Abstract
The motivation and interpretation of classical linear filtering strategies are closely linked to eigendecomposition of positive semidefinite linear operators (derivatives of quadratic functionals). In the following chapters, we show that one can define a nonlinear spectral decomposition framework based on eigenfunctions of convex one-homogeneous functionals and obtain a remarkable number of analogies to linear filtering techniques. In this chapter, we give an introduction of previous studies on the topic and give preliminary settings and properties of one-homogeneous functionals. We then explain in more detail the derivation of eigenfunctions of total variation.
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Gilboa, G. (2018). Eigenfunctions of One-Homogeneous Functionals. In: Nonlinear Eigenproblems in Image Processing and Computer Vision. Advances in Computer Vision and Pattern Recognition. Springer, Cham. https://doi.org/10.1007/978-3-319-75847-3_4
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