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We endow the inhomogeneous wave equation with time-dependent parameters and consider the task of reconstructing these parameters from the wave field. This dynamic inverse problem is more involved compared to static parameters. We give existence and uniqueness results for the equation and compute the Fréchet derivative of the solution operator, for which we also show ill-posedness. These results motivate the numerical reconstruction using regularized Newton-like methods.
This presentation is part of Minisymposium “MS6 - Time-dependent problems in imaging (2 parts)”
organized by: Thomas Schuster (Saarland University) , Anne Wald (Saarland University) .