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Regularization of some linear ill-posed problems with discretized random noisy data |
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| Authors: | Peter Mathé Sergei V. Pereverzev. |
| Affiliation: | Weierstraß{} Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D--10117 Berlin, Germany ; Johann-Radon-Institute (RICAM), Altenberger Strasse 69, A-4040 Linz, Austria |
| Abstract: | For linear statistical ill-posed problems in Hilbert spaces we introduce an adaptive procedure to recover the unknown solution from indirect discrete and noisy data. This procedure is shown to be order optimal for a large class of problems. Smoothness of the solution is measured in terms of general source conditions. The concept of operator monotone functions turns out to be an important tool for the analysis. |
| Keywords: | Statistical ill-posed problem general source condition operator monotone function |
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