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arXiv · 1601.02912

Spectral Decompositions using One-Homogeneous Functionals

Martin Burger·Guy Gilboa·Michael Moeller·Lina Eckardt·Daniel Cremers
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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.

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Martin Burger, Guy Gilboa, Michael Moeller, Lina Eckardt, Daniel Cremers. 2016-01-12. Spectral Decompositions using One-Homogeneous Functionals. https://arxiv.org/abs/1601.02912

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