ABSTRACTS

Workshop on Electromagnetic Inverse Problems
and
10th International Conference on Biomedical Applications of Electrical Impedance Tomography (EIT 2009)
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Here are the titles and abstracts for some of the invited speakers

Aria Abubakar

Nonlinear Imaging and Inversion Approaches for Large-Scale Geophysical Electromagnetic Measurements.

The marine controlled-source electromagnetic (CSEM) technology has attracted much attention for its capability in directly detecting thin hydrocarbon reservoirs. The approach is based on comparing the electric field amplitude as a function of the source-receiver offset with a similar measurement for a non-hydrocarbon bearing reservoir. The presence of hydrocarbon raises the amplitude of the measured electric field indicating the existence and to some degree determining the horizontal extent of the hydrocarbon zone; however with this approach it is difficult to know the reservoir's depth and shape. A more rigorous approach to address this type of application is the full nonlinear inversion. In this presentation we present two rigorous nonlinear inversion algorithms. The first method is the so-called pixel-based inversion (PBI). In this approach the investigation domain is subdivided into pixels, and by using an optimization process the conductivity distribution of the investigated domain is reconstructed. The optimization process uses the Gauss-Newton minimization method augmented with various types of regularization. This PBI approach has demonstrated its ability to retrieve reasonably good conductivity images. However, the reconstructed boundaries and conductivity values of the imaged anomalies are still not adequately resolved. Nevertheless, the PBI approach can provide some useful information on the location, the shape and the conductivity of the hydrocarbon reservoir. The second method is the so-called parametric inversion algorithm (PIA), which uses a priori information on the geometry to reduce the number of unknown parameters and to improve the quality of the reconstructed conductivity image. This PIA approach can be also used to refine the conductivity image that we obtained using the PBI algorithm. The PIA also adopts the Gauss-Newton minimization method. The parameters that govern the location and the shape of an anomaly include the depth and the location of the user-defined nodes for the boundary of the region. The unknown parameter that describes the physical property of the region is the conductivity. We will show some inversion results of synthetic and field data to illustrate the PBI and PIA approaches. We further show that by combining both inversion algorithms we arrive at a better interpretation of the controlled-source electromagnetic data. This work is a joint work with T.M. Habashy, M. Li and J. Liu

Habib Ammari

Multi-scale imaging of defects

Abstract: In this talk we will report our recent findings on imaging small defects from measurements at a single or multiple frequencies. The defect could be an acoustic, an elastic, or an electromagnetic one. Two different kinds of defects will be considered: cracks and inclusions. Our general approach is based on asymptotic formulas for the signature of the defect which remain valid at high frequencies.

Victor Isakov

Increasing stability in continuation and inverse problems

Abstract: We show that the (exponential) instability of the continuation for solutions of Helmholtz type equations is decreasing with growing frequency/energy. We also demonstrate the same effect for recovery of the Schroedinger potential from many boundary measurements in the three dimensional domain. This better stability creates a possibility for better resolution in numerical solution of important inverse problems, in particular with medical applications. We outline proofs based on the Fourier analysis, Carleman estimates, and complex geometrical optics.

Mark Nelson

Electrosensory data acquisition and signal processing strategies in electric fish

Abstract: Certain freshwater electric fish from South America and Africa are able to sense their surroundings by emitting weak electric discharges and detecting the electric field perturbations arising from nearby objects in the water. This ability, referred to as electrolocation, allows weakly electric fish to hunt and navigate in the absence of visual cues at night and in turbid waters. While foraging for small aquatic prey, weakly electric fish are able to detect microvolt-level voltage perturbations, localize potential targets in 3D space, and assess target characteristics such as size, shape and electrical impedance. Here we review the neural and behavioral strategies used by the fish to carry out these challenging information processing tasks.

Gunther Uhlmann

EIT with partial data

Unfortunately Gunther Uhlmann can no longer come.