Sampling methods for low-frequency electromagnetic imaging

For the detection of hidden objects by low-frequency electromagnetic imaging the Linear Sampling Method works remarkably well despite the fact that the rigorous mathematical justification is still incomplete. In this work, we give an explanation for this good performance by showing that in the low-frequency limit the measurement operator fulfills the assumptions for the fully justified variant of the Linear Sampling Method, the so-called Factorization Method. We also show how the method has to be modified in the physically relevant case of electromagnetic imaging with divergence-free currents. We present numerical results to illustrate our findings, and to show that similar performance can be expected for the case of conducting objects and layered backgrounds

A sampling method for detecting buried objects using electromagnetic scattering

We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scattering theory for this particular set-up

Mathematisches Forschungsinstitut Oberwolfach Report No. 13/2007 Inverse Problems in Wave Scattering

Abstract. The workshop treated inverse problems for partial differential equations, especially inverse scattering problems, and their applications in technology. While special attention was paid to sampling methods, decomposition methods, Newton methods and questions of unique determination were also investigated. Mathematics Subject Classification (2000): 14Q05, 35Rxx, 65Jxx, 65N21, 74Jxx, 78Axx. Introduction by the Organisers Since this was only a “half workshop”, the organisers intended to focus on a relatively small number of topics. We selected scattering from an obstacle and with primarily the Maxwell equations as the underlying structure. We also wanted to concentrate on analytic methods where questions of uniqueness and (if appropriate