On Simultaneous Recovery Of Sources/Obstacles And Surrounding Mediums By Boundary Measurements

Xiaoping Fang; Youjun Deng; Wing Yan Tsui; Zaiyun Zhang

doi:10.3934/era.2020068

On Simultaneous Recovery Of Sources/Obstacles And Surrounding Mediums By Boundary Measurements

Xiaoping Fang
, Youjun Deng^*
, Wing Yan Tsui
, Zaiyun Zhang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

3 Citations (Scopus)

Abstract

We consider a particular type of inverse problems where an unknown source embedded in an inhomogeneous medium, and one intends to recover the source and/or the medium by knowledge of the wave field (generated by the unknown source) outside the medium. This type of inverse problems arises in many applications of practical importance, including photoacoustic and thermoacoustic tomography, brain imaging and geomagnetic anomaly detections. We survey the recent mathematical developments on this type of inverse problems. We discuss the mathematical tools developed for effectively tackling this type of inverse problems. We also discuss a related inverse problem of recovering an embedded obstacle and its surrounding medium by active measurements.

Original language	English
Pages (from-to)	1239-1255
Number of pages	17
Journal	Electronic Research Archive
Volume	28
Issue number	3
DOIs	https://doi.org/10.3934/era.2020068
Publication status	Published - Sept 2020

User-Defined Keywords

asymptotic analysis
frequency domain
geomagnetism
inverse problem
magnetized anomalies
uniqueness
Wave scattering

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10.3934/era.2020068

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@article{7cd95e960c5940e8be035b57aa73fbc8,

title = "On Simultaneous Recovery Of Sources/Obstacles And Surrounding Mediums By Boundary Measurements",

abstract = "We consider a particular type of inverse problems where an unknown source embedded in an inhomogeneous medium, and one intends to recover the source and/or the medium by knowledge of the wave field (generated by the unknown source) outside the medium. This type of inverse problems arises in many applications of practical importance, including photoacoustic and thermoacoustic tomography, brain imaging and geomagnetic anomaly detections. We survey the recent mathematical developments on this type of inverse problems. We discuss the mathematical tools developed for effectively tackling this type of inverse problems. We also discuss a related inverse problem of recovering an embedded obstacle and its surrounding medium by active measurements.",

keywords = "asymptotic analysis, frequency domain, geomagnetism, inverse problem, magnetized anomalies, uniqueness, Wave scattering",

author = "Xiaoping Fang and Youjun Deng and Tsui, \{Wing Yan\} and Zaiyun Zhang",

note = "Funding Information: The work of X. Fang was supported by Humanities and Social Sciences Foundation of the Ministry of Education no. 20YJC910005, Major Project for National Natural Science Foundation of China no. 71991465, PSCF of Hunan No. 18YBQ077 and RFEB of Hunan No. 18B337. The work of Y. Deng was supported by NSF grant of China No. 11971487 and NSF grant of Hunan No.2020JJ2038 and No.2017JJ3432. The work of Z. Zhang was supported by Scientific Research Fund of Hunan Provincial Education Department No.18A325, Open project of Hainan Key Laboratory of Computing Science and Application No.JSKX201905, NNSF of China Grant Nos.11671101. Also, this work was partially supported by Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering of Changsha University of Science and Technology Grant No. 2018MMAEZD05. Publisher Copyright: {\textcopyright} 2020 the Author(s), licensee AIMS Press.",

year = "2020",

month = sep,

doi = "10.3934/era.2020068",

language = "English",

volume = "28",

pages = "1239--1255",

journal = "Electronic Research Archive",

issn = "1935-9179",

publisher = "American Mathematical Society",

number = "3",

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T1 - On Simultaneous Recovery Of Sources/Obstacles And Surrounding Mediums By Boundary Measurements

AU - Fang, Xiaoping

AU - Deng, Youjun

AU - Tsui, Wing Yan

AU - Zhang, Zaiyun

N1 - Funding Information: The work of X. Fang was supported by Humanities and Social Sciences Foundation of the Ministry of Education no. 20YJC910005, Major Project for National Natural Science Foundation of China no. 71991465, PSCF of Hunan No. 18YBQ077 and RFEB of Hunan No. 18B337. The work of Y. Deng was supported by NSF grant of China No. 11971487 and NSF grant of Hunan No.2020JJ2038 and No.2017JJ3432. The work of Z. Zhang was supported by Scientific Research Fund of Hunan Provincial Education Department No.18A325, Open project of Hainan Key Laboratory of Computing Science and Application No.JSKX201905, NNSF of China Grant Nos.11671101. Also, this work was partially supported by Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering of Changsha University of Science and Technology Grant No. 2018MMAEZD05. Publisher Copyright: © 2020 the Author(s), licensee AIMS Press.

PY - 2020/9

Y1 - 2020/9

N2 - We consider a particular type of inverse problems where an unknown source embedded in an inhomogeneous medium, and one intends to recover the source and/or the medium by knowledge of the wave field (generated by the unknown source) outside the medium. This type of inverse problems arises in many applications of practical importance, including photoacoustic and thermoacoustic tomography, brain imaging and geomagnetic anomaly detections. We survey the recent mathematical developments on this type of inverse problems. We discuss the mathematical tools developed for effectively tackling this type of inverse problems. We also discuss a related inverse problem of recovering an embedded obstacle and its surrounding medium by active measurements.

AB - We consider a particular type of inverse problems where an unknown source embedded in an inhomogeneous medium, and one intends to recover the source and/or the medium by knowledge of the wave field (generated by the unknown source) outside the medium. This type of inverse problems arises in many applications of practical importance, including photoacoustic and thermoacoustic tomography, brain imaging and geomagnetic anomaly detections. We survey the recent mathematical developments on this type of inverse problems. We discuss the mathematical tools developed for effectively tackling this type of inverse problems. We also discuss a related inverse problem of recovering an embedded obstacle and its surrounding medium by active measurements.

KW - asymptotic analysis

KW - frequency domain

KW - geomagnetism

KW - inverse problem

KW - magnetized anomalies

KW - uniqueness

KW - Wave scattering

UR - https://www.scopus.com/pages/publications/85120062014

U2 - 10.3934/era.2020068

DO - 10.3934/era.2020068

M3 - Journal article

AN - SCOPUS:85120062014

SN - 1935-9179

VL - 28

SP - 1239

EP - 1255

JO - Electronic Research Archive

JF - Electronic Research Archive

IS - 3

ER -

On Simultaneous Recovery Of Sources/Obstacles And Surrounding Mediums By Boundary Measurements

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