Spectral Decompositions using One-Homogeneous Functionals

2016/01/12 by Burger, Martin, Gilboa, Guy, Moeller, Michael +2 · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1601.02912

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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