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.
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This paper is part of special issue devoted to the 2nd Dolomites Workshop on Constructive Approximation and Applications, 2009.
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Hämarik, U., Palm, R. & Raus, T. Comparison of parameter choices in regularization algorithms in case of different information about noise level. Calcolo 48, 47–59 (2011). https://doi.org/10.1007/s10092-010-0027-4
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DOI: https://doi.org/10.1007/s10092-010-0027-4
Keywords
- Ill-posed problem
- Noise level
- Regularization
- Tikhonov method
- Extrapolated Tikhonov method
- Landweber method
- Regularization parameter choice