Spectral representations of one-homogeneous functionals

Beitrag bei einer Tagung

Details zur Publikation

Autorinnen und Autoren: Burger M, Eckardt L, Gilboa G, Moeller M
Titel Sammelwerk: Scale Space and Variational Methods in Computer Vision - 5th International Conference, SSVM 2015, Proceedings
Verlag: Springer Verlag
Jahr der Veröffentlichung: 2015
Titel der Reihe: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Seitenbereich: 16-27
ISBN: 9783319184609
ISSN: 0302-9743


This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or ℓ 1-norms. Those functionals serve as a substitute for a Hilbert space structure (and the related norm) in classical linear spectral transforms, e.g. Fourier and wavelet analysis. We discuss three meaningful definitions of spectral representations by scale space and variational methods and prove that (nonlinear) eigenfunctions of the regularization functionals are indeed atoms in the spectral representation. Moreover, we verify further useful properties related to orthogonality of the decomposition and the Parseval identity. The spectral transform is motivated by total variation and further developed to higher order variants. Moreover, we show that the approach can recover Fourier analysis as a special case using an appropriate ℓ1-type functional and discuss a coupled sparsity example.

Einrichtungen weiterer Autorinnen und Autoren

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


Burger, M., Eckardt, L., Gilboa, G., & Moeller, M. (2015). Spectral representations of one-homogeneous functionals. (pp. 16-27). fra: Springer Verlag.

Burger, Martin, et al. "Spectral representations of one-homogeneous functionals." Proceedings of the 5th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2015, fra Springer Verlag, 2015. 16-27.


Zuletzt aktualisiert 2018-03-12 um 12:53