ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
KAUST Grant NumberKUK-I1-007-43
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AbstractWe 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.
CitationCalatroni L, Düring B, Schönlieb C-B (2013) ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. DCDS-A 34: 931–957. Available: http://dx.doi.org/10.3934/dcds.2014.34.931.
SponsorsCarola-Bibiane Schonlieb acknowledges the financial support provided by the Cambridge Centre for Analysis (CCA), the Royal Society International Exchanges Award IE110314 for the project High-order Compressed Sensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse & Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust Small Grant on Non-smooth geometric reconstruction for high resolution MRI imaging of fluid transport in bed reactors. Further, this publication is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).