Frank Bauer and Markus Reiß 2008 Inverse Problems 24 055009 doi:10.1088/0266-5611/24/5/055009
Frank Bauer1 and Markus Reiß2
Show affiliationsThe 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 (also known as truncated singular value decomposition, TSVD) and we prove that the quasi-optimality criterion determines estimators which are rate-optimal on average. Its practical performance is illustrated with a calibration problem from mathematical finance.
60D05 Geometric probability, stochastic geometry, random sets (See also 52A22, 53C65)
Issue 5 (October 2008)
Received 21 June 2007, in final form 27 July 2008
Published 19 August 2008
Frank Bauer and Markus Reiß 2008 Inverse Problems 24 055009
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