Workshop on Electromagnetic Inverse Problems
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
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
Multi-scale imaging of defects
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.
Increasing stability in continuation and inverse problems
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.
Electrosensory data acquisition and signal processing strategies in
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.
EIT with partial data
Unfortunately Gunther Uhlmann can no longer come.