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.

Detection of small buried objects: asymptotic factorization and MUSIC

In this work, we consider a simple model problem for the electromagnetic exploration of small perfectly conducting objects buried within the lower halfspace of an unbounded two–layered background medium. In possible applications, such as, e.g., humanitarian demining, the two layers would correspond to air and soil. Moving a set of electric devices parallel to the surface of ground to generate a time–harmonic field, the induced field is measured within the same devices. The goal is to retrieve information about buried scatterers from these data. In mathematical terms, we are concerned with the analysis and numerical solution of the inverse scattering problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two–layered background medium from near field measurements of time–harmonic electromagnetic waves. For this purpose, we first study the corresponding direct scattering problem in detail and derive an asymptotic expansion of the scattered field as the size of the scatterers tends to zero. Then, we use this expansion to justify a noniterative MUSIC–type reconstruction method for the solution of the inverse scattering problem. We propose a numerical implementation of this reconstruction method and provide a series of numerical experiments.

Stimulus-induced gamma activity in the electrocorticogram of freely moving telemetric implanted rats: the neuronal signature of novelty detection

During this thesis a new telemetric recording system has been developed allowing ECoG/EEG recordings in freely behaving rodents (Lapray et al., 2008; Lapray et al., in press). This unit has been shown to not generate any discomfort in the implanted animals and to allow recordings in a wide range of environments. In the second part of this work the developed technique has been used to investigate what cortical activity was related to the process of novelty detection in rats’ barrel cortex. We showed that the detection of a novel object is accompanied in the barrel cortex by a transient burst of activity in the γ frequency range (40-47 Hz) around 200 ms after the whiskers contact with the object (Lapray et al., accepted). This activity was associated to a decrease in the lower range of γ frequencies (30-37 Hz). This network activity may represent the optimal oscillatory pattern for the propagation and storage of new information in memory related structures. The frequency as well as the timing of appearance correspond well with other studies concerning novelty detection related burst of activity in other sensory systems (Barcelo et al., 2006; Haenschel et al., 2000; Ranganath & Rainer, 2003). Here, the burst of activity is well suited to induce plastic and long-lasting modifications in neuronal circuits (Harris et al., 2003). The debate is still open whether synchronised activity in the brain is a part of information processing or an epiphenomenon (Shadlen & Movshon, 1999; Singer, 1999). The present work provides further evidence that neuronal network activity in the γ frequency range plays an important role in the neocortical processing of sensory stimuli and in higher cognitive functions.