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Computational Methods in Applied Mathematics

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Volume 16, Issue 3

Issues

Stability and Experimental Comparison of Prototypical Iterative Schemes for Total Variation Regularized Problems

Sören Bartels
  • Corresponding author
  • Department of Applied Mathematics, Mathematical Institute, University of Freiburg, Hermann-Herder-Str. 9, 79104 Freiburg i. Br., Germany
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/ Marijo Milicevic
  • Department of Applied Mathematics, Mathematical Institute, University of Freiburg, Hermann-Herder-Str. 9, 79104 Freiburg i. Br., Germany
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Published Online: 2016-04-13 | DOI: https://doi.org/10.1515/cmam-2016-0014

Abstract

Various iterative methods are available for the approximate solution of non-smooth minimization problems. For a popular non-smooth minimization problem arising in image processing, we discuss the suitable application of three prototypical methods and their stability. The methods are compared experimentally with a focus on choice of stopping criteria, influence of rough initial data, step sizes as well as mesh sizes. An overview of existing algorithms is given.

Keywords: Total Variation; Finite Elements; Iterative Schemes; Stability

MSC 2010: 65K15; 49M29

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About the article

Received: 2015-12-23

Revised: 2016-03-18

Accepted: 2016-03-20

Published Online: 2016-04-13

Published in Print: 2016-07-01


Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: SPP 1748: BA 2268/2-1

The authors acknowledge financial support by the Deutsche Forschungsgemeinschaft for the project “Finite Element Approximation of Functions of Bounded Variation and Application to Model of Damage, Fracture and Plasticity” (BA 2268/2-1) via the priority program “Reliable Simulation Techniques in Solid Mechanics, Development of Non-Standard Discretization Methods, Mechanical and Mathematical Analysis” (SPP 1748), and by the Sino-German Science Center (grant id 1228) on the occasion of the Chinese-German Workshop on Computational and Applied Mathematics in Augsburg 2015.


Citation Information: Computational Methods in Applied Mathematics, Volume 16, Issue 3, Pages 361–388, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2016-0014.

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