Detection of irregular points by regularization in numerical differentiation and application to edge detection
- 22 May 2006
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 22 (3), 1089-1103
- https://doi.org/10.1088/0266-5611/22/3/022
Abstract
Numerical differentiation is a typical ill-posed problem which can be treated by the Tikhonov regularization. In this paper, we prove that the L2-norms of the second-order derivatives of the regularized solutions blow up in any small interval I where the exact solution is not in H2(I). This generalizes the previous results by Wang, Jia and Cheng (2002 Inverse Problems 18 1461–76) where the interval I is assumed to be the whole interval. One application for image edge detection is presented.Keywords
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