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 - <p style="text-align: justify;">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.</p>