Optical tomography on graphs

Francis J. Chung; Anna C. Gilbert; Jeremy G. Hoskins; John C. Schotland

doi:10.1088/1361-6420/aa66d1

Optical tomography on graphs

Francis J. Chung, Anna C. Gilbert, Jeremy G. Hoskins, John C. Schotland

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Article number	055016
Journal	Inverse Problems
Volume	33
Issue number	5
DOIs	https://doi.org/10.1088/1361-6420/aa66d1
State	Published - Apr 5 2017

Bibliographical note

Publisher Copyright:
© 2017 IOP Publishing Ltd.

Funding

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.

Funders	Funder number
National Science Foundation Arctic Social Science Program	1115574, 0910765, 1108969, 1161233, DMS-1108969, CCF-1161233, CIF-0910765, DMS-1115574, DMS-1619907

Keywords

inverse Born series
optical tomograpy
spectral graph theory

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Mathematical Physics
Computer Science Applications
Applied Mathematics

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10.1088/1361-6420/aa66d1

Cite this

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AU - Hoskins, Jeremy G.

AU - Schotland, John C.

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AB - 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.

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KW - spectral graph theory

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Optical tomography on graphs

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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