Asymptotic Expansions for Higher Order Elliptic Equations with an Application to Quantitative Photoacoustic Tomography

Andrea Aspri, Elena Beretta, Otmar Scherzer, Monika Muszkieta

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

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.

OriginalspracheEnglisch
Seiten (von - bis)1781-1833
Seitenumfang53
FachzeitschriftSIAM Journal on Imaging Sciences
Jahrgang13
Ausgabenummer4
DOIs
PublikationsstatusVeröffentlicht - 2020

ÖFOS 2012

  • 101028 Mathematische Modellierung

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