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A new constrained total variational deblurring model and its fast algorithm

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Abstract

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.

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Authors and Affiliations

  1. Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK

    Bryan Michael Williams & Ke Chen

  2. St. Paul’s Eye Unit, Royal Liverpool and Broadgreen University Hospitals NHS Trust, Liverpool, UK

    Simon P. Harding

Authors
  1. Bryan Michael Williams
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  2. Ke Chen
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  3. Simon P. Harding
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Correspondence to Ke Chen.

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Williams, B.M., Chen, K. & Harding, S.P. A new constrained total variational deblurring model and its fast algorithm. Numer Algor 69, 415–441 (2015). https://doi.org/10.1007/s11075-014-9904-2

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  • DOI: https://doi.org/10.1007/s11075-014-9904-2

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