Image Deblurring Using a Projective Inertial Parallel Subgradient Extragradient-Line Algorithm of Variational Inequality Problems

Abstract

In this paper, we introduce projective inertial parallel subgradient extragradient-line algorithm for solving variational inequalites of L-Lipschitz continuous and monotone mappings which L is unknown. We prove a strong convergence result under some mild conditions in Hilbert space. We also present some numerical examples in Euclidean space R3 compared with Parallel-Viscosity-Type Subgradi-ent Extragradient-Line Method. Finally, we deblur the Grey and RGB images from common types of blur matrixes Gaussian blur, Out of focus blur and Motion blur using our proposed algorithm and show the better efficeincy when the number of types of blur matrixes is large.