@inbook{aad0cf503ca740449538df3c94ac7e7b,
title = "Beyond convex analysis—decompositions with nonlinear flows",
abstract = "In this chapter, we generalize the notion of nonlinear spectral decomposition beyond the convex case. It is shown how general denoisers can be viewed as nonlinear operators, and the coarsening scale space they induce can be analyzed in a spectral manner. We provide some basic assumptions that help us solve the new spectral decomposition problem. Essentially, a common decay profile is sought in order to decompose the image. It is shown that this generalizes both Fourier transform and the TV (or 1-homogeneous) transform. This work is still in research progress. The ideas presented here are a result of a collaboration of Oren Katzir, Tomer Michaeli, and the author, where the essential ideas are presented in Oren{\textquoteright}s thesis (On the scale space of filters and their applications, 2017, [1]). The major implication of these initial findings is that nonlinear eigenfunctions are fundamental in the understanding and analysis of a broad class of nonlinear systems.",
author = "Guy Gilboa",
note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.",
year = "2018",
doi = "10.1007/978-3-319-75847-3_9",
language = "الإنجليزيّة",
series = "Advances in Computer Vision and Pattern Recognition",
number = "9783319758466",
pages = "133--140",
booktitle = "Nonlinear Eigenproblems in Image Processing and Computer Vision",
edition = "9783319758466",
}