Fast imaging of local perturbations in a unknown bi-periodic layered medium

Fioralba Cakoni, Houssem Haddar, Thi Phong Nguyen

Research output: Contribution to journalArticlepeer-review


We discuss a novel approach for imaging local faults inside an infinite bi-periodic layered medium in R3 using acoustic measurements of scattered fields at the bottom or the top of the layer. The faulted area is represented by compactly supported perturbations with erroneous material properties. Our method reconstructs the support of perturbations without knowing or reconstructing the constitutive material parameters of healthy or faulty bi-period layer; only the size of the period is needed. This approach falls under the class of non-iterative imaging methods, known as the generalized linear sampling method with differential measurements, first introduced in [2] and adapted to periodic layers in [25]. The advantage of applying differential measurements to our inverse problem is that instead of comparing the measured data against measurements due to healthy structures, one makes use of periodicity of the layer where the data operator restricted to single Floquet-Bloch modes plays the role of the one corresponding to healthy material. This leads to a computationally efficient and mathematically rigorous reconstruction algorithm. We present numerical experiments that confirm the viability of the approach for various configurations of defects.

Original languageEnglish (US)
Article number112773
JournalJournal of Computational Physics
StatePublished - Mar 15 2024

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Differential imaging
  • Fast reconstruction methods
  • Infinite bi-periodic layered medium
  • Inverse scattering problem
  • Local perturbations


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