polynomial sums. The author is indebted to the Institut für Numerische und instrumentelle Mathematik der Üniversitat Münster for the display programs for figures 1 and 2, to Tufts University undergraduate Scott Turner for his help testing the algorithm, as well as to Peter Maass for clever suggestions about the algorithm and display programs.

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References

  • M. D. Altschuler 1979, Reconstruction of the global-scale three-dimensional solar corona, in “Image Reconstruction from Projections, Implementation and Applications” (G. T. Herman, Ed.), pp. 105–145, Topics in Applied Physics, Vol. 32, Springer-Verlag, New York/Berlin.

    Chapter  Google Scholar 

  • P. Burstein 1989, private communication.

    Google Scholar 

  • A. M. Cormack 1963, Representation of a function by its line integrals with some radiological applications, J. Appl. Phys. 34, 2722–2727.

    Article  Google Scholar 

  • A. M. Cormack 1964, Representation of a function by its line integrals with some radiological applications, II J. Appl. Phys. 35, 2908–2913

    Article  Google Scholar 

  • M. Davison 1983, The ill-conditioned nature of the limited angle tomography problem, SIAM J. Appl. Math., 43, 428–448.

    Article  Google Scholar 

  • D. V. Finch 1985, Cone beam reconstruction with sources on a curve, SIAM J. Appl. Math. 45, 665–673.

    Article  Google Scholar 

  • R. M. Lewitt 1988, Overview of inversion methods used in computed tomography, in Advances in Remote Sensing Retrieval Methods, Deepak Publishing, Hampton, VA.

    Google Scholar 

  • R. M. Lewitt and R. H. T. Bates 1978, Image reconstruction from projections. II, Projection completion methods (theory), Optik 50, 189–204, III: Projection completion methods (computational examples), Optik 50, 269–278.

    Google Scholar 

  • A. Louis 1986, Incomplete data problems in X-ray computerized tomography 1. Singular value decomposition of the limited angle transform, Numer. Math. 48, 251–262.

    Article  Google Scholar 

  • A. Louis 1988, private communication.

    Google Scholar 

  • A. Louis 1989, Incomplete data problems in X-ray computerized tomography 2. truncated projections and region-of-interest tomography, Numer. Math. 56, 371–383.

    Article  Google Scholar 

  • P. Maass 1990, The interior Radon transform, submitted.

    Google Scholar 

  • F. Natterer 1980, Efficient implementation of “optimal” algorithms in computerized tomography, Math. Meth. Appl. Sci. 2, 545–555.

    Article  Google Scholar 

  • R. M. Perry 1977, On reconstruction a function on the exterior of a disc from its Radon transform, J. Math. Anal. Appl. 59, 324–341.

    Article  Google Scholar 

  • E. T. Quinto 1980, The dependence of the generalized Radon transform on defining measures, Trans. Amer. Math. Soc. 257, 331–346.

    Article  Google Scholar 

  • E. T. Quinto 1983, The invertibility of rotation invariant Radon transforms, J. Math. Anal. Appl. 91, 510–522.

    Article  Google Scholar 

  • E. T. Quinto 1988, Tomographic reconstructions from incomplete data-numerical inversion of the exterior Radon transform., Inverse Problems 4, 867–876.

    Article  Google Scholar 

  • E. T. Quinto 1990, Limited data tomography in non-destructive evaluation, Signal Processing Part II: Control Theory and Applications, IMA Volumes in Mathematics and its Applications, Vol. 23, 347–354, Springer-Verlag 1990.

    Google Scholar 

  • R. J. Schneider, P. Burstein, F. H. Seguin, and A. S. Kreiger 1986, High-spacial-resolution computed tomography for thin annular geometries, Review of progress in qualitative non-destructive evaluation, Vol. 5a, Donald O. Thompson and Dale E. Chimenti editors, Plenum Press.

    Google Scholar 

  • L. A. Shepp and J. B. Kruskal 1978, Computerized tomography: The new medical X-ray technology, Amer. Math. Monthly 85, 420–439.

    Article  Google Scholar 

  • L. A. Shepp and S. Srivastava 1986, Computed tomography of PKM and AKM exit cones, A. T & T. Technical Journal, 65, 78–88.

    Article  Google Scholar 

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© 1991 Springer-Verlag Berlin Heidelberg

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Quinto, E.T. (1991). Computed tomography and rockets. In: Herman, G.T., Louis, A.K., Natterer, F. (eds) Mathematical Methods in Tomography. Lecture Notes in Mathematics, vol 1497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084523

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  • DOI: https://doi.org/10.1007/BFb0084523

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  • Print ISBN: 978-3-540-54970-3

  • Online ISBN: 978-3-540-46615-4

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