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- Publisher Website: 10.1109/TIP.2009.2034701
- Scopus: eid_2-s2.0-77249156864
- WOS: WOS:000274732000022
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Article: On the total variation dictionary model
| Title | On the total variation dictionary model |
|---|---|
| Authors | |
| Keywords | Dual problem Dictionary Curvature Total variation Sparse representation |
| Issue Date | 2010 |
| Citation | IEEE Transactions on Image Processing, 2010, v. 19, n. 3, p. 821-825 How to Cite? |
| Abstract | The goal of this paper is to provide a theoretical study of a total variation (TV) dictionary model. Based on the properties of convex analysis and bounded variation functions, the existence of solutions of the TV dictionary model is proved. We then show that the dual form of the model can be given by the minimization of the sum of the l1-norm of the dual solution and the Bregman distance between the curvature of the primal solution and the subdifferential of TV norm of the dual solution. This theoretical result suggests that the dictionary must represent sparsely the curvatures of solution image in order to obtain a better denoising performance. © 2010 IEEE. |
| Persistent Identifier | http://hdl.handle.net/10722/276857 |
| ISSN | 2021 Impact Factor: 11.041 2020 SCImago Journal Rankings: 1.778 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Zeng, Tieyong | - |
| dc.contributor.author | Ng, Michael K. | - |
| dc.date.accessioned | 2019-09-18T08:34:52Z | - |
| dc.date.available | 2019-09-18T08:34:52Z | - |
| dc.date.issued | 2010 | - |
| dc.identifier.citation | IEEE Transactions on Image Processing, 2010, v. 19, n. 3, p. 821-825 | - |
| dc.identifier.issn | 1057-7149 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/276857 | - |
| dc.description.abstract | The goal of this paper is to provide a theoretical study of a total variation (TV) dictionary model. Based on the properties of convex analysis and bounded variation functions, the existence of solutions of the TV dictionary model is proved. We then show that the dual form of the model can be given by the minimization of the sum of the l1-norm of the dual solution and the Bregman distance between the curvature of the primal solution and the subdifferential of TV norm of the dual solution. This theoretical result suggests that the dictionary must represent sparsely the curvatures of solution image in order to obtain a better denoising performance. © 2010 IEEE. | - |
| dc.language | eng | - |
| dc.relation.ispartof | IEEE Transactions on Image Processing | - |
| dc.subject | Dual problem | - |
| dc.subject | Dictionary | - |
| dc.subject | Curvature | - |
| dc.subject | Total variation | - |
| dc.subject | Sparse representation | - |
| dc.title | On the total variation dictionary model | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1109/TIP.2009.2034701 | - |
| dc.identifier.scopus | eid_2-s2.0-77249156864 | - |
| dc.identifier.volume | 19 | - |
| dc.identifier.issue | 3 | - |
| dc.identifier.spage | 821 | - |
| dc.identifier.epage | 825 | - |
| dc.identifier.isi | WOS:000274732000022 | - |
| dc.identifier.issnl | 1057-7149 | - |