Download PDF by Ibrahim Akduman, Jan Grochmalicki, Roy Pike (auth.), Prof.: Inverse Problems in Medical Imaging and Nondestructive

By Ibrahim Akduman, Jan Grochmalicki, Roy Pike (auth.), Prof. Dr. Heinz W. Engl, Prof. Dr. Alfred K. Louis, Prof. Dr. William Rundell (eds.)

14 contributions current mathematical types for various imaging options in drugs and nondestructive checking out. The underlying mathematical versions are awarded in a fashion that still beginners within the box have an opportunity to appreciate the relation among the specific purposes and the maths wanted for effectively treating those difficulties. The reader will get an perception right into a glossy box of medical computing with functions previously no longer offered in such shape, best from the fundamentals to genuine study activities.

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Read Online or Download Inverse Problems in Medical Imaging and Nondestructive Testing: Proceedings of the Conference in Oberwolfach, Federal Republic of Germany, February 4–10, 1996 PDF

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Extra info for Inverse Problems in Medical Imaging and Nondestructive Testing: Proceedings of the Conference in Oberwolfach, Federal Republic of Germany, February 4–10, 1996

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H. , Constructive Methods for the Practical Treatment of Integral Equations, Birkhiiuser, Basel, 1985, 234-243. 63. T. R. VOGEL, Well posedness and convergence for some regularisation methods for non-linear ill posed problems, Inverse Problems 5 (1989), 227-238. 64. N. A. ARSENIN, Methods for Solving Ill-Posed Problems, Nauka, Moscow, 1979. 65. M. Y. VETERENNIKOV, Iteration Procedures in Ill-Posed Problems, Nauka, Moscow, 1986. In Russian. 66. V. V. VASIN, Iterative methods for solving ill-posed problems with a priori information in Hilbert spaces, USSR Comput.

34 32. M. HANKE, A. NEUBAUER, AND O. SCHERZER, A convergence analysis of the Landweber iteration for nonlinear ill-posed problems, Numer. Math. 72 (1995), 21-37. 33. F. HETTLICH, J. MORGAN, O. SCHERZER, On the estimation of interfaces from boundary measurements, to appear in: Proceedings of the SIAM conference "Symposion on Inverse Problems: Geophysical Applications", Yosemite, USA 1995. 34. B. HOFMANN AND O. SCHERZER, Influence factors of ill-posedness for nonlinear problems, Inverse Problems 10 (1994), 1277-1297.

The second problem we will address is that of determining an estimate of the magnitude of the index of refraction from a knowledge of U oo or, more specifically, from a knowledge of the eigenvalues of the far field operator F : L2(il) --+ L2(il) defined by (Fg) (:e) := I uoo(:ej d)g(d)ds(d). (6) n Finally, we will show how the support of m = 1- n can be determined by solving the set of linear integral equations of the first kind (Fg)(:e) = e- iU ' 1Io (7) where Yo is on a rectangular grid known a priori to contain the support of m in its interior.

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