Inverse reconstruction from optimal input data
(English)Manuscript (Other academic)
This report concerns the problem to find optimal input data for an inverse reconstruction problem. In a classical parameter reconstruction problem the goal is to determine a spacially distributed (and optionally time dependent) coefficient of a partial differential equation from observed data. Here, the spacially dependent wave speed coefficient of the acoustic wave equation is sought, given observations of the solution on the boundary. The reconstruction of the coefficient is highly dependent on input data, e.g. if Neumann boundary values serve as input data it is in general not possible to determine the coefficient for all possible input data. It is shown that it is possible to formulate meaningful optimality criteria for the input data that enhances quality of the reconstructed coefficient. Both the problem of estimating the coefficient and the problem of finding optimal input data are ill-posed inverse problems and need to be regularized.
IdentifiersURN: urn:nbn:se:kth:diva-9378OAI: oai:DiVA.org:kth-9378DiVA: diva2:113752
QC 201007122008-10-272008-10-272010-07-12Bibliographically approved