Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 55, Issue 2, Pages 598-620Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1067445
Keywords
inverse problems; variational source condition; spectral regularization; converse results; maxisets
Categories
Funding
- German Research Foundation (DFG) [CRC 755]
Ask authors/readers for more resources
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 illposedness 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 of spectral regularization methods, which are slower than the square root of the noise level. A similar result is shown for linear inverse problems with white noise. In many cases variational source conditions can be characterized by Besov spaces. This is discussed for a number of prominent inverse problems.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available