Errors ofregularisation under range inclusions using variable Hilbert scales

Markus Hegland; Bernd Hofmann

doi:10.3934/ipi.2011.5.619

Article Contents

2011, Volume 5, Issue 3: 619-643. Doi: 10.3934/ipi.2011.5.619

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Errors of regularisation under range inclusions using variable Hilbert scales

Markus Hegland^1, and
Bernd Hofmann^2,

1.
Centre for Mathematics and its Applications, The Australian National University, Canberra ACT, 0200
2.
Department of Mathematics, Chemnitz University of Technology, 09107 Chemnitz

Received: April 30, 2010

Revised: May 31, 2011

Published: July 2011

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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.

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Mathematics Subject Classification: Primary: 47A52; Secondary: 65J20.

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