Spectral decompositions using one-homogeneous functionals
Burger M, Gilboa G, Moeller M, Eckardt L, Cremers D (2016)
Publication Type: Journal article
Publication year: 2016
Journal
Publisher: Society for Industrial and Applied Mathematics Publications
Book Volume: 9
Pages Range: 1374-1408
Issue: 3
DOI: 10.1137/15M1054687
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.
Authors with CRIS profile
Involved external institutions
Technische Universität München (TUM)
Germany (DE)
Westfälische Wilhelms-Universität (WWU) Münster
Germany (DE)
Technion - Israel Institute of Technology
Israel (IL)
Germany (DE)
Westfälische Wilhelms-Universität (WWU) Münster
Germany (DE)
Technion - Israel Institute of Technology
Israel (IL)
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.
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