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ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

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posted on 2023-06-09, 00:16 authored by Luca Calatroni, Bertram Duering, Carola-Bibiane Schönlieb
We 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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Discrete and Continuous Dynamical Systems - Series A

ISSN

1078-0947

Publisher

American Institute of Mathematical Sciences

Issue

3

Volume

34

Page range

931-957

Department 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

2016-02-11

First Open Access (FOA) Date

2016-02-11

First Compliant Deposit (FCD) Date

2016-02-11

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