Smoothing via elliptic operators with application to edge detection

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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.

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

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Inverse Problems in Science and Engineering