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Volume 33, Issue 4
Adaptive Choice of the Regularization Parameter in Numerical Differentiation

Heng Mao

DOI: 10.4208/jcm.1503-m2014-0134

J. Comp. Math., 33 (2015), pp. 415-427.

Published online: 2015-08

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  • 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.

  • Keywords

Numerical differentiation, Tikhonov regularization, Edge detection, Adaptive regularization.

  • AMS Subject Headings

65D25, 65J20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hmao12@fudan.edu.cn (Heng Mao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-415, author = {Mao , Heng}, title = {Adaptive Choice of the Regularization Parameter in Numerical Differentiation}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1503-m2014-0134}, url = {http://global-sci.org/intro/article_detail/jcm/9851.html} }
TY - JOUR T1 - Adaptive Choice of the Regularization Parameter in Numerical Differentiation AU - Mao , Heng JO - Journal of Computational Mathematics VL - 4 SP - 415 EP - 427 PY - 2015 DA - 2015/08 SN - 33 DO - http://doi.org/10.4208/jcm.1503-m2014-0134 UR - https://global-sci.org/intro/article_detail/jcm/9851.html KW - Numerical differentiation, Tikhonov regularization, Edge detection, Adaptive regularization. AB -

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.

Mao , Heng. (2015). Adaptive Choice of the Regularization Parameter in Numerical Differentiation. Journal of Computational Mathematics. 33 (4). 415-427. doi:10.4208/jcm.1503-m2014-0134
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