Abstract

We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving estimates characterizing the domain of convergence, approximation errors, and stability of our approach. We also present a modification which allows additional information on the structure of the potential to be incorporated, facilitating recovery for a broader class of problems.

Document Type

Article

Publication Date

5-2017

Notes/Citation Information

Published in Inverse Problems, v. 33, no. 5, 055016, p. 1-21.

© 2017 IOP Publishing Ltd

After a 12-month embargo period from the publication of the Version of Record of this article, everyone is permitted to use, copy, and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license: https://creativecommons.org/licences/by-nc-nd/3.0

The document available for download is the authors' post-peer-review final draft of the article.

Digital Object Identifier (DOI)

https://doi.org/10.1088/1361-6420/aa66d1

Funding Information

This work was supported in part by the National Science Foundation grants DMS- 1115574, DMS-1108969 and DMS-1619907 to JCS, and National Science Foundation grants CCF-1161233 and CIF-0910765 to ACG.

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Mathematics Commons

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