Combined higher order non-convex total variation with overlapping group sparsity for impulse noise removal
A typical approach to eliminate impulse noise is to use the ℓ 1 -norm for both the data fidelity term and the regularization terms. However, the ℓ 1 -norm tends to over penalize signal entries which is one of its underpinnings. Hence, we propose a variational model that uses the non-convex ℓ p -norm...
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| Veröffentlicht in: | Multimedia tools and applications 2021-05, Vol.80 (12), p.18503-18530 |
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| container_title | Multimedia tools and applications |
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| creator | Adam, Tarmizi Paramesran, Raveendran Mingming, Yin Ratnavelu, Kuru |
| description | A typical approach to eliminate impulse noise is to use the
ℓ
1
-norm for both the data fidelity term and the regularization terms. However, the
ℓ
1
-norm tends to over penalize signal entries which is one of its underpinnings. Hence, we propose a variational model that uses the non-convex
ℓ
p
-norm, 0 <
p |
| doi_str_mv | 10.1007/s11042-021-10583-y |
| format | Article |
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ℓ
1
-norm for both the data fidelity term and the regularization terms. However, the
ℓ
1
-norm tends to over penalize signal entries which is one of its underpinnings. Hence, we propose a variational model that uses the non-convex
ℓ
p
-norm, 0 <
p
< 1 for both the data fidelity and a second-order total variation regularization term combined with an overlapping group sparse regularizer. Specifically, to robustly eliminate impulse noise, the proposed method uses a non-convex data fidelity term. The hybrid combination of a second-order non-convex total variation and an overlapping group sparse regularization term is used to eliminate the remaining staircase artifacts while maintaining a sharp restored image. A mathematical formulation is derived and to implement it, the iterative re-weighted
ℓ
1
(IRL1) based alternating direction method of multipliers (ADMM) is used to solve the constraints and the subproblems. Experimental results for image denoising and deblurring on several widely used standard images demonstrate that the proposed method performed better when compared to the
ℓ
1
-norm total variation (TV), total generalized variation (TGV) model, and the non-convex
ℓ
p
-norm TV-based data fidelity model in terms of peak signal-to-noise ratio (PSNR) and structure similarity index measure (SSIM).</description><identifier>ISSN: 1380-7501</identifier><identifier>EISSN: 1573-7721</identifier><identifier>DOI: 10.1007/s11042-021-10583-y</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Accuracy ; Computer Communication Networks ; Computer Science ; Data Structures and Information Theory ; Image restoration ; Iterative methods ; Multimedia Information Systems ; Noise ; Noise reduction ; Regularization ; Signal to noise ratio ; Special Purpose and Application-Based Systems</subject><ispartof>Multimedia tools and applications, 2021-05, Vol.80 (12), p.18503-18530</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-d00a7a6118cbf374bd0884dd4afb8e16a08a42302e9fa74d4540d1120396bf1b3</citedby><cites>FETCH-LOGICAL-c319t-d00a7a6118cbf374bd0884dd4afb8e16a08a42302e9fa74d4540d1120396bf1b3</cites><orcidid>0000-0002-5599-5071</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11042-021-10583-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11042-021-10583-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Adam, Tarmizi</creatorcontrib><creatorcontrib>Paramesran, Raveendran</creatorcontrib><creatorcontrib>Mingming, Yin</creatorcontrib><creatorcontrib>Ratnavelu, Kuru</creatorcontrib><title>Combined higher order non-convex total variation with overlapping group sparsity for impulse noise removal</title><title>Multimedia tools and applications</title><addtitle>Multimed Tools Appl</addtitle><description>A typical approach to eliminate impulse noise is to use the
ℓ
1
-norm for both the data fidelity term and the regularization terms. However, the
ℓ
1
-norm tends to over penalize signal entries which is one of its underpinnings. Hence, we propose a variational model that uses the non-convex
ℓ
p
-norm, 0 <
p
< 1 for both the data fidelity and a second-order total variation regularization term combined with an overlapping group sparse regularizer. Specifically, to robustly eliminate impulse noise, the proposed method uses a non-convex data fidelity term. The hybrid combination of a second-order non-convex total variation and an overlapping group sparse regularization term is used to eliminate the remaining staircase artifacts while maintaining a sharp restored image. A mathematical formulation is derived and to implement it, the iterative re-weighted
ℓ
1
(IRL1) based alternating direction method of multipliers (ADMM) is used to solve the constraints and the subproblems. Experimental results for image denoising and deblurring on several widely used standard images demonstrate that the proposed method performed better when compared to the
ℓ
1
-norm total variation (TV), total generalized variation (TGV) model, and the non-convex
ℓ
p
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ℓ
1
-norm for both the data fidelity term and the regularization terms. However, the
ℓ
1
-norm tends to over penalize signal entries which is one of its underpinnings. Hence, we propose a variational model that uses the non-convex
ℓ
p
-norm, 0 <
p
< 1 for both the data fidelity and a second-order total variation regularization term combined with an overlapping group sparse regularizer. Specifically, to robustly eliminate impulse noise, the proposed method uses a non-convex data fidelity term. The hybrid combination of a second-order non-convex total variation and an overlapping group sparse regularization term is used to eliminate the remaining staircase artifacts while maintaining a sharp restored image. A mathematical formulation is derived and to implement it, the iterative re-weighted
ℓ
1
(IRL1) based alternating direction method of multipliers (ADMM) is used to solve the constraints and the subproblems. Experimental results for image denoising and deblurring on several widely used standard images demonstrate that the proposed method performed better when compared to the
ℓ
1
-norm total variation (TV), total generalized variation (TGV) model, and the non-convex
ℓ
p
-norm TV-based data fidelity model in terms of peak signal-to-noise ratio (PSNR) and structure similarity index measure (SSIM).</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11042-021-10583-y</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0002-5599-5071</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1380-7501 |
| ispartof | Multimedia tools and applications, 2021-05, Vol.80 (12), p.18503-18530 |
| issn | 1380-7501 1573-7721 |
| language | eng |
| recordid | cdi_proquest_journals_2529604607 |
| source | SpringerLink Journals |
| subjects | Accuracy Computer Communication Networks Computer Science Data Structures and Information Theory Image restoration Iterative methods Multimedia Information Systems Noise Noise reduction Regularization Signal to noise ratio Special Purpose and Application-Based Systems |
| title | Combined higher order non-convex total variation with overlapping group sparsity for impulse noise removal |
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