Applications of CGO solutions to coupled-physics inverse problems

Ilker Kocyigit; Ru Yu Lai; Lingyun Qiu; Yang Yang; Ting Zhou

doi:10.3934/ipi.2017014

Applications of CGO solutions to coupled-physics inverse problems

Ilker Kocyigit, Ru Yu Lai, Lingyun Qiu, Yang Yang, Ting Zhou

Mathematics

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

2 Scopus citations

Abstract

This paper surveys inverse problems arising in several coupled-physics imaging modalities for both medical and geophysical purposes. These include Photo-acoustic Tomography (PAT), Thermo-acoustic Tomography (TAT), Electro-Seismic Conversion, Transient Elastrography (TE) and Acousto-Electric Tomography (AET). These inverse problems typically consists of multiple inverse steps, each of which corresponds to one of the wave propagations involved. The review focuses on those steps known as the inverse problems with internal data, in which the complex geometrical optics (CGO) solutions to the underlying equations turn out to be useful in showing the uniqueness and stability in determining the desired information.

Original language	English (US)
Pages (from-to)	277-304
Number of pages	28
Journal	Inverse Problems and Imaging
Volume	11
Issue number	2
DOIs	https://doi.org/10.3934/ipi.2017014
State	Published - Apr 2017

Bibliographical note

Funding Information:
R.-Y. L. was partly supported by the AMS-Simons Travel Grants. TZ. was supported by NSF grant DMS-1501049 and Alfred P. Sloan Research Fellowship FR-2015-65641.

Publisher Copyright:
©2017 American Institute of Mathematical Sciences.

Keywords

CGO solutions
Coupled-physics imaging modalities
Internal data
Stability
Uniqueness

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abstract = "This paper surveys inverse problems arising in several coupled-physics imaging modalities for both medical and geophysical purposes. These include Photo-acoustic Tomography (PAT), Thermo-acoustic Tomography (TAT), Electro-Seismic Conversion, Transient Elastrography (TE) and Acousto-Electric Tomography (AET). These inverse problems typically consists of multiple inverse steps, each of which corresponds to one of the wave propagations involved. The review focuses on those steps known as the inverse problems with internal data, in which the complex geometrical optics (CGO) solutions to the underlying equations turn out to be useful in showing the uniqueness and stability in determining the desired information.",

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AU - Zhou, Ting

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Applications of CGO solutions to coupled-physics inverse problems

Abstract

Bibliographical note

Keywords

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