Smoothing via elliptic operators with application to edge detection

Document Type

Article

Publication Date

6-7-2017

Abstract

We propose a new regularization scheme for stable numerical differentiation of noisy data defined on a bounded domain with . The method generates a sequence of smoothed (regularized) data obtained by solving a perturbed elliptic boundary-value problem. Assuming the measured data are in and the true underlying data are sufficiently smooth, we prove convergence results in the -norm, provided the noisy data converge to true data in the sense. Using the finite element method, we derive error bounds and prove convergence theorems in the case of discrete data. Numerical examples indicate noteworthy results and shed light on some possible applications in image processing and computer vision.

Publisher's Statement

Publisher's version of record: https://doi.org/10.1080/17415977.2017.1336552

Publication Title

Inverse Problems in Science and Engineering

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