Convergence analysis in near-field imaging for elastic waves

Peijun Li*, Yuliang WANG, Yue Zhao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

A significant method has recently been developed for solving the inverse elastic surface scattering problem which arises from near-field imaging applications. The method utilizes the transformed field expansion along with the Fourier series expansion to deduce an analytic solution for the direct problem. Implemented via the fast Fourier transform, an explicit reconstruction formula is obtained to solve the linearized inverse problem. Numerical examples show that the method is efficient and effective to reconstruct scattering surfaces with subwavelength resolution. This paper is devoted to the mathematical analysis of the proposed method. The well-posedness is established for the solution of the direct problem. The convergence of the power series solution is examined. A local uniqueness result is proved for the inverse problem where a single incident field with a fixed frequency is needed. The error estimate is derived for the reconstruction formula. It provides a deep insight on the trade-off among resolution, accuracy, and stability of the solution for the inverse problem.

Original languageEnglish
Pages (from-to)2339-2360
Number of pages22
JournalApplicable Analysis
Volume95
Issue number11
DOIs
Publication statusPublished - 1 Nov 2016

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • convergence analysis
  • error estimate
  • Inverse elastic scattering
  • near-field imaging

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