Year: 2015
Author: Heng Mao
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 4 : pp. 415–427
Abstract
We investigate a novel adaptive choice rule of the Tikhonov regularization parameter in numerical differentiation which is a classic ill-posed problem. By assuming a general unknown Hölder type error estimate derived for numerical differentiation, we choose a regularization parameter in a geometric set providing a nearly optimal convergence rate with very limited a-priori information. Numerical simulation in image edge detection verifies reliability and efficiency of the new adaptive approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1503-m2014-0134
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 4 : pp. 415–427
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Numerical differentiation Tikhonov regularization Edge detection Adaptive regularization.
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