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Inverse Problems and Imaging (IPI)
 

Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems

Pages: 203 - 220, Volume 11, Issue 1, February 2017      doi:10.3934/ipi.2017010

 
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Frederic Weidling - Institute for Numerical and Applied Mathematics, University of Göttingen, Lotzestr. 16-18, D-37083 Göttingen, Germany (email)
Thorsten Hohage - Institute for Numerical and Applied Mathematics, University of Göttingen, Lotzestr. 16-18, D-37083 Göttingen, Germany (email)

Abstract: This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two variational source conditions for near and far field data, which imply logarithmic rates of convergence of regularization methods, in particular Tikhonov regularization, as the noise level tends to $0$. Moreover, these variational source conditions imply conditional stability estimates which improve and complement known stability estimates in the literature.

Keywords:  Inverse scattering, Maxwell equations, stability, regularization, source condition.
Mathematics Subject Classification:  Primary: 47J06, 35R30; Secondary: 35Q60, 47A52.

Received: December 2015;      Revised: November 2016;      Available Online: January 2017.

 References