Non-Local Morphological PDEs and $p$-Laplacian Equation on Graphs With Applications in Image Processing and Machine Learning
Abderrahim Elmoataz, Xavier Desquesnes, Olivier Lézoray · IEEE Journal of Selected Topics in Signal Processing · 2012
In this paper, we introduce a new class of non-localp-Laplacian operators that interpolate between non-local Laplacian and infinity Laplacian. These operators are discrete analogous of the gamep-laplacian operators on Euclidean spaces, and involve discrete morphological gradient on graphs. We study the Dirichlet problem associated with the newp-Laplacian equation and prove existence and uniqueness of it's solution. We also consider non-local diffusion on graphs involving these operators. Finally, we propose to use these operators as a unified framework for solution of many inverse problems in image processing and machine learning.