Errors ofregularisation under range inclusions using variable Hilbert scales
Open Access
- 1 January 2011
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Inverse Problems and Imaging
- Vol. 5 (3) , 619-643
Abstract
Based on the variable Hilbert scale interpolation inequality, bounds for the error of regularisation methods are derived under range inclusions. In this context, new formulae for the modulus of continuity of the inverse of bounded operators with non-closed range are given. Even if one can show the equivalence of this approach to the version used previously in the literature, the new formulae and corresponding conditions are simpler than the former ones. Several examples from image processing and spectral enhancement illustrate how the new error bounds can be applied.Keywords
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This publication has 37 references indexed in Scilit:
- Sharp converse results for the regularization error using distance functionsInverse Problems, 2011
- Error bounds for spectral enhancement which are based on variable Hilbert scale inequalitiesJournal of Integral Equations and Applications, 2010
- Range Inclusions and Approximate Source Conditions with General Benchmark FunctionsNumerical Functional Analysis and Optimization, 2007
- Convergence rates for Tikhonov regularization from different kinds of smoothness conditionsApplicable Analysis, 2006
- Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operatorsMathematical Methods in the Applied Sciences, 2005
- One new strategy for a priori choice of regularizing parameters in Tikhonov's regularizationInverse Problems, 2000
- Matrix Analysis1997
- Variable hilbert scales and their interpolation inequalities with applications to tikhonov regularizationApplicable Analysis, 1995
- An Optimal Order Regularization Method which Does Not Use Additional Smoothness AssumptionsSIAM Journal on Numerical Analysis, 1992
- Regularization with Differential Operators: An Iterative ApproachNumerical Functional Analysis and Optimization, 1992