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Journal article
Nonlinearity helps the convergence of the inverse Born series
Inverse problems, v 40(12), 125020
26 Nov 2024
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Abstract
In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type [8]. We reported conditions which guarantee convergence of the inverse Born series, enabling recovery of the coefficients of the linear and nonlinear terms. In this work, we show that if the coefficient of the linear term is known, that an arbitrarily strong Kerr nonlinearity can be reconstructed, for sufficiently small data. Additionally, we show that similar convergence results hold for general polynomial nonlinearities. Our results are illustrated with numerical examples.
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Details
- Title
- Nonlinearity helps the convergence of the inverse Born series
- Creators
- Nicholas Defilippis - New York UniversityShari Moskow (Corresponding Author) - Drexel UniversityJohn Schotland - Yale University
- Publication Details
- Inverse problems, v 40(12), 125020
- Publisher
- Institute of Physics
- Number of pages
- 15
- Grants
- Data driven inversion methods and image reconstruction for nonlinear media, 2308200, National Science Foundation (United States, Arlington) - NSF
- Grant note
S Moskow was supported by the NSF Grants DMS-2008441 and DMS-2308200. J Schotland was supported by the NSF Grant DMS-1912821 and the AFOSR Grant FA9550-19-1-0320.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001364648500001
- Scopus ID
- 2-s2.0-85213383222
- Other Identifier
- 991021961001704721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical