Handbook of Geomathematics 2015
DOI: 10.1007/978-3-642-54551-1_99
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Evaluation of Parameter Choice Methods for Regularization of Ill-Posed Problems in Geomathematics

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Cited by 29 publications
(42 citation statements)
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“…Many sophisticated approaches for selecting an appropriate value of α could be employed [15], but we restrict ourselves to a heuristic approach due to successful past experience.…”
Section: A) Regularized Linear Regressionmentioning
confidence: 99%
“…Many sophisticated approaches for selecting an appropriate value of α could be employed [15], but we restrict ourselves to a heuristic approach due to successful past experience.…”
Section: A) Regularized Linear Regressionmentioning
confidence: 99%
“…Numerous approaches exist to determine tuning parameter values, e.g. the number of respective basis vectors for PCR and PLS, or the ridge value for RR [37][38][39][40][41][42][43][44][45][46]. Typically, a single criterion is used based on some sort of cross-validation (CV) procedure such as leave-one-out CV (LOOCV) or leave multiple out CV (LMOCV) to compute the root mean square error of CV (RMSECV) values.…”
Section: Selecting Final Tuning Parameter Values and Assessing Effectmentioning
confidence: 99%
“…The recent literature shows an increasing interest in heuristic (or noise-level-free) parameter choice strategies, even if the well-known Bakushinsky veto [1] states that, in Hilbert spaces, all heuristic parameter choice rules, which do not make use of the knowledge about the exact noise level, will never converge in the worst-case scenario analysis. Nevertheless, heuristic parameter selection techniques are used quite frequently in practical applications, often giving good results [46,3]. The L-curve method [40,26] and the Generalized Cross Validation method [14] are likely the most popular heuristic parameter selection strategies; they have been deeply investigated by several authors [9,34,17,53].…”
Section: Introductionmentioning
confidence: 99%
“…Several minimization rules for the selection of the regularization parameter for many iterative regularization methods as the Landweber method and the CGLS method are given in [15], both in case of known and unknown noise norm. A detailed and careful comparison of many parameter choice rules is performed in [3,46].…”
Section: Introductionmentioning
confidence: 99%