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ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
journal contribution
posted on 2023-06-09, 00:16 authored by Luca Calatroni, Bertram Duering, Carola-Bibiane SchönliebWe present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H-1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
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Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems - Series AISSN
1078-0947Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
3Volume
34Page range
931-957Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Numerical Analysis and Scientific Computing Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2016-02-11First Open Access (FOA) Date
2016-02-11First Compliant Deposit (FCD) Date
2016-02-11Usage metrics
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