Frederic Weidling
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View article: Inverse Problems
Inverse Problems Open
Generally speaking, inverse problems typically consist in the reconstruction of causes for observed effects. In imaging applications the cause is usually a probe and the effect are observed data. The corresponding forward problems then con…
View article: Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces
Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces Open
This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We show order optimal rates of convergence for finitely smoothing operators and for the backwards heat e…
View article: Variational Source Conditions and Conditional Stability Estimates for Inverse Problems in PDEs
Variational Source Conditions and Conditional Stability Estimates for Inverse Problems in PDEs Open
Inverse Probleme befassen sich mit der Schätzung eines Parameters aus indirekten Messungen. Die Messung ist üblicherweise fehlerbehaftet während die Identifizierung des Parameters aus der Messung schlecht gestellt (d.h. unstetig) ist. Dahe…
View article: Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods
Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods Open
We describe a general strategy for the verification of variational source condition by formulating two sufficient criteria describing the smoothness of the solution and the degree of ill-posedness of the forward operator in terms of a fami…
View article: Verification of a variational source condition for acoustic inverse medium scattering problems
Verification of a variational source condition for acoustic inverse medium scattering problems Open
This paper is concerned with the classical inverse scattering problem to\nrecover the refractive index of a medium given near or far field measurements\nof scattered time-harmonic acoustic waves. It contains the first rigorous proof\nof (l…