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

Guy Gilboa; Michael Moeller; Martin Burger

doi:https://doi.org/10.1007/s10851-016-0665-5

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

Guy Gilboa, Michael Moeller, Martin Burger

Electrical and Computer Engineering

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	300-319
Number of pages	20
Journal	Journal of Mathematical Imaging and Vision
Volume	56
Issue number	2
DOIs	https://doi.org/10.1007/s10851-016-0665-5
State	Published - 1 Oct 2016

Keywords

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

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modelling and Simulation
Condensed Matter Physics
Computer Vision and Pattern Recognition
Geometry and Topology
Applied Mathematics

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Cite this

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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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KW - Image decomposition

KW - Nonlinear eigenvalue problem

KW - Nonlinear spectral representations

KW - One-homogeneous functionals

KW - Total variation

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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