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Mat. Sb., 2015, Volume 206, Number 1, Pages 131–146 (Mi msb8277)  

This article is cited in 13 scientific papers (total in 13 papers)

An iterative approach to non-overdetermined inverse scattering at fixed energy

R. G. Novikovabc

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS
c École Polytechnique, Centre de Mathématiques Appliquées

Abstract: We present an iterative approximate reconstruction algorithm for non-overdetermined inverse scattering at fixed energy $E$ with incomplete data, where the dimension $d\ge 2$. In particular, we obtain rapidly converging approximate reconstructions for this inverse scattering for $E\to +\infty$.
Bibliography: 38 titles.

Keywords: inverse scattering problem, non-overdetermined monochromatic data, iterative approximate reconstruction, rapid high energy convergence.


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English version:
Sbornik: Mathematics, 2015, 206:1, 120–134

Bibliographic databases:

UDC: 517.958+530.145.81
MSC: 35P25, 65N21
Received: 22.06.2013 and 25.04.2014

Citation: R. G. Novikov, “An iterative approach to non-overdetermined inverse scattering at fixed energy”, Mat. Sb., 206:1 (2015), 131–146; Sb. Math., 206:1 (2015), 120–134

Citation in format AMSBIB
\by R.~G.~Novikov
\paper An iterative approach to non-overdetermined inverse scattering at fixed energy
\jour Mat. Sb.
\yr 2015
\vol 206
\issue 1
\pages 131--146
\jour Sb. Math.
\yr 2015
\vol 206
\issue 1
\pages 120--134

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    This publication is cited in the following articles:
    1. R. G. Novikov, “Formulas for phase recovering from phaseless scattering data at fixed frequency”, Bull. Sci. Math., 139:8 (2015), 923–936  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. D. Agaltsov, “Finding scattering data for a time-harmonic wave equation with first order perturbation from the Dirichlet-to-Neumann map”, J. Inverse Ill-Posed Probl., 23:6 (2015), 627–645  crossref  mathscinet  zmath  isi  elib  scopus
    3. R. G. Novikov, “Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensions”, J. Geom. Anal., 26:1 (2016), 346–359  crossref  mathscinet  zmath  isi  elib  scopus
    4. J. A. Barcelo, C. Castro, J. M. Reyes, “Numerical approximation of the potential in the two-dimesional inverse scattering problem”, Inverse Problems, 32:1 (2016), 015006, 19 pp.  crossref  mathscinet  zmath  isi  scopus
    5. A. E. Kolesov, M. V. Klibanov, L. H. Nguyen, D.-L. Nguyen, N. T. Thành, “Single measurement experimental data for an inverse medium problem inverted by a multi-frequency globally convergent numerical method”, Appl. Numer. Math., 120 (2017), 176–196  crossref  mathscinet  zmath  isi  scopus
    6. D.-L. Nguyen, M. V. Klibanov, L. H. Nguyen, A. E. Kolesov, M. A. Fiddy, H. Liu, “Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm”, J. Comput. Phys., 345 (2017), 17–32  crossref  mathscinet  zmath  isi  scopus
    7. M. V. Klibanov, A. E. Kolesov, L. Nguyen, A. Sullivan, “Globally strictly convex cost functional for a 1-D inverse medium scattering problem with experimental data”, SIAM J. Appl. Math., 77:5 (2017), 1733–1755  crossref  mathscinet  zmath  isi
    8. Dinh-Liem Nguyen, V M. Klibanov, L. H. Nguyen, M. A. Fiddy, “Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method”, J. Inverse Ill-Posed Probl., 26:4 (2018), 501–522  crossref  mathscinet  zmath  isi  scopus
    9. M. V. Klibanov, Dinh-Liem Nguyen, L. H. Nguyen, H. Liu, “A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data”, Inverse Probl. Imaging, 12:2 (2018), 493–523  crossref  mathscinet  zmath  isi  scopus
    10. J. A. Barcelo, C. Castro, T. Luque, M. C. Vilela, “A new convergent algorithm to approximate potentials from fixed angle scattering data”, SIAM J. Appl. Math., 78:5 (2018), 2714–2736  crossref  mathscinet  zmath  isi
    11. Agaltsov A.D., Hohage T., Novikov R.G., “An Iterative Approach to Monochromatic Phaseless Inverse Scattering”, Inverse Probl., 35:2 (2019), 024001  crossref  mathscinet  zmath  isi  scopus
    12. Hamad A., Tadi M., “Inverse Scattering Based on Proper Solution Space”, J. Theor. Comput. Acoust., 27:3 (2019), 1850033  crossref  mathscinet  isi
    13. Novikov R.G., Sivkin V.N., “Error Estimates For Phase Recovering From Phaseless Scattering Data”, Eurasian J. Math. Comput. Appl., 8:1 (2020), 44–61  crossref  isi
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