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

Calatroni, Luca, Düring, Bertram and Schönlieb, Carola-Bibiane (2014) ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. Discrete and Continuous Dynamical Systems - Series A, 34 (3). pp. 931-957. ISSN 1078-0947

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[img] PDF (This is the final accepted version of: L. Calatroni, B. Düring, and C.-B. Schönlieb. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. Discrete Contin. Dyn. Syst. Ser. A 34(3) (2014), 931-957.) - Accepted Version
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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics
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Depositing User: Bertram During
Date Deposited: 11 Feb 2016 10:32
Last Modified: 07 Sep 2017 10:07
URI: http://sro.sussex.ac.uk/id/eprint/59615

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