Asymptotic expansions for higher order elliptic equations with an application to quantitative photoacoustic tomography

Andrea Aspri; Elena Beretta; Otmar Scherzer; Monika Muszkieta

doi:10.1137/20M1317062

Asymptotic expansions for higher order elliptic equations with an application to quantitative photoacoustic tomography

Andrea Aspri, Elena Beretta, Otmar Scherzer, Monika Muszkieta

Mathematics

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

Abstract

In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of piecewise smooth functions. This algorithm can be used for edge detection in imaging, topological optimization, and inverse problems, such as quantitative photoacoustic tomography, for which we demonstrate the effectiveness of our asymptotic expansion method numerically.

Original language	English (US)
Pages (from-to)	1781-1833
Number of pages	53
Journal	SIAM Journal on Imaging Sciences
Volume	13
Issue number	4
DOIs	https://doi.org/10.1137/20M1317062
State	Published - 2020

Keywords

Asymptotic expansions
Higher order equations
Inverse problems
Quantitative photoacoustic
Thin stripes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1137/20M1317062

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abstract = "In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of piecewise smooth functions. This algorithm can be used for edge detection in imaging, topological optimization, and inverse problems, such as quantitative photoacoustic tomography, for which we demonstrate the effectiveness of our asymptotic expansion method numerically.",

keywords = "Asymptotic expansions, Higher order equations, Inverse problems, Quantitative photoacoustic, Thin stripes",

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AU - Beretta, Elena

AU - Scherzer, Otmar

AU - Muszkieta, Monika

PY - 2020

Y1 - 2020

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AB - In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of piecewise smooth functions. This algorithm can be used for edge detection in imaging, topological optimization, and inverse problems, such as quantitative photoacoustic tomography, for which we demonstrate the effectiveness of our asymptotic expansion method numerically.

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KW - Higher order equations

KW - Inverse problems

KW - Quantitative photoacoustic

KW - Thin stripes

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Asymptotic expansions for higher order elliptic equations with an application to quantitative photoacoustic tomography

Abstract

Keywords

ASJC Scopus subject areas

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