Spectral decompositions using one-homogeneous functionals

Journal article


Publication Details

Author(s): Burger M, Gilboa G, Moeller M, Eckardt L, Cremers D
Journal: Siam Journal on Imaging Sciences
Publisher: Society for Industrial and Applied Mathematics Publications
Publication year: 2016
Volume: 9
Pages range: 1374-1408
ISSN: 1936-4954


Abstract

This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical results that explain the relation between the different definitions. Additionally, results on the orthogonality of the decomposition, a Parseval-type identity, and the notion of generalized (nonlinear) eigenvectors closely link our nonlinear multiscale decompositions to the well-known linear filtering theory. Numerical results are used to illustrate our findings.


External institutions with authors

Technion - Israel Institute of Technology
Technische Universität München (TUM)
Westfälische Wilhelms-Universität (WWU) Münster


How to cite

APA:
Burger, M., Gilboa, G., Moeller, M., Eckardt, L., & Cremers, D. (2016). Spectral decompositions using one-homogeneous functionals. Siam Journal on Imaging Sciences, 9, 1374-1408. https://dx.doi.org/10.1137/15M1054687

MLA:
Burger, Martin, et al. "Spectral decompositions using one-homogeneous functionals." Siam Journal on Imaging Sciences 9 (2016): 1374-1408.

BibTeX: 

Last updated on 2018-30-11 at 14:38