On two wavefied-based inverse problems: scatterer shape detection and localization, and material profile reconstruction

Professor Loukas F. Kallivokas
Department of Civil, Architectural and Environmental Engineering
The University of Texas at Austin

Abstract

Abstract: I will discuss a framework for tackling in a systematic way inverse problems in wave-supporting media. Of interest here are two distinct classical problems: a) shape detection and localization of unknown objects, embedded in either full- or half-space, when illuminated by traveling waves; and b) problems involving the reconstruction of the material profile of interrogated structures, with particular focus on the soil. The common framework relies on a governing-equation-constrained optimization approach endowed with problem-specific regularization schemes that have, thus far, allowed for robust performance. The numerical treatment of the resulting first-order optimality conditions is based on both boundary- and finite-element methods. I will discuss the technical details that include problem-specific misfit functional choices, continuation schemes, material differentiation of integrals on evolving shapes, time-dependent regularization, and present numerical results for both the detection and reconstruction problems.

Thursday, May 18, 2006
2 PM, Wu & Chen Auditorium, Levine Hall