Spectral decompositions using one-homogeneous functionals

Burger M, Gilboa G, Moeller M, Eckardt L, Cremers D (2016)


Publication Type: Journal article

Publication year: 2016

Journal

Publisher: Society for Industrial and Applied Mathematics Publications

Book Volume: 9

Pages Range: 1374-1408

Issue: 3

DOI: 10.1137/15M1054687

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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APA:

Burger, M., Gilboa, G., Moeller, M., Eckardt, L., & Cremers, D. (2016). Spectral decompositions using one-homogeneous functionals. Siam Journal on Imaging Sciences, 9, 1374-1408. https://doi.org/10.1137/15M1054687

MLA:

Burger, Martin, et al. "Spectral decompositions using one-homogeneous functionals." Siam Journal on Imaging Sciences 9 (2016): 1374-1408.

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