@inbook{a8a3175a10a94904b44f7bc5775fd2ba,
title = "Fast operator-splitting algorithms for variational imaging models: Some recent developments",
abstract = "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.",
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",
author = "Roland Glowinski and Shousheng Luo and Xue-Cheng TAI",
note = "Funding Information: R.G. was supported by the Hong Kong Baptist University and by the Kennedy Wong Foundation. S.L. was supported by the Programs for Science and Technology Development of Henan Province (192102310181). X.C.T. was supported by the startup grant at Hong Kong Baptist University, grants RG(R)-RC/17-18/02-MATH and FRG2/17-18/033. ",
year = "2019",
month = oct,
day = "15",
doi = "10.1016/bs.hna.2019.08.002",
language = "English",
isbn = "9780444641403",
series = "Handbook of Numerical Analysis",
publisher = "Elsevier B.V.",
pages = "191--232",
editor = "Ron Kimmel and Xue-Cheng Tai",
booktitle = "Processing, Analyzing and Learning of Images, Shapes, and Forms",
}