Lipschitz stability estimates for translations and balls in inverse scattering

Ohin Kwon, Jin Keun Seo

Research output: Contribution to journalConference article

6 Citations (Scopus)

Abstract

We consider the inverse scattering problem for the Helmholtz equation determining the unknown sound-soft obstacle for a fixed wavenumber k > 0. The far-field pattern for the translation of a connected bounded obstacle is represented for the one fixed reference obstacle. Using this representation, we establish Lipschitz stability of the recovery of the translated location from knowledge of the far-field pattern for one incident plane wave. Lipschitz stability estimates for balls in ℝ3 are also obtained from two incident plane waves and far-field patterns.

Original languageEnglish
Pages (from-to)293-301
Number of pages9
JournalInverse Problems
Volume16
Issue number2
DOIs
Publication statusPublished - 2000 Apr 1
Event1st World Congress on Industrial Process Tomography - Buxton, United Kingdom
Duration: 1999 Apr 141999 Apr 17

Fingerprint

Lipschitz Stability
Far-field Pattern
Stability Estimates
Inverse Scattering
inverse scattering
far fields
balls
Ball
Scattering
Plane Wave
Helmholtz equation
plane waves
estimates
Helmholtz equations
Inverse Scattering Problem
Acoustic waves
Helmholtz Equation
Recovery
recovery
Unknown

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Cite this

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Lipschitz stability estimates for translations and balls in inverse scattering. / Kwon, Ohin; Seo, Jin Keun.

In: Inverse Problems, Vol. 16, No. 2, 01.04.2000, p. 293-301.

Research output: Contribution to journalConference article

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AU - Seo, Jin Keun

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N2 - We consider the inverse scattering problem for the Helmholtz equation determining the unknown sound-soft obstacle for a fixed wavenumber k > 0. The far-field pattern for the translation of a connected bounded obstacle is represented for the one fixed reference obstacle. Using this representation, we establish Lipschitz stability of the recovery of the translated location from knowledge of the far-field pattern for one incident plane wave. Lipschitz stability estimates for balls in ℝ3 are also obtained from two incident plane waves and far-field patterns.

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