On the taut string interpretation of the one-dimensional rudin–osher–fatemi model
(2018) 7th International Conference on Pattern Recognition Applications and Methods, ICPRAM 2018 p.233-244- Abstract
A new proof of the equivalence of the Taut String Algorithm and the one-dimensional Rudin–Osher–Fatemi model is presented. Based on duality and the projection theorem in Hilbert space, the proof is strictly elementary. Existence and uniqueness of solutions (in the continuous case) to both denoising models follow as by-products. The standard convergence properties of the denoised signal, as the regularizing parameter tends to zero, are recalled and efficient proofs provided. Moreover, a new and fundamental estimate on the denoised signal is derived. It implies, among other things, the strong convergence (in the space of functions of bounded variation) of the denoised signal to the in-signal as the regularization parameter vanishes.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/58cc55c1-eb9e-4966-8b57-5ca499b3072f
- author
- Overgaard, Niels Chr LU
- organization
- publishing date
- 2018
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Denoising, Isotonic Regression, Lewy–Stampacchia Inequality, Moreau-Yosida Approximation, Regression Splines, Sub-modularity, Taut String, Total Variation Minimization
- host publication
- ICPRAM 2018 - Proceedings of the 7th International Conference on Pattern Recognition Applications and Methods
- pages
- 12 pages
- publisher
- SciTePress
- conference name
- 7th International Conference on Pattern Recognition Applications and Methods, ICPRAM 2018
- conference location
- Funchal, Portugal
- conference dates
- 2018-01-16 - 2018-01-18
- external identifiers
-
- scopus:85052013050
- ISBN
- 9789897582769
- DOI
- 10.5220/0006720402330244
- language
- English
- LU publication?
- yes
- id
- 58cc55c1-eb9e-4966-8b57-5ca499b3072f
- date added to LUP
- 2018-09-28 07:46:48
- date last changed
- 2022-04-25 17:27:15
@inproceedings{58cc55c1-eb9e-4966-8b57-5ca499b3072f, abstract = {{<p>A new proof of the equivalence of the Taut String Algorithm and the one-dimensional Rudin–Osher–Fatemi model is presented. Based on duality and the projection theorem in Hilbert space, the proof is strictly elementary. Existence and uniqueness of solutions (in the continuous case) to both denoising models follow as by-products. The standard convergence properties of the denoised signal, as the regularizing parameter tends to zero, are recalled and efficient proofs provided. Moreover, a new and fundamental estimate on the denoised signal is derived. It implies, among other things, the strong convergence (in the space of functions of bounded variation) of the denoised signal to the in-signal as the regularization parameter vanishes.</p>}}, author = {{Overgaard, Niels Chr}}, booktitle = {{ICPRAM 2018 - Proceedings of the 7th International Conference on Pattern Recognition Applications and Methods}}, isbn = {{9789897582769}}, keywords = {{Denoising; Isotonic Regression; Lewy–Stampacchia Inequality; Moreau-Yosida Approximation; Regression Splines; Sub-modularity; Taut String; Total Variation Minimization}}, language = {{eng}}, pages = {{233--244}}, publisher = {{SciTePress}}, title = {{On the taut string interpretation of the one-dimensional rudin–osher–fatemi model}}, url = {{http://dx.doi.org/10.5220/0006720402330244}}, doi = {{10.5220/0006720402330244}}, year = {{2018}}, }