REGULARIZATION FOR CURVE REPRESENTATIONS - UNIFORM-CONVERGENCE FOR DISCONTINUOUS SOLUTIONS OF ILL-POSED PROBLEMS

Authors
NEUBAUER A SCHERZER O
Citation
A. Neubauer et O. Scherzer, REGULARIZATION FOR CURVE REPRESENTATIONS - UNIFORM-CONVERGENCE FOR DISCONTINUOUS SOLUTIONS OF ILL-POSED PROBLEMS, SIAM journal on applied mathematics (Print), 58(6), 1998, pp. 1891-1900
Citations number
14
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on applied mathematics (Print) → ACNP
ISSN journal
00361399
Volume
58
Issue
6
Year of publication
1998
Pages
1891 - 1900
Database
ISI
SICI code
0036-1399(1998)58:6<1891:RFCR-U>2.0.ZU;2-M
Abstract
This paper is concerned with a new approach for regularizing problems with discontinuous solutions: regularization for curve representations . The idea of this approach is to represent a (discontinous) function as a curve with parameterization (a(t); b(t)). A combination with nonl inear Tikhonov regularization then yields uniform convergence of the r egularized solutions. The method is applied to deblurring and denoisin g problems in signal processing. A numerical example for a deblurring problem is presented.