Abstract
According to T.J. Rivlin (these Proc.) “The problem of optimal recovery is that of approximating as effectively as possible a given map of any function known to belong to a certain class from limited and possibly error-contaminated information about it.” More precisely, in the scheme envisioned by Rivlin there are given spaces X of possible objects, Y of possible data, and Z of possible reconstructions of certain features of the objects.
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References
R. Guenther, C. Kerber, E. Killian, K. Smith, and S. Wagner, “Reconstruction of Objects from Radiographs and the Location of Brain Tumors”, Proc. Natl. Acad. Sci. USA 71: 4884–4886 (1974).
R. Mersereau and A. Oppenheim, “Digital Reconstruction of Multidimensional Signals from their Projections”, Proc. IEEE 62: 1319–1338 (1974).
K. Smith, D. Solmon, and S. Wagner, “Practical and Mathematical Aspects of the Problem of Reconstructing Objects from Radiographs”, Bull. Amer. Math. Soc. (To appear).
K. Smith, S. Wagner, R. Guenther, and D. Solmon, “The Diagnosis of Breast Cancer in Mammograms by the Evaluation of Density Patterns” (To appear).
K. Smith, S. Wagner, R. Guenther, and D. Solmon, “Computerized Axial Tomography from Ordinary Radiographs - An Alternative to Scanners” (To appear).
D. Solmon, K. Smith, S. Wagner, and R. Guenther, “Breast Cancer Diagnosis from Density Studies of Mamograms”, International Conference on Cybernetics and Society, IEEE, November 1–3, 1976, Washington, D. C.
D. Solmon and C. Hamaker, “The Rate of Convergence of the Kacmarz Method”, J. Math. Anal. & Appl. (To appear).
S. Wagner, K. Smith, R. Guenther, and D. Solmon, “Computer Assisted Densitometric Detection of Breast Cancer”, Application of Optical Instrumentation in Medicine V, SPIE 96: 418–422 (1976).
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Smith, K.T., Wagner, S.L., Guenther, R.B., Solmon, D.C. (1977). Reconstruction from X-Rays. In: Micchelli, C.A., Rivlin, T.J. (eds) Optimal Estimation in Approximation Theory. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2388-4_10
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DOI: https://doi.org/10.1007/978-1-4684-2388-4_10
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