Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces
Numerical Analysis
2019-04-03 v2
Abstract
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 equation for a range of Besov spaces using variational source conditions. We also derive order optimal rates for a white noise model with the help of variational source conditions and concentration inequalities for sharp negative Besov norms of the noise.
Keywords
Cite
@article{arxiv.1803.11019,
title = {Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces},
author = {Frederic Weidling and Benjamin Sprung and Thorsten Hohage},
journal= {arXiv preprint arXiv:1803.11019},
year = {2019}
}