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

Andrea Aspri, Elena Beretta, Otmar Scherzer, Monika Muszkieta

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)1781-1833
Number of pages53
JournalSIAM Journal on Imaging Sciences
Volume13
Issue number4
DOIs
StatePublished - 2020

Keywords

  • Asymptotic expansions
  • Higher order equations
  • Inverse problems
  • Quantitative photoacoustic
  • Thin stripes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Asymptotic expansions for higher order elliptic equations with an application to quantitative photoacoustic tomography'. Together they form a unique fingerprint.

Cite this