An Application of Source Inequalities for Convergence Rates of Tikhonov\n Regularization with a Non-differentiable Operator

2012/09/11 by Markus Grasmair, Grasmair, Markus
Computer Science · Engineering · Mathematics · #65J20 #65J22 #FOS: Mathematics #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1209.2246

openalex publication_date 2012/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study Tikhonov regularization for the stable solution of an\nill-posed non-linear operator equation. The operator we consider, which is\nrelated to an active contour model for image segmentation, is continuous,\ncompact, but nowhere differentiable. Nevertheless we are able to derive\nconvergence rates under different smoothness assumptions on the true solution\nby employing the method of variational or source inequalities. With this\napproach, we can prove up to linear convergence with respect to the norm.\n

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