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Beyond the Bakushinskii veto: Regularising linear inverse problems without knowing the noise distribution
Bastian Harrach, Tim Jahn, Roland Potthast
This article deals with the solution of linear ill-posed equations in Hilbert spaces. Often, one only has a corrupted measurement of the right hand side at hand and the Bakushinski…
Local uniqueness for an inverse boundary value problem with partial data
Bastian Harrach, Marcel Ullrich
In dimension , we prove a local uniqueness result for the potentials of the Schrödinger equation from partial boundary data. More precisely, we show that po…
A learning-based method for solving ill-posed nonlinear inverse problems: a simulation study of Lung EIT
Jin Keun Seo, Kang Cheol Kim, Ariungerel Jargal +2
This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedan…
On localizing and concentrating electromagnetic fields
Bastian Harrach, Yi-Hsuan Lin, Hongyu Liu
We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always…
Monotonicity in inverse medium scattering on unbounded domains
Roland Griesmaier, Bastian Harrach
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded h…