Comparison of parameter choices in regularization algorithms in case of different information about noise level

Authors:
Uno Hämarik;Reimo Palm;Toomas Raus
Affiliations:
Faculty of Mathematics and Informatics, University of Tartu, Tartu, Estonia 50409;Faculty of Mathematics and Informatics, University of Tartu, Tartu, Estonia 50409;Faculty of Mathematics and Informatics, University of Tartu, Tartu, Estonia 50409
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2011

Citing 5
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Abstract

We consider linear ill-posed problems in Hilbert space with noisy data. The noise level may be given exactly or approximately or there may be no information about the noise level. We regularize the problem using the Landweber method, the Tikhonov method or the extrapolated version of the Tikhonov method. For all three cases of noise information we propose rules for choice of the regularization parameter. Extensive numerical experiments show the advantage of the proposed rules over known rules, including the discrepancy principle, the quasioptimality criterion, the Hanke-Raus rule, the Brezinski-Rodriguez-Seatzu rule and others. Numerical comparison also shows at which information about the noise level our rules for approximately given noise level should be preferred to other rules.