Structural Adaptive Total Variation-Type Image Denoising Model

The regularization methods of image restoration problem have become an increasing-ly popular method,the key problem is to choose an effective regular term in the model.In the past few decades,a regularization methods based on total variation(TV)have been used for many image processing problems.Although the total variation(TV)model has a better edge preservation ability,since only the difference between the horizontal and vertical directions is considered in the calculation,so it does not effectively describe the local features of the image.Then the difference operator is rotated and weighted by intro-ducing a rotation matrix and a weighted matrix,researchers proposed a directional total variation(DTV)model.Our thesis proposes a new model based on the direction total variation(DTV)model,and solved it by effective numerical method.The main contents are as follows:· In order to more effectively describe the local structure of the image and make the restoration effect more robust,this thesis proposes an adaptive direction total vari-ation(ADTV)model based on the direction total variation model,which the local structure of the image can be effectively described by the gradient operator coupling the rotation operator and the weighting operator.Obtaining the adaptive angle used in the rotation operator ?(f)through the orientation field estimation(OFE)?it mainly depends on the average phase angle of pixels with a neighborhood.· Made some improvements based on the regular term of adaptive direction total varia-tion(ADTV)model,which using the non-convex lP-module term as the regular term,we propose a robust structural adaptive total variation-type image denoising mod-el(ADTVP).· Since the proposed model is non-convex and non-Lipschitz,therefore,we use the alternating direction multiplier method(ADMM)to solve the original problem,and use the alternating direction method(ADM)to solve the l2—lp subproblem under the semi-quadratic type,then the convergence analysis of the Lagrangian function is proved in the theoretical part.By comparing numerical results with the total variation model(ROF),the directional total variation model(DTV):the high-order total vari-ation model(HOTV)and the generalized total variation model(TGV),experimental results show that the proposed model and numerical method can effectively preserve the texture and details of the image structure.