Reconstruction of shapes and refractive indices from backscattering experimental data using the adaptivity

Larisa Beilina, Nguyen Trung Thành, Michael V. Klibanov, John Bondestam Malmberg

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant εr (x), x ∈ R3, which is an unknown coefficient in the Maxwell's equations, from time-dependent backscattering experimental radar data associated with a single source of electric pulses. The refractive index is n (x) = √εr (x). The coefficient εr (x) is reconstructed using a twostage reconstruction procedure. In the first stage an approximately globally convergent method proposed is applied to get a good first approximation of the exact solution. In the second stage a locally convergent adaptive finite element method is applied, taking the solution of the first stage as the starting point of the minimization of the Tikhonov functional. This functional is minimized on a sequence of locally refined meshes. It is shown here that all three components of interest of targets can be simultaneously accurately imaged: refractive indices, shapes and locations.

Original languageEnglish (US)
Article number105007
JournalInverse Problems
Issue number10
StatePublished - Oct 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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