||Sala conferenza - DISI - 3 piano
||Nonlinear Estimation for Linear Inverse Problems with Error in the Operator
||Institute of Mathematics Stochastic Group Humboldt University Berlin
||We consider statistical inverse problems where the operator itself is
not known, but needs to be estimated, which is often the case in applications.
For a general model we develop different estimation strategies based on
wavelet decompositions and thresholding. Optimal rates of convergence for our
adaptive estimators are derived, with a special emphasis on the different noise
levels in the data and the operator. The operator noise is reduced by
thresholding the wavelet representation of the operator componentwise.
Simulation results illustrate the practical performances.