RECENT ADVANCES IN DOMAIN DECOMPOSITION METHODS FOR TOTAL VARIATION MINIMIZATION

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Total variation minimization is standard in mathematical imaging and there have been numerous researches over the last decades. In order to process large-scale images in real-time, it is essential to design parallel algorithms that utilize distributed memory computers efficiently. The aim of this paper is to illustrate recent advances of domain decomposition methods for total variation minimization as parallel algorithms. Domain decomposition methods are suitable for parallel computation since they solve a large-scale problem by dividing it into smaller problems and treating them in parallel, and they already have been widely used in structural mechanics. Differently from problems arising in structural mechanics, energy functionals of total variation minimization problems are in general nonlinear, nonsmooth, and nonseparable. Hence, designing efficient domain decomposition methods for total variation minimization is a quite challenging issue. We describe various existing approaches on domain decomposition methods for total variation minimization in a unified view. We address how the direction of research on the subject has changed over the past few years, and suggest several interesting topics for further research.
Publisher
KOREAN SOC INDUSTRIAL & APPLIED MATHEMATICS
Issue Date
2020-06
Language
English
Article Type
Article
Citation

JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, v.24, no.2, pp.161 - 197

ISSN
1226-9433
DOI
10.12941/jksiam.2020.24.161
URI
http://hdl.handle.net/10203/277119
Appears in Collection
MA-Journal Papers(저널논문)
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