Nonlinear Spectral Analysis via One-homogeneous Functionals - Overview and Future Prospects

TL;DR

This paper explores nonlinear spectral representations using convex regularizing functionals, comparing them to traditional signal processing methods, and discusses their potential applications, open problems, and future research directions.

Contribution

It provides an overview of the motivation, theory, and initial applications of nonlinear spectral analysis based on one-homogeneous functionals, highlighting future research avenues.

Findings

Comparison to harmonic analysis and sparse representations

Introduction of the basic approach and main results

Discussion of open problems and future directions

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.