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Mathematical Methods in Elasticity Imaging$
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Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

Print publication date: 2015

Print ISBN-13: 9780691165318

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691165318.001.0001

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Optimal Control Imaging of Extended Inclusions

Optimal Control Imaging of Extended Inclusions

(p.148) Chapter Nine Optimal Control Imaging of Extended Inclusions
Mathematical Methods in Elasticity Imaging

Habib Ammari

Elie Bretin

Josselin Garnier

Hyeonbae Kang

Hyundae Lee

Abdul Wahab

Princeton University Press

This chapter describes the use of time-reversal imaging techniques for optimal control of extended inclusions. It first considers the problem of reconstructing shape deformations of an extended elastic target before reconstructing the perturbations from boundary measurements of the displacement field. As for small-volume inclusions, direct imaging algorithms based on an asymptotic expansion for the perturbations in the data due to small shape deformations is introduced. The chapter also presents a concept equivalent to the polarization tensor for small-volume inclusions as well as the nonlinear optimization problem for reconstructing the shape of an extended inclusion from boundary displacement measurements. Finally, it develops iterative algorithms to address the nonlinearity of the problem.

Keywords:   time-reversal imaging, optimal control, extended inclusion, shape deformation, displacement field, small-volume inclusion, direct imaging, asymptotic expansion, nonlinear optimization problem, boundary displacement

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