期刊
SIAM JOURNAL ON IMAGING SCIENCES
卷 9, 期 3, 页码 1374-1408出版社
SIAM PUBLICATIONS
DOI: 10.1137/15M1054687
关键词
nonlinear spectral decomposition; nonlinear eigenfunctions; total variation; convex regularizatio
类别
资金
- ERC via EU [615216]
- Israel Science Foundation [718/15]
- Magnet program of the OCS, Israel Ministry of Economy
- ERC [240168]
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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