Regularity and Stability for the Scattering Map of a Linearized Inverse Medium Problem

Gang Bao; Yu Chen; Fuming Ma

doi:10.1006/jmaa.2000.6856

Regularity and Stability for the Scattering Map of a Linearized Inverse Medium Problem

Gang Bao, Yu Chen, Fuming Ma

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The main goal of this paper is to study the linearization of an inverse medium problem. Regularity and stability results are established for the near-field scattering map (or scattering matrix) which maps the scatterer to the scattered field. Properties on continuity and Fréchet differentiability of the scattering map are examined. A lower bound of the linearized scattering map is obtained, which in particular characterizes the stability properties. These results are useful in the analysis of the nonlinear inverse scattering problem.

Original language	English (US)
Pages (from-to)	255-271
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	247
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.2000.6856
State	Published - Jul 1 2000

Keywords

Inverse scattering; Helmholtz equation; linearization; regularity; stability

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jmaa.2000.6856

Cite this

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title = "Regularity and Stability for the Scattering Map of a Linearized Inverse Medium Problem",

abstract = "The main goal of this paper is to study the linearization of an inverse medium problem. Regularity and stability results are established for the near-field scattering map (or scattering matrix) which maps the scatterer to the scattered field. Properties on continuity and Fr{\'e}chet differentiability of the scattering map are examined. A lower bound of the linearized scattering map is obtained, which in particular characterizes the stability properties. These results are useful in the analysis of the nonlinear inverse scattering problem.",

keywords = "Inverse scattering; Helmholtz equation; linearization; regularity; stability",

author = "Gang Bao and Yu Chen and Fuming Ma",

note = "Funding Information: The research of G. Bao was partially supported by the NSF Grant DMS 98-03604, the NSF University-Industry Cooperative Research Programs Grant DMS 98-03809, DMS 99-72292, the NSF Western Europe Programs Grant INT 98-15798, and the ONR Grant N00014-00-1-0299. The research of Y. Chen was partially funded by the ONR Grant N00014-98-1-0514. The research of F. Ma was supported in part by the China State Major Key Project for Basic Research.",

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doi = "10.1006/jmaa.2000.6856",

language = "English (US)",

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AU - Bao, Gang

AU - Chen, Yu

AU - Ma, Fuming

N1 - Funding Information: The research of G. Bao was partially supported by the NSF Grant DMS 98-03604, the NSF University-Industry Cooperative Research Programs Grant DMS 98-03809, DMS 99-72292, the NSF Western Europe Programs Grant INT 98-15798, and the ONR Grant N00014-00-1-0299. The research of Y. Chen was partially funded by the ONR Grant N00014-98-1-0514. The research of F. Ma was supported in part by the China State Major Key Project for Basic Research.

PY - 2000/7/1

Y1 - 2000/7/1

N2 - The main goal of this paper is to study the linearization of an inverse medium problem. Regularity and stability results are established for the near-field scattering map (or scattering matrix) which maps the scatterer to the scattered field. Properties on continuity and Fréchet differentiability of the scattering map are examined. A lower bound of the linearized scattering map is obtained, which in particular characterizes the stability properties. These results are useful in the analysis of the nonlinear inverse scattering problem.

AB - The main goal of this paper is to study the linearization of an inverse medium problem. Regularity and stability results are established for the near-field scattering map (or scattering matrix) which maps the scatterer to the scattered field. Properties on continuity and Fréchet differentiability of the scattering map are examined. A lower bound of the linearized scattering map is obtained, which in particular characterizes the stability properties. These results are useful in the analysis of the nonlinear inverse scattering problem.

KW - Inverse scattering; Helmholtz equation; linearization; regularity; stability

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JO - Journal of Mathematical Analysis and Applications

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Regularity and Stability for the Scattering Map of a Linearized Inverse Medium Problem

Abstract

Keywords

ASJC Scopus subject areas

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