Enhanced Total Generalized Variation Method Based On Generalized Moreau Envelope

Image restoration with total variation(TV)and total generalized variation(TGV)reg-ularization has been proved to be a creditable method and used broadly,but this method is imperfect in retaining image details.This paper proposes a non-convex and non-separable regularization term based on TGV enhancement,which can maintain the strict convexity of the total cost function and avoid the underestimation of the TGV method.The new regularization is obtained by subtracting the Moreau envelope of TGV from the TGV term,in which the former is defined by infimal convolution.At the same time,the propoesd non-convex model constructed in this paper has higher accuracy than TGV model in so-lution estimation,it also overcomes the drawback of TGV model in signal smoothing and can retain the details of the image well.To minimize the cost function,the proximal forward-backward splitting(FBS)al-gorithm is applied,and the alternating direction method of multipliers with adaptive pa-rameter estimation(APEADMM),which avoids the drawbacks of FBS algorithm,is proposed by applying the variable splitting and the augment Lagrangian method(ALM).This proposed algorithm with GMETGV method can update the regularization parame-ter adaptively.Experiments varify that the proposed method is more accurate in solution estimation than the other promoted ones,and the new APEADMM algorithm with new regularization shows improved effects of image restoration.