Linearized inverse Schrödinger potential problem at a large wavenumber

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Isakov, Victor
Lu, Shuai
Xu, Boxi

Victor Isakov, Shuai Lu, and Boxi Xu Linearized Inverse Schrödinger Potential Problem at a Large Wavenumber SIAM Journal on Applied Mathematics 2020 80:1, 338-358


We investigate recovery of the (Schrodinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a Holder type stability which is a big improvement over a logarithmic stability in low wavenumbers. Furthermore we extend the discussion to the linearized inverse Schrodinger 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.

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