期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 55, 期 2, 页码 598-620出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M1067445
关键词
inverse problems; variational source condition; spectral regularization; converse results; maxisets
资金
- German Research Foundation (DFG) [CRC 755]
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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据