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Journal of Mathematical Imaging and Vision

, Volume 56, Issue 2, pp 300–319 | Cite as

Nonlinear Spectral Analysis via One-Homogeneous Functionals: Overview and Future Prospects

  • Guy GilboaEmail author
  • Michael Moeller
  • Martin Burger
Article

Abstract

We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis, and sparse representations. The basic approach, main results, and initial applications are shown. A discussion of open problems and future directions concludes this work.

Keywords

Nonlinear spectral representations One-homogeneous functionals Total variation Nonlinear eigenvalue problem Image decomposition 

Notes

Acknowledgments

GG acknowledges support by the Israel Science Foundation (ISF), Grant 2097/15 and by the Magnet program of the OCS, Israel Ministry of Economy, in the framework of Omek Consortium. MB acknowledges support by ERC via Grant EU FP 7—ERC Consolidator Grant 615216 LifeInverse.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentTechnion IITHaifaIsrael
  2. 2.Department of Computer ScienceTechnische Universität MünchenMunichGermany
  3. 3.Institute for Computational and Applied MathematicsWestfälische Wilhelms-UniversitätMünsterGermany

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