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Volume 39, Issue 1
Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation

Miyoun Jung & Myungjoo Kang

DOI: 10.4208/jcm.1907-m2018-0234

J. Comp. Math., 39 (2021), pp. 81-107.

Published online: 2020-09

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  • Abstract

This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring. The model integrates a nonconvex data-fidelity term with two regularization terms, a sparse representation prior over dictionary learning and total generalized variation (TGV) regularization. The sparse representation prior exploiting patch information enables the preservation of fine features and textural patterns, while adequately denoising in homogeneous regions and contributing natural visual quality. TGV regularization further assists in effectively denoising in smooth regions while retaining edges. By adopting the penalty method and an alternating minimization approach, we present an efficient iterative algorithm to solve the proposed model. Numerical results establish the superiority of the proposed model over other existing models in regard to visual quality and certain image quality assessments.

  • Keywords

Image restoration, Cauchy noise, Sparse representation prior, Dictionary learning, Total generalized variation.

  • AMS Subject Headings

68U10, 65K10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mjung@hufs.ac.kr (Miyoun Jung)

mkang@snu.ac.kr (Myungjoo Kang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-81, author = {Jung , Miyoun and Kang , Myungjoo}, title = {Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {1}, pages = {81--107}, abstract = {

This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring. The model integrates a nonconvex data-fidelity term with two regularization terms, a sparse representation prior over dictionary learning and total generalized variation (TGV) regularization. The sparse representation prior exploiting patch information enables the preservation of fine features and textural patterns, while adequately denoising in homogeneous regions and contributing natural visual quality. TGV regularization further assists in effectively denoising in smooth regions while retaining edges. By adopting the penalty method and an alternating minimization approach, we present an efficient iterative algorithm to solve the proposed model. Numerical results establish the superiority of the proposed model over other existing models in regard to visual quality and certain image quality assessments.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1907-m2018-0234}, url = {http://global-sci.org/intro/article_detail/jcm/18279.html} }
TY - JOUR T1 - Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation AU - Jung , Miyoun AU - Kang , Myungjoo JO - Journal of Computational Mathematics VL - 1 SP - 81 EP - 107 PY - 2020 DA - 2020/09 SN - 39 DO - http://doi.org/10.4208/jcm.1907-m2018-0234 UR - https://global-sci.org/intro/article_detail/jcm/18279.html KW - Image restoration, Cauchy noise, Sparse representation prior, Dictionary learning, Total generalized variation. AB -

This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring. The model integrates a nonconvex data-fidelity term with two regularization terms, a sparse representation prior over dictionary learning and total generalized variation (TGV) regularization. The sparse representation prior exploiting patch information enables the preservation of fine features and textural patterns, while adequately denoising in homogeneous regions and contributing natural visual quality. TGV regularization further assists in effectively denoising in smooth regions while retaining edges. By adopting the penalty method and an alternating minimization approach, we present an efficient iterative algorithm to solve the proposed model. Numerical results establish the superiority of the proposed model over other existing models in regard to visual quality and certain image quality assessments.

Jung , Miyoun and Kang , Myungjoo. (2020). Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation. Journal of Computational Mathematics. 39 (1). 81-107. doi:10.4208/jcm.1907-m2018-0234
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