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  An iterative approach to monochromatic phaseless inverse scattering

Agaltsov, A., Hohage, T., & Novikov, R. G. (2019). An iterative approach to monochromatic phaseless inverse scattering. Inverse Problems, 35(2): 024001. doi:10.1088/1361-6420/aaf097.

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 Creators:
Agaltsov, Alexey1, Author           
Hohage, T, Author
Novikov, R G, Author
Affiliations:
1Max Planck Institute for Solar System Research, Max Planck Society, ou_1125546              

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 Abstract: This paper is concerned with the inverse problem to recover a compactly supported Schrödinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for the missing phase information we assume additional measurements of the differential cross section in the presence of known background objects. We propose an iterative scheme for the numerical solution of this problem and prove that it converges globally of arbitrarily high order depending on the smoothness of the unknown potential as the energy tends to infinity. At fixed energy, however, the proposed iteration does not converge to the true solution even for exact data. Nevertheless, numerical experiments show that it yields remarkably accurate approximations with small computational effort even for moderate energies. At small noise levels it may be worth to improve these approximations by a few steps of a locally convergent iterative regularization method, and we demonstrate to which extent this reduces the reconstruction error.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1088/1361-6420/aaf097
 Degree: -

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Title: Inverse Problems
Source Genre: Journal
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Publ. Info: London? : IOP Pub.
Pages: - Volume / Issue: 35 (2) Sequence Number: 024001 Start / End Page: - Identifier: ISSN: 0266-5611
CoNE: https://pure.mpg.de/cone/journals/resource/954925499121