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arXiv · 1803.05008

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

Mirza Karamehmedović
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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' forward 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 for the spectral location of this cut-off. We also conjecture and support numerically a tight upper bound for the cut-off. The bounds are expressed in terms of zeros of Bessel functions of the first and second kind.

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Mirza Karamehmedović. 2018-03-13. Explicit tight bounds on the stably recoverable information for the inverse source problem. https://arxiv.org/abs/1803.05008

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