Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation

04/12/2021 ∙ by Barbara Kaltenbacher, et al. ∙ 0

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 an adjoint based scheme for gradient computation. Numerical reconstructions in two space dimensions illustrate the performance of the devised methods.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 6

page 8

page 19

page 20

page 21

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.