Optimal Control Imaging of Extended Inclusions
Optimal Control Imaging of Extended Inclusions
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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