Near-field imaging of obstacles

Peijun Li*, Yuliang WANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

A novel method is developed for solving the inverse obstacle scattering problem in near-field imaging. The obstacle surface is assumed to be a small and smooth deformation of a circle. Using the transformed field expansion, the direct obstacle scattering problem is reduced to a successive sequence of two-point boundary value problems. Analytical solutions of these problems are derived by a Green's function method. The nonlinear inverse problem is linearized by dropping the higher order terms in the power series expansion. Based on the linear model and analytical solutions, an explicit reconstruction formula is obtained. In addition, a nonlinear correction scheme is devised to improve the results dramatically when the deformation is large. The method requires only a single incident wave at a fixed frequency. Numerical tests show that the method is stable and effective for near-field imaging of obstacles with subwavelength resolution.

Original languageEnglish
Pages (from-to)189-210
Number of pages22
JournalInverse Problems and Imaging
Volume9
Issue number1
DOIs
Publication statusPublished - 2015

Scopus Subject Areas

  • Analysis
  • Modelling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

User-Defined Keywords

  • Inverse obstacle scattering
  • Near-field imaging
  • Transformed field expansion

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