Regularization independent of the noise level: an analysis of quasi-optimality

Details Regularization independent of the noise level: an analysis of quasi-optimality Regularization independent of the noise level: an analysis of quasi-optimality

2007-10-04

arxiv.org/abs/0710.1045v1

Mathematics

Numerical Analysis

18 pages, 3 figures

Scientific paper

10.1088/0266-5611/24/5/055009

The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cut-off estimators and we prove that the quasi-optimality criterion determines estimators which are rate-optimal {\em on average}. Its practical performance is illustrated with a calibration problem from mathematical finance.

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