2020/10/06 by Guy Gilboa, Gilboa, Guy · 1 citation
Computer Science · Engineering · #Analysis of PDEs (math.AP) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2010.02890
openalex publication_date 2020/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we solve is T(u)=λu, where T:\Rn→ \Rn is some bounded nonlinear operator. Other variations of eigenvalue problems are also discussed. We present a progression of 5 algorithms, coauthored in recent years by the author and colleagues. Each algorithm attempts to solve a unique problem or to improve the theoretical foundations. The algorithms can be understood as nonlinear PDE's which converge to an eigenfunction in the continuous time domain. This allows a unique view and understanding of the discrete iterative process. Finally, it is shown how to evaluate numerically the results, along with some examples and insights related to priors of nonlinear denoisers, both classical algorithms and ones based on deep networks.