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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
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.