Martin Burger, Guy Gilboa, Michael Moeller, Lina Eckardt, Daniel Cremers “Spectral Decompositions using One-Homogeneous Functionals”, SIAM Journal on Imaging Sciences, Vol. 9, No. 3, pp. 1374-1408, 2016.
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