We present a new differential factorization method to recover local perturbations in a periodic layered media. This method provides an indicator function of the support of a perturbation without using any model for the healthy periodic layer. Essential to this type of imaging approach is that the scattering (measurement) operator is injective. In other words, it is important to know whether there is an incident wave that does not scatter by the unknown inhomogeneity. Until recently this question was largely open. We will present some recent developments in this direction. Parts of this presentation are based on joint works with H. Haddar and TP. Nguyen, and with M. Vogelius.
Fast Imaging of Local Perturbations in Periodic Layers: Some Remarks on Non-scattering Waves*
Fioralba Cakoni, Rutgers Universith, New BrunswickAuthors: Fioralba Cakoni
2022 AWM Research Symposium
Recent Advancements in Inverse Problems and Imaging