Nonlinear estimation for linear inverse problems with error in the operator
- Hoffmann, Marc
- Reiß, Markus
2010 Mathematics Subject Classification
- 65J20 62G07
- statistical inverse problem, Galerkin projection method, wavelet thresholding, minimax rate, degree of ill-posedness, matrix compression
We consider nonlinear estimation methods for statistical inverse problems in the case where the operator is not exactly known. For a canonical formulation a Gaussian operator white noise framework is developed. Two different nonlinear estimators are constructed, which correspond to the different order of the linear inversion and nonlinear smoothing step. We show that both estimators are rate-optimal over a wide range of Besov smoothness classes. The construction is based on the Galerkin projection method and wavelet thresholding schemes for the data and the operator.