Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

Olga Doeva; Romina Gaburro; William R.B. Lionheart; Clifford J. Nolan

doi:10.1080/00036811.2020.1758314

Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

Olga Doeva, Romina Gaburro, William R.B. Lionheart, Clifford J. Nolan

Department of Mathematics and Statistics

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

Abstract

We study the inverse problem in Optical Tomography of determining the optical properties of a medium (Formula presented.), with (Formula presented.), under the so-called diffusion approximation. We consider the time-harmonic case where Ω is probed with an input field that is modulated with a fixed harmonic frequency (Formula presented.), where c is the speed of light and k is the wave number. We prove a result of Lipschitz stability of the absorption coefficient (Formula presented.) at the boundary (Formula presented.) in terms of the measurements in the case when the scattering coefficient (Formula presented.) is assumed to be known and k belongs to certain intervals depending on some a-priori bounds on (Formula presented.), (Formula presented.).

Original language	English
Pages (from-to)	3697-3715
Number of pages	19
Journal	Applicable Analysis
Volume	101
Issue number	10
DOIs	https://doi.org/10.1080/00036811.2020.1758314
Publication status	Published - 2022

Keywords

diffuse optical tomography
Inverse problems
partial differential equations

Access to Document

10.1080/00036811.2020.1758314

Cite this

@article{56ac467ce47148c3a44298cdeefcb8c0,

title = "Lipschitz stability at the boundary for time-harmonic diffuse optical tomography",

abstract = "We study the inverse problem in Optical Tomography of determining the optical properties of a medium (Formula presented.), with (Formula presented.), under the so-called diffusion approximation. We consider the time-harmonic case where Ω is probed with an input field that is modulated with a fixed harmonic frequency (Formula presented.), where c is the speed of light and k is the wave number. We prove a result of Lipschitz stability of the absorption coefficient (Formula presented.) at the boundary (Formula presented.) in terms of the measurements in the case when the scattering coefficient (Formula presented.) is assumed to be known and k belongs to certain intervals depending on some a-priori bounds on (Formula presented.), (Formula presented.).",

keywords = "diffuse optical tomography, Inverse problems, partial differential equations",

author = "Olga Doeva and Romina Gaburro and Lionheart, {William R.B.} and Nolan, {Clifford J.}",

note = "Publisher Copyright: {\textcopyright} 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.",

year = "2022",

doi = "10.1080/00036811.2020.1758314",

language = "English",

volume = "101",

pages = "3697--3715",

journal = "Applicable Analysis",

issn = "0003-6811",

number = "10",

}

TY - JOUR

T1 - Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

AU - Doeva, Olga

AU - Gaburro, Romina

AU - Lionheart, William R.B.

AU - Nolan, Clifford J.

PY - 2022

Y1 - 2022

N2 - We study the inverse problem in Optical Tomography of determining the optical properties of a medium (Formula presented.), with (Formula presented.), under the so-called diffusion approximation. We consider the time-harmonic case where Ω is probed with an input field that is modulated with a fixed harmonic frequency (Formula presented.), where c is the speed of light and k is the wave number. We prove a result of Lipschitz stability of the absorption coefficient (Formula presented.) at the boundary (Formula presented.) in terms of the measurements in the case when the scattering coefficient (Formula presented.) is assumed to be known and k belongs to certain intervals depending on some a-priori bounds on (Formula presented.), (Formula presented.).

AB - We study the inverse problem in Optical Tomography of determining the optical properties of a medium (Formula presented.), with (Formula presented.), under the so-called diffusion approximation. We consider the time-harmonic case where Ω is probed with an input field that is modulated with a fixed harmonic frequency (Formula presented.), where c is the speed of light and k is the wave number. We prove a result of Lipschitz stability of the absorption coefficient (Formula presented.) at the boundary (Formula presented.) in terms of the measurements in the case when the scattering coefficient (Formula presented.) is assumed to be known and k belongs to certain intervals depending on some a-priori bounds on (Formula presented.), (Formula presented.).

KW - diffuse optical tomography

KW - Inverse problems

KW - partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=85084428611&partnerID=8YFLogxK

U2 - 10.1080/00036811.2020.1758314

DO - 10.1080/00036811.2020.1758314

M3 - Article

AN - SCOPUS:85084428611

SN - 0003-6811

VL - 101

SP - 3697

EP - 3715

JO - Applicable Analysis

JF - Applicable Analysis

IS - 10

ER -

Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this