Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II : Algorithm, Its Analysis and Numerical Tests

Hintermüller, Michael ; Rautenberg, Carlos N. ; Wu, Tao and Langer, Andreas LU (2017) In Journal of Mathematical Imaging and Vision 59(3). p.515-533
Abstract

Based on the weighted total variation model and its analysis pursued in Hintermüller and Rautenberg 2016, in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.

Please use this url to cite or link to this publication:
author
; ; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bilevel optimization, Convergence analysis, Fenchel predual, Image restoration, Projected gradient method, Spatially distributed regularization weight, Variance corridor, Weighted total variation regularization
in
Journal of Mathematical Imaging and Vision
volume
59
issue
3
pages
19 pages
publisher
Springer
external identifiers
  • scopus:85020658187
ISSN
0924-9907
DOI
10.1007/s10851-017-0736-2
language
English
LU publication?
no
additional info
Funding Information: This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as by the DFG under Grant No.?HI 1466/7-1 ?Free Boundary Problems and Level Set Methods?. Funding Information: This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as by the DFG under Grant No. HI 1466/7-1 “Free Boundary Problems and Level Set Methods”. Publisher Copyright: © 2017, Springer Science+Business Media New York. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
id
5a8042db-e26c-47d4-b35d-432d88edc40f
date added to LUP
2021-03-15 22:31:14
date last changed
2022-04-19 05:07:00
@article{5a8042db-e26c-47d4-b35d-432d88edc40f,
  abstract     = {{<p>Based on the weighted total variation model and its analysis pursued in Hintermüller and Rautenberg 2016, in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.</p>}},
  author       = {{Hintermüller, Michael and Rautenberg, Carlos N. and Wu, Tao and Langer, Andreas}},
  issn         = {{0924-9907}},
  keywords     = {{Bilevel optimization; Convergence analysis; Fenchel predual; Image restoration; Projected gradient method; Spatially distributed regularization weight; Variance corridor; Weighted total variation regularization}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{3}},
  pages        = {{515--533}},
  publisher    = {{Springer}},
  series       = {{Journal of Mathematical Imaging and Vision}},
  title        = {{Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II : Algorithm, Its Analysis and Numerical Tests}},
  url          = {{http://dx.doi.org/10.1007/s10851-017-0736-2}},
  doi          = {{10.1007/s10851-017-0736-2}},
  volume       = {{59}},
  year         = {{2017}},
}