TY - CHAP
T1 - Relations to other decomposition methods
AU - Gilboa, Guy
N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2018
Y1 - 2018
N2 - We discuss here the spectral nonlinear framework through different perspectives, related to well-known signal processing disciplines. The relations to wavelets are given, showing one can recover wavelet processing within this framework. In the specific case of Haar wavelet, which is actually a small subset of the eigenfunction of TV, it is shown how the spectral TV can adapt better to the signal. A numerical example shows that fewer elements are needed to encode the signal. We further discuss the relation to generalized Rayleigh quotients and to sparse representations, where nonlinear eigenfunctions can be viewed as an overcomplete dictionary.
AB - We discuss here the spectral nonlinear framework through different perspectives, related to well-known signal processing disciplines. The relations to wavelets are given, showing one can recover wavelet processing within this framework. In the specific case of Haar wavelet, which is actually a small subset of the eigenfunction of TV, it is shown how the spectral TV can adapt better to the signal. A numerical example shows that fewer elements are needed to encode the signal. We further discuss the relation to generalized Rayleigh quotients and to sparse representations, where nonlinear eigenfunctions can be viewed as an overcomplete dictionary.
UR - http://www.scopus.com/inward/record.url?scp=85044821394&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-75847-3_10
DO - 10.1007/978-3-319-75847-3_10
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AN - SCOPUS:85044821394
T3 - Advances in Computer Vision and Pattern Recognition
SP - 141
EP - 150
BT - Nonlinear Eigenproblems in Image Processing and Computer Vision
ER -