Degree of ill-posedness of statistical inverse problems
- Mathé, Peter
2010 Mathematics Subject Classification
- 65J20 62G20
- Degree of ill--posedness, statistical inverse problem, variable Hilbert scale
We introduce the notion of the degree of ill--posedness of linear operators in operator equations between Hilbert spaces. For specific assumptions on the noise this quantity can be computed explicitely. Next it is shown that the degree of ill--posedness as introduced explains the loss of accuracy when solving inverse problems in Hilbert spaces for a variety of instances.