Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-25T04:12:37.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse obstacle backscattering problems with phaseless data

Published online by Cambridge University Press:  31 July 2015

JAEMIN SHIN
JAEMIN SHIN*
Affiliation:
Department of Mathematical Sciences, Hanbat National University, Daejeon, Republic of Korea email: jaemin.shin@hanbat.ac.kr
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we provide a numerical algorithm to reconstruct a convex sound-soft scatterer from phaseless backscattering data, assuming sufficiently high frequency. Certain uniqueness and existence results for the case of circular scatterers are given as well, based on the asymptotic expansion for the normal derivative of the total field.

Keywords

Inverse obstacle scatteringbackscatteringphaseless far field patternhigh-frequency
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 1 , February 2016 , pp. 111 - 130
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Colton, D. & Kress, R. (1998) Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[2] Colton, D. & Sleeman, B. D. (1983) Uniqueness theorems for the inverse problem of acoustic scattering. IMA J. Appl. Math. 31 (3), 253–259.CrossRefGoogle Scholar
[3] Domínguez, V., Graham, I. G. & Smyshlyaev, V. P. (2007) A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Numer. Math. 106 (3), 471–510.Google Scholar
[4] Ecevit, F. & Reitich, F. (2009) Analysis of multiple scattering iterations for high-frequency scattering problems. I: The two-dimensional case. Numer. Math. 114 (2), 271–354.CrossRefGoogle Scholar
[5] Hähner, P. & Kress, R. (2000) Uniqueness for a linearized, inverse obstacle problem using backscattering data. In: Proceedings of the Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation (Santiago de Compostela, 2000), SIAM, Philadelphia, PA, pp. 488–493.Google Scholar
[6] Ivanyshyn, O. (2007) Shape reconstruction of acoustic obstacles from the modulus of the far field pattern. Inverse Probl. Imaging. 1 (4), 609–622.Google Scholar
[7] Ivanyshyn, O. & Kress, R. (2010) Identification of sound-soft 3D obstacles from phaseless data. Inverse Probl. Imaging. 4 (1), 131–149.Google Scholar
[8] Kirsch, A. (1993) The domain derivative and two applications in inverse scattering theory. Inverse Problems. 9 (1), 81–96.Google Scholar
[9] Kress, R. & Rundell, W. (1997) Inverse obstacle scattering with modulus of the far field pattern as data. In: Inverse Problems in Medical Imaging and Nondestructive Testing (Oberwolfach, 1996), Springer, Vienna, pp. 75–92.Google Scholar
[10] Kress, R. & Rundell, W. (1999) Inverse obstacle scattering using reduced data. SIAM J. Appl. Math. 59 (2), 442–454 (electronic).Google Scholar
[11] Liu, X. & Zhang, B. (2010) Unique determination of a sound-soft ball by the modulus of a single far field datum. J. Math. Anal. Appl. 365 (2), 619–624.CrossRefGoogle Scholar
[12] Majda, A. (1976) High frequency asymptotics for the scattering matrix and the inverse problem of acoustical scattering. Comm. Pure Appl. Math. 29 (3), 261–291.Google Scholar
[13] Melrose, R. B. & Taylor, M. E. (1985) Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle. Adv. Math. 55 (3), 242–315.Google Scholar
[14] Potthast, R. (1994) Fréchet differentiability of boundary integral operators in inverse acoustic scattering. Inverse Problems. 10 (2), 431–447.Google Scholar
[15] Wong, R. (1989) Asymptotic Approximations of Integrals, Computer Science and Scientific Computing. Academic Press Inc., Boston, MA.Google Scholar