Learning truly monotone operators with applications to nonlinear inverse problems

arXiv:2404.00390v1 Announce Type: cross
Abstract: This article introduces a novel approach to learning monotone neural networks through a newly defined penalization loss. The proposed method is particularly effective in solving classes of variational problems, specifically monotone inclusion problems, commonly encountered in image processing tasks. The Forward-Backward-Forward (FBF) algorithm is employed to address these problems, offering a solution even when the Lipschitz constant of the neural network is unknown. Notably, the FBF algorithm provides convergence guarantees under the condition that the …

abstract algorithm applications article arxiv cs.lg cs.na image image processing inclusion loss math.na math.oc networks neural networks novel operators processing tasks through type