University of Oulu

Tyni, T. (2018) Recovery of singularities from a backscattering Born approximation for a biharmonic operator in 3D. Inverse Problems, 34 (4), 045007. doi:10.1088/1361-6420/aaaf7f

Recovery of singularities from a backscattering Born approximation for a biharmonic operator in 3D

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Author: Tyni, Teemu1
Organizations: 1Department of Mathematical Sciences, University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: IOP Publishing, 2018
Publish Date: 2019-04-03


We consider a backscattering Born approximation for a perturbed biharmonic operator in three space dimensions. Previous results on this approach for biharmonic operator use the fact that the coefficients are real-valued to obtain the reconstruction of singularities in the coefficients. In this text we drop the assumption about real-valued coefficients and also establish the recovery of singularities for complex coefficients. The proof uses mapping properties of the Radon transform.

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Series: Inverse problems
ISSN: 0266-5611
ISSN-E: 1361-6420
ISSN-L: 0266-5611
Volume: 34
Issue: 4
Article number: 045007
DOI: 10.1088/1361-6420/aaaf7f
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: The author was supported by the Doctoral Programme of Exact Sciences at the University of Oulu, Finland and by the Academy of Finland (application number 250215, Finnish Programme for Centres of Excellence in Research 2012–2017).
Academy of Finland Grant Number: 250215
Detailed Information: 250215 (Academy of Finland Funding decision)
Copyright information: © 2018 IOP Publishing Ltd. This is a peer-reviewed, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at