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

Luca Calatroni, Bertram Düring, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

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.
Original languageEnglish (US)
Pages (from-to)931-957
Number of pages27
JournalDiscrete and Continuous Dynamical Systems
Volume34
Issue number3
DOIs
StatePublished - Aug 20 2013
Externally publishedYes

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