Advanced

On the taut string interpretation of the one-dimensional rudin–osher–fatemi model

Overgaard, Niels Chr LU (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:
author
organization
publishing date
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
2018-11-21 21:41:52
@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},
  isbn         = {9789897582769},
  keyword      = {Denoising,Isotonic Regression,Lewy–Stampacchia Inequality,Moreau-Yosida Approximation,Regression Splines,Sub-modularity,Taut String,Total Variation Minimization},
  language     = {eng},
  location     = {Funchal, Portugal},
  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},
  year         = {2018},
}