Explicit tight bounds on the stably recoverable information for the inverse source problem

Mirza Karamehmedović*

*Corresponding author for this work

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Abstract

For the inverse source problem with the two-dimensional Helmholtz equation, the singular values of the source-to-near-field operator reveal a sharp frequency cut-off in the stably recoverable information on the source. We prove and numerically validate an explicit, tight lower bound B- for the spectral location B of this cut-off. We also conjecture, justify and support numerically a tight upper bound B+ for the cut-off. The bounds are expressed in terms of zeros of Bessel functions of the first and second kind. Finally, we propose our near-field upper bound B+ as an improvement of a commonly used upper bound on the spectral cutoff for the source-to-far-field operator.
Original languageEnglish
Article number095021
JournalJournal of Physics Communications
Volume2
Number of pages15
ISSN2399-6528
DOIs
Publication statusPublished - 2018

Keywords

  • Scattering
  • Radiation
  • Inverse source problem
  • Helmholtz equation
  • Singular value decomposition

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