The Second-Order Shannon Total Generalized Variation for Image Restoration

Abstract

In this paper, a Shannon-based second-order TGV (Shannon TGV) is proposed. Shannon first and second-order operators are defined and their corresponding adjoints are investigated leading to design a variational model as an optimization problem. We obtain the dual form of the proposed model and utilize it to formulate imaging problems, i.e., denoising and deconvolution. Moreover, we examine numerically the effectiveness of the proposed scheme in imaging problems and compare the results to the classic total variation (TV), the second-order total generalized variation (TGV) and Shannon total variation. The outcomes confirm that the proposed model retains the advantages of both TGV and Shannon TV in elimination of artifacts simultaneously and admit the greater capability of the new model to remove artifacts.