@article{3c5025c29f9143f6b44344f5904f7e21,
title = "Asymptotic expansions for higher order elliptic equations with an application to quantitative photoacoustic tomography",
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",
author = "Andrea Aspri and Elena Beretta and Otmar Scherzer and Monika Muszkieta",
note = "Funding Information: \ast Received by the editors February 5, 2020; accepted for publication August 5, 2020; published electronically October 22, 2020. https://doi.org/10.1137/20M1317062 Funding: The work of the third author was supported by the Austrian Science Fund (FWF), with SFB F68, projects F6807-N36 (Tomography with Uncertainties), and I3661-N27 (Novel Error Measures and Source Conditions of Regularization Methods for Inverse Problems). \dagger Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, 4040, Austria (andrea. aspri@ricam.oeaw.ac.at). \ddagger Departments of Mathematics, New York University Abu Dhabi, UAE, and Dipartimento di Matematica, Politec-nico di Milano, Milan, 20133, Italy (elena.beretta@polimi.it). \S Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, 4040, Austria, and Faculty of Mathematics, University of Vienna, Vienna, 1090, Austria (otmar.scherzer@univie.ac.at). \P Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wroclaw, 50-370, Poland (monika.muszkieta@pwr.edu.pl). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics.",
year = "2020",
doi = "10.1137/20M1317062",
language = "English (US)",
volume = "13",
pages = "1781--1833",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}