Abstract
Radar identification is often based on the study of the so-called resonant frequencies. But no inverse problem can emerge from this since the resonant frequencies do not uniquely determine the obstacle. We propose to consider also the eigenfunctions associated with the resonant frequencies. We first show the uniqueness of our inverse problem: the resonant frequencies and the associated eigenfunctions uniquely determine the obstacle. Then the stability of this problem is shown. Finally some numerical examples of the inversion are given.
This work has been carried out while the author was visiting the University of Delaware, USA.
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References
Angell T., Jiang X., Kleinman R. (1995): On a Numerical Method for Inverse Acoustic Scattering. Technical Report No. 95-9 of Department of Mathematical Sciences, University of Delaware, USA.
Baum C. (1976): The Singularity Expansion Method. In Transient Electromagnetic Fields. Ed. Felsen L. Springer-Verlag, 129–179.
Bushuyev I. (1996): Stability of the Recovering the Near Field Wave from the Scattering Amplitude. preprint of the University of Wichita, USA.
Colton D., Kress R. (1983): Integral Equation Methods in Scattering Theory (Wiley-Interscience Publication).
Colton D., Kress R. (1992): Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin Heidelberg New York).
Gilbarg D., Trudinger N. (1977): Elliptic Partial Differential Equations of Second Order (Springer-Verlag, Berlin).
Grisvard P. (1985): Elliptic Problems in Nonsmooth Domains (Monographs and Studies in Mathematics 24, Pitman, Boston).
Isakov V. (1991): Inverse Source Problems (AMS Mathematical Monographs Series, Number 34, Providence RI).
Isakov V. (1992): Stability Estimates for Obstacles in Inverse Scattering. J. Comp. Appl. Math. 42, 79–88.
Isakov V. (1993): New Stability Results for Soft Obstacles in Inverse Scattering. Inverse Problems 9, 535–543.
Lax P., Philipps R. (1967): Scattering Theory (Academic press).
Lax P., Philipps R. (1969): Decaying Modes for the Wave Equation in the Exterior of an Obstacle. Comm. Pure Appl. Math. 22, 737–787.
Lax P., Philipps R. (1971): On the Scattering Frequencies of the Laplace Operator for the Exterior Domain. Comm. Pure Appl. Math. 25, 85–101.
Melrose R. (1995): Geometric Scattering Theory (Stanford lectures, Cambridge University press).
Poisson O. (1992): Calculs des Pôles Associés à la Diffraction d'Ondes Acoustiques et Élastiques en Dimension 2 (Thesis of the University of Paris IX Dauphine, France).
Zworski M. (1994): Counting Scattering Poles. In Spectral and Scattering Theory. Ed. Ikawa, Marcel Dekker, New York, 301–331.
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© 1997 Springer-Verlag
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Labreuche, C. (1997). Inverse obstacle scattering problem based on resonant frequencies. In: Chavent, G., Sabatier, P.C. (eds) Inverse Problems of Wave Propagation and Diffraction. Lecture Notes in Physics, vol 486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105769
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DOI: https://doi.org/10.1007/BFb0105769
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