Year: 2020
Type: article
Abstract: We investigate recovery of the (Schrödinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a Hölder type stability which is a big improvement over a logarithmic stability in low wavenumbers. Furthermore we extend the discussion to the linearized inverse Schrödinger potential problem with attenuation, where an exponential dependence of the attenuation constant is traced in the stability estimate. Based on the linearized problem, a reconstruction algorithm is proposed aiming at the recovery of the Fourier modes of the potential function. By choosing the large wavenumber appropriately, we verify the efficiency of the proposed algorithm by several numerical examples.
DOI: 10.1137/18m1226932
Authors: Victor Isakov, Shuai Lu, Boxi Xu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2904630433