Fast operator-splitting algorithms for variational imaging models: Some recent developments

Roland Glowinski, Shousheng Luo, Xue-Cheng TAI*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingChapterpeer-review

6 Citations (Scopus)


We present in this chapter fast operator-splitting-based algorithms for the solutions of variational problems from image processing. The models we consider use geometrical information and rely on the minimization of appropriate energy functionals. These energy functionals are nonquadratic, possibly nonconvex and nonsmooth, making their minimization a nontrivial endeavour. We show in this chapter that operator-splitting methods based on the Lie scheme, and variants of it, can provide algorithms that are efficient, robust and nearly parameter free. These new algorithms are simpler to use, and often more efficient, than those relying on alternating direction methods of multipliers (ADMM). We want to emphasize that one can use the methods discussed in this chapter for a wide range of applications; actually it has already been done for several of them.

Original languageEnglish
Title of host publicationProcessing, Analyzing and Learning of Images, Shapes, and Forms
Subtitle of host publicationPart 2
EditorsRon Kimmel, Xue-Cheng Tai
PublisherElsevier B.V.
Number of pages42
ISBN (Print)9780444641403
Publication statusPublished - 15 Oct 2019

Publication series

NameHandbook of Numerical Analysis
ISSN (Print)1570-8659

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • 49M27
  • 49M99
  • 65C20
  • 65K10
  • 68U10
  • 94A08
  • Euler's elastica
  • Gaussian/mean curvature
  • Geometric information
  • Image processing
  • Lie scheme
  • Operator splitting
  • Total variation
  • Variational method
  • Willmore energy


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