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

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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.

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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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Authors and Affiliations

  1. Electrical Engineering Department, Technion IIT, Haifa, Israel

    Guy Gilboa

  2. Department of Computer Science, Technische Universität München, Munich, Germany

    Michael Moeller

  3. Institute for Computational and Applied Mathematics, Westfälische Wilhelms-Universität, Münster, Germany

    Martin Burger

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  1. Guy Gilboa
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  2. Michael Moeller
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  3. Martin Burger
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Correspondence to Guy Gilboa.

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Gilboa, G., Moeller, M. & Burger, M. Nonlinear Spectral Analysis via One-Homogeneous Functionals: Overview and Future Prospects. J Math Imaging Vis 56, 300–319 (2016). https://doi.org/10.1007/s10851-016-0665-5

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