Optical tomography on graphs

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, approximati...

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Bibliographic Details
Published in:arXiv.org 2016-09
Main Authors: Chung, Francis J, Gilbert, Anna C, Hoskins, Jeremy G, Schotland, John C
Format: Article
Language:English
Subjects:
Algorithms
Graphs
Inverse problems
Tomography
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1609.03041