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

Gilboa G., Moeller M., Burger M.

Research article (journal) | Peer reviewed

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.

Details about the publication

Journal: Journal of Mathematical Imaging and Vision (J Math Imaging Vis)

Volume: 56

Issue: 2

Page range: 300-319

Status: Published

Release year: 2016

Language in which the publication is written: English

DOI: 10.1007/s10851-016-0665-5

Link to the full text: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84976287014&origin=inward

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

Authors from the University of Münster

Professorship for applied mathematis, especially numerics (Prof. Burger)