Centrala begrepp
Proving convergence rates for regularization methods under variational source conditions.
Sammanfattning
The paper discusses convergence rates of variational and iterative regularization methods under a range invariance condition. Three approaches are analyzed: variational, split minimization, and Newton type methods. The range invariance condition is crucial for coefficient identification problems in tomographic imaging modalities, particularly in electrical impedance tomography (EIT). The paper establishes convergence rates for these methods in EIT, focusing on relaxation techniques and variational source conditions. Examples and mathematical proofs are provided to support the theoretical framework.
Statistik
Often an appropriate relaxation of the problem is needed based on an augmentation of the set of unknowns.
The range invariance condition has been verified for several coefficient identification problems.
Conditions on the nonlinearity of the forward operator are crucial for proving convergence.
Citat
"We analyze three approaches that make use of this structure, namely a variational and a Newton type scheme."