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References
Angell, T.S., Colton, D., Kirsch, A.: The three dimensional inverse scattering problem for acoustic waves. J. Diff. Equations 46 (1982) 46–58
Angell, T.S., Kleinman, R.E., Kok, B., Roach, G.F.: A constructive method for identification of an impenetrable scatterer. Wave Motion 11 (1989) 185–200
Angell, T.S., Kleinman, R.E., Kok, B., Roach, G.F.: Target reconstruction from scattered far field data. Ann. des Télécommunications 44 (1989) 456–463
Angell, T.S., Kleinman, R.E., Roach, G.F.: An inverse transmission problem for the Helmholtz equation. Inverse Problems 3 (1987) 149–180
Blöhbaum, J.: Optimisation methods for an inverse problem with time-harmonic electromagnetic waves: an inverse problem in electromagnetic scattering. Inverse Problems 5 (1989) 463–482
Colton, D., Kress, R.: Integral Equation Methods in Scattering Theory. Wiley, New York (1983)
Colton, D., Monk, P.: A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region. SIAM J. Appl. Math. 45 (1985) 1039–1053
Colton, D., Monk, P.: A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region II. SIAM J. Appl. Math. 46 (1986) 506–523
Colton, D., Monk, P.: The numerical solution of the three dimensional inverse scattering problem for time-harmonic acoustic waves. SIAM J. Sci. Stat. Comp. 8 (1987) 278–291
Colton, D., Sleeman, B.D.: Uniqueness theorems for the inverse problem of acoustic scattering. IMA J. Appl. Math. 31 (1983) 253–259
Jones, D.S.: Note on a uniqueness theorem of Schiffer. Applicable Analysis 19 (1985) 181–188
Jones, D.S., Mao, X.Q.: The inverse problem in hard acoustic scattering. Inverse Problems 5 (1989) 731–748
Kirsch, A., Kress, R.: On an integral equation the first kind in inverse acoustic scattering. In: Inverse Problems. (Cannon, Hornug eds.) ISNM 77 (1986) 93–102
Kirsch, A., Kress, R.: A numerical method for an inverse scattering problem. In: Inverse Problems (Engl, Groetsch eds.), Academic Press, (1987) 279–290
Kirsch, A., Kress, R.: An optimization method in inverse acoustic scattering. In: Boundary elements IX, Vol 3. Fluid Flow and Potential Applications (Brebbia, Wendland and Kuhn, eds). Springer-Verlag, Heidelberg, (1987) 3–18
Kirsch, A., Kress, R., Monk, P., Zinn, A.: Two methods for solving the inverse acoustic scattering problem. Inverse Problems 4 (1988) 749–770
Kress, R.: Linear Integral Equations. Springer-Verlag, New York (1989)
Kristensson, G., Vogel, C.R.: Inverse problems for acoustic waves using the penalised likelihood method. Inverse Problems 2 (1986) 461–479
Murch, R.D., Tan, D.G.H., Wall, D.J.N.: Newton-Kantorovich method applied to two-dimensional inverse scattering for an exterior Helmholtz problem. Inverse Problems 4 (1988) 1117–1128
Ochs, R.L.: The limited aperture problem of inverse scattering: Dirichlet boundary conditions. SIAM J. Appl. Math. 6 (1987) 1320–1341
Onishi, K.: Numerical methods for inverse scattering problems in two-dimensional scalar field. (to appear)
Pironneau, O.: Optimal shape design for elliptic systems. Springer-Verlag, New York (1984)
Roger, A.: Newton Kantorovitch algorithm applied to an electromagnetic inverse problem. IEEE Trans. Ant. Prop. AP-29 (1981) 232–238
Wang, S.L., Chen, Y.M.: An efficient numerical method for exterior and interior inverse problems of Helmholtz equation. (to appear)
Wienert, L.: Die numerische Approximation von Randintegraloperatoren für die Helmholtzgleichung im ℝ3. Dissertation, Göttingen (1990)
Zinn, A.: On an optimisation method for the full-and limited-aperture problem in inverse acoustic scattering for a sound-soft obstacle. Inverse Problems 5 (1989) 239–253
Zinn, A.: Ein Rekonstruktionsverfahren für ein inverses Streuproblem bei der zeitharmonischen Wellengleichung. Dissertation, Göttingen (1990)
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Kress, R., Zinn, A. (1991). Three dimensional reconstructions in inverse obstacle scattering. 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/BFb0084512
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DOI: https://doi.org/10.1007/BFb0084512
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