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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.24 No.2
- 발행연도
- 2020.6
- 수록면
- 161 - 197 (37page)
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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.
목차
ABSTRACT
1. INTRODUCTION
2. TOTAL VARIATION MINIMIZATION IN MATHEMATICAL IMAGING
3. SCHWARZ METHODS FOR THE PRIMAL PROBLEM
4. SCHWARZ METHODS FOR THE DUAL PROBLEM
5. ITERATIVE SUBSTRUCTURING METHODS FOR THE DUAL PROBLEM
6. NUMERICAL COMPARISON
7. CONCLUDING REMARKS
REFERENCES
참고문헌 (65)
참고문헌 신청
A. TOSELLI / 2005 / Domain Decomposition Methods-Algorithms and Theory, vol. 34 / Springer
A. QUARTERONI / 1999 / Domain Decomposition Methods for Partial Differential Equations / Oxford University Press
J. XU / 1992 / Iterative methods by space decomposition and subspace correction / SIAM Rev. 34:581~613
C. R. DOHRMANN / 2003 / A preconditioner for substructuring based on constrained energy minimization / SIAM J. Sci. Comput 25:246~258
J. MANDEL / 1993 / Balancing domain decomposition / Commun. Numer. Methods Engrg. 9:233~241
A. QUARTERONI / 1999 / Domain Decomposition Methods for Partial Differential Equations / Oxford University Press
J. XU / 1992 / Iterative methods by space decomposition and subspace correction / SIAM Rev. 34:581~613
C. R. DOHRMANN / 2003 / A preconditioner for substructuring based on constrained energy minimization / SIAM J. Sci. Comput 25:246~258
J. MANDEL / 1993 / Balancing domain decomposition / Commun. Numer. Methods Engrg. 9:233~241
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UCI(KEPA) : I410-ECN-0101-2020-410-000855154