Nonlinear Spectral Analysis via One-homogeneous Functionals - Overview and Future Prospects
This foundational work addresses the problem of developing nonlinear spectral analysis methods for researchers in signal processing and harmonic analysis, but it appears incremental as it builds on existing convex regularization concepts.
The paper introduces the motivation and theory of nonlinear spectral representations using convex regularizing functionals, drawing comparisons to signal processing and harmonic analysis, and discusses initial applications and future directions.
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.