A numerical method to solve a phaseless coefficient inverse problem from a single measurement of experimental data

Michael V. Klibanov, Nikolay A. Koshev, Dinh Liem Nguyen, Loc H. Nguyen, Aaron Brettin, Vasily N. Astratov

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

The goal of this paper is to develop a globally convergent numerical method for the inverse problem which would work with the optical experimental data collected by this research group. Only the intensity (modulus square) of the total complex valued wave field is measured at an array of light detectors located on a measurement plane. The phase is not measured. We solve numerically the phaseless coefficient inverse problem to reconstruct locations and refractive indices of unknown scatterers from those measurements. Our method consists of two stages. In the first stage, we obtain an upper estimate for the modulus of the scattered wave field. This estimate allows us to approximately reconstruct the wave field at the measurement plane using a resulting inversion formula. This reduces the phaseless inverse scattering problem to the phased one. In the second stage, we apply a recently developed globally convergent numerical method to reconstruct the desired refractive index from the total wave obtained at the first stage. Unlike the optimization approach, our two-stage numerical method is global in the sense that it does not require a good initial guess of the true solution. A significant part of this work is devoted to testing our numerical method on both computationally simulated and experimental data.

Original languageEnglish
Pages (from-to)2339-2367
Number of pages29
JournalSIAM Journal on Imaging Sciences
Volume11
Issue number4
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • New numerical method
  • Numerical reconstructions
  • Optical experimental data
  • Phased coefficient inverse problem
  • Phaseless coefficient inverse problem
  • Single measurement

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