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Advances in Computational Mathematics

, Volume 45, Issue 2, pp 589–610 | Cite as

On the discontinuity of images recovered by noncovex nonsmooth regularized isotropic models with box constraints

  • Chao Zeng
  • Chunlin WuEmail author
Article
  • 90 Downloads

Abstract

Nonconvex nonsmooth regularizations have exhibited the ability of restoring images with neat edges in many applications, which has been provided a mathematical explanation by analyzing the discontinuity of the local minimizers of the variational models. Since in many applications the pixel intensity values in digital images are restricted in a certain given range, box constraints are adopted to improve the restorations. A similar property of nonconvex nonsmooth regularization for box-constrained models has been proved in the literature. While many theoretical results are available for anisotropic models, we investigate the isotropic case. We establish similar theoretical results for isotropic nonconvex nonsmooth models with box constraints. Numerical experiments are presented to validate our theoretical results.

Keywords

Box constraint Image restoration Nonconvex nonsmooth regularization 

Mathematics Subject Classification (2010)

49K30 49N45 49N60 90C26 94A08 94A12 

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Notes

Acknowledgements

The authors would like to thank the anonymous referees for the careful reading of the manuscript and providing valuable suggestions that helped improve this paper. This work is supported by Postdoctoral Science Foundation of China (2016M601248), National Natural Science Foundation of China (Grants 11301289, 11531013 and 11871035), Recruitment Program of Global Young Expert, and the Fundamental Research Funds for the Central Universities.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesNankai UniversityTianjinChina

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