Finding latent structures in data is drawing increasing attention in diverse fields such as
image and signal processing, fluid dynamics, and machine learning. In this work we …

In this work we develop a nonlinear decomposition, associated with nonlinear
eigenfunctions of the p-Laplacian for p∈(1, 2). With this decomposition we can process …

The p-Laplacian is a non-linear generalization of the Laplace operator. In the graph context,
its eigenfunctions are used for data clustering, spectral graph theory, dimensionality …

Hele-Shaw problems are prototypes to study the interface dynamics. Linear theory suggests
the existence of self-similar patterns in a Hele-Shaw flow. That is, with a specific injection …

Neural networks have revolutionized the field of data science, yielding remarkable solutions
in a data-driven manner. For instance, in the field of mathematical imaging, they have …

This chapter describes how gradient flows and nonlinear power methods in Banach spaces
can be used to solve nonlinear eigenvector-dependent eigenvalue problems, and how …

Implementation of nonlinear flows by explicit schemes can be very convenient, due to their
simplicity and low-computational cost per time step. A well known drawback is the small time …

We examine nonlinear scale-spaces in the general form ut= P (u (t)), where P is a bounded
nonlinear operator. We seek solutions with separation of variables in space and time u (x, t) …

In this chapter we are examining several iterative methods for solving nonlinear eigenvalue
problems. These arise in variational image processing, graph partition and classification …

In this paper, we propose to analyze stable and unstable modes of black-box image
denoisers through nonlinear eigenvalue analysis. We aim to find input images for which the …