Spectral Decompositions using One-Homogeneous Functionals
Numerical Analysis
2016-01-13 v1 Optimization and Control
Spectral Theory
Abstract
This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical results that explain the relation between the different definitions. Additionally, results on the orthogonality of the decomposition, a Parseval-type identity and the notion of generalized (nonlinear) eigenvectors closely link our nonlinear multiscale decompositions to the well-known linear filtering theory. Numerical results are used to illustrate our findings.
Cite
@article{arxiv.1601.02912,
title = {Spectral Decompositions using One-Homogeneous Functionals},
author = {Martin Burger and Guy Gilboa and Michael Moeller and Lina Eckardt and Daniel Cremers},
journal= {arXiv preprint arXiv:1601.02912},
year = {2016}
}