Characterizations of variational source conditions, converse results, and maxisets of spectral regularization methods
Numerical Analysis
2017-03-28 v4
Abstract
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 family of subspaces. For linear deterministic inverse problems we show that variational source conditions are necessary and sufficient for convergence rates slower than the square root of the noise level. A similar result is shown for linear inverse problems with white noise. If the forward operator can be written in terms of the functional calculus of a Laplace-Beltrami operator, variational source conditions can be characterized by Besov spaces. This is discussed for a number of prominent inverse problems.
Keywords
Cite
@article{arxiv.1603.05133,
title = {Characterizations of variational source conditions, converse results, and maxisets of spectral regularization methods},
author = {Thorsten Hohage and Frederic Weidling},
journal= {arXiv preprint arXiv:1603.05133},
year = {2017}
}