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.