A new constrained total variational deblurring model and its fast algorithm

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• 作者：Bryan Michael Williams ; Ke Chen ; Simon P. Harding
• 关键词：Total variation ; Image deblurring ; Alternating direction method of multipliers ; Box constraint ; Transforms ; 68U10 ; 65J22 ; 65K10 ; 65T50 ; 90C25
• 刊名：Numerical Algorithms
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：69
• 期：2
• 页码：415-441
• 全文大小：4,764 KB
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• 作者单位：Bryan Michael Williams (1)
  Ke Chen (1)
  Simon P. Harding (2)
  
  1. Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK
  2. St. Paul鈥檚 Eye Unit, Royal Liverpool and Broadgreen University Hospitals NHS Trust, Liverpool, UK
  
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing
  Algorithms
  Mathematics
  Algebra
  Theory of Computation
  
• 出版者：Springer U.S.
• ISSN：1572-9265

文摘

Although image intensities are non-negative quantities, imposing positivity is not always considered in restoration models due to a lack of simple and robust methods of imposing the constraint. This paper proposes a suitable exponential type transform and applies it to the commonly-used total variation model to achieve implicitly constrained solution (positivity at its lower bound and a prescribed intensity value at the upper bound). Further to establish convergence, a convex model is proposed through a relaxation of the transformed functional. Numerical algorithms are presented to solve the resulting non-linear partial differential equations. Test results show that the proposed method is competitive when compared with existing methods in simple cases and more superior in other cases.