Appears in collection : 2019 - T1 - WS1 - Variational methods and optimization in imaging

Nonquadratic regularizers and nonlinear flows are often difficult to characterize analytically. Nonlinear eigenvalue analysis can provide a convenient framework for such investigations. Two examples are given. First, we examine nonlinear eigenfunctions (calibrable sets) of adaptive-anisotropic total-variation. Theoretical and experimental results show the type of geometrical structures that can be perfectly preserved under the regularization or descent flow, generalizing the TV theory. A second part examines explicit methods for p-Laplacian flows. Analytic solutions of the flow for p-Laplacian eigenfunctions suggest a new type of stability criterion, generalizing the CFL time-step bound.