A Total Variation Diminishing Interpolation Operator and Applications
Ricardo H. Nochetto, Abner J. Salgado

TL;DR
This paper introduces a new interpolation operator for finite elements that preserves total variation, leading to improved error estimates in total variation denoising and flows.
Contribution
It constructs a total variation diminishing interpolation operator on Cartesian meshes, enhancing stability and approximation accuracy in finite element methods.
Findings
Operator does not increase total variation
Provides second order approximation in L^1
Improves error estimates in TV denoising and flows
Abstract
We construct, on continuous finite elements over Cartesian meshes, an interpolation operator that does not increase the total variation. The operator is stable in and exhibits second order approximation properties. With the help of it we provide improved error estimates for discrete minimizers of the total variation denoising problem and for total variation flows.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Advanced Numerical Analysis Techniques · Advanced Mathematical Modeling in Engineering
