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

9 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.

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

Access to Document

10.1088/1361-6420/aa66d1

Cite this

@article{bf39df45b33d4780ac0d093fe83ee8a3,

title = "Optical tomography on graphs",

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.",

keywords = "inverse Born series, optical tomograpy, spectral graph theory",

author = "Chung, {Francis J.} and Gilbert, {Anna C.} and Hoskins, {Jeremy G.} and Schotland, {John C.}",

note = "Publisher Copyright: {\textcopyright} 2017 IOP Publishing Ltd.",

year = "2017",

month = apr,

day = "5",

doi = "10.1088/1361-6420/aa66d1",

language = "English",

volume = "33",

number = "5",

}

TY - JOUR

T1 - Optical tomography on graphs

AU - Chung, Francis J.

AU - Gilbert, Anna C.

AU - Hoskins, Jeremy G.

AU - Schotland, John C.

PY - 2017/4/5

Y1 - 2017/4/5

N2 - 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.

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.

KW - inverse Born series

KW - optical tomograpy

KW - spectral graph theory

UR - http://www.scopus.com/inward/record.url?scp=85019151735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019151735&partnerID=8YFLogxK

U2 - 10.1088/1361-6420/aa66d1

DO - 10.1088/1361-6420/aa66d1

M3 - Article

AN - SCOPUS:85019151735

SN - 0266-5611

VL - 33

JO - Inverse Problems

JF - Inverse Problems

IS - 5

M1 - 055016

ER -

Optical tomography on graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this