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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.

Heng Mao. (2019). 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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