Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation
Barbara Kaltenbacher,
Anna Schlintl
Abstract:In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze a time stepping method for the numerical solution of the corresponding forward problem. Moreover, to efficiently obtain reconstructions by minimizing a Tikhonov regularization functional (or alternatively, by computing the MAP estimator in a Bayesian approach), we develop a… Show more
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