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

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.