Korpela, J;
Lassas, M;
Oksanen, L;
(2016)
Regularization strategy for an inverse problem for a 1+1 dimensional wave equation.
Inverse Problems
, 32
(6)
, Article 065001. 10.1088/0266-5611/32/6/065001.
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Abstract
An inverse boundary value problem for a 1 + 1 dimensional wave equation with a wave speed c(x) is considered. We give a regularization strategy for inverting the map where Λ is the hyperbolic Neumann-to-Dirichlet map corresponding to the wave speed c. That is, we consider the case when we are given a perturbation of the Neumann-to-Dirichlet map, where corresponds to the measurement errors, and reconstruct an approximative wave speed. We emphasize that may not be in the range of the map. We show that the reconstructed wave speed satisfies. Our regularization strategy is based on a new formula to compute c from Λ.
| Type: | Article |
|---|---|
| Title: | Regularization strategy for an inverse problem for a 1+1 dimensional wave equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/0266-5611/32/6/065001 |
| Publisher version: | http://doi.org/10.1088/0266-5611/32/6/065001 |
| Language: | English |
| Additional information: | Copyright © 2016 IOP Publishing Ltd. All rights reserved. This is an author-created, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0266-5611/32/6/065001. |
| Keywords: | Inverse problem, regularization theory, wave equation |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1508485 |
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