We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
'Society for Industrial & Applied Mathematics (SIAM)'
Doi
Abstract
This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right-hand side, i.e., the noise is large on a small part of the domain and small or zero outside. It is well known that Tikhonov regularization with an L1 data fidelity term outperforms Tikhonov regularization with an L2 fidelity term in this case. This effect has recently been explained and quantified for the case of finitely smoothing operators. Here we extend this analysis to the case of infinitely smoothing forward operators under standard Sobolev smoothness assumptions on the solution, i.e., exponentially ill-posed inverse problems. It turns out that high order polynomial rates of convergence in the size of the support of large noise can be achieved rather than the poor logarithmic convergence rates typical for exponentially ill-posed problems. The main tools of our analysis are Banach spaces of analytic functions and interpolation-type inequalities for such spaces. We discuss two examples, the (periodic) backward heat equation and an inverse problem in gradiometry
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.