Inverse Problems for Material Characterization Using Thermoacoustic ImagingKyle Hickmann
Department of Mathematics, Tulane University
Friday, November 16, 2012 15:00-16:00,
Thermoacoustic tomography is an imaging modality used to recover electromagnetic properties of a material sample. As a hybrid imaging method it combines the electromagnetic illumination of a body using microwave frequencies with a measurement of the induced ultrasound fields. The advantage of this approach is to combine the large contrast properties of electromagnetic imaging with the high resolution properties of ultrasound imaging. We will present several variations for the mathematical model. These will start with the simple case of a body with constant acoustic properties in the interior. Models of increasing complexity will then be introduced, ending with the case of a heterogeneous elastic body with cubic anisotropy. Our results deal with the feasibility of thermoacoustic imaging when the interior acoustic properties are unknown or known only imprecisely. Methods using a Bayesian approach for statistical surrogate modelling are presented to quantify the uncertainty introduced from the unknown interior acoustic properties.
Speaker Bio: Dr. Hickmann received his Doctorate in Mathematics from Oregon State University in June 2010. His research has focused on inverse problems for hyperbolic systems of equations related to elastic media. The techniques used in his work have been variational methods for partial differential equations and microlocal analysis. He is currently a Postdoctoral researcher in the mathematics department at Tulane University where he is working on developing uncertainty quantification methods for stochastic models of epidemics in large populations.
Contact: J. T. Fong
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