关键词: 总广义变分小波修复, 紧框架系统, 多层紧框架分解, 低阶与高阶导数项, 分裂技术, 原始-对偶算法

Abstract: In view of the disadvantage of traditional Total Generalized Variational（TGV） wavelet inpainting model, which adopts a single wavelet transforms and has a good effect on the image with less textures details and simple structure merely, a new model named total generalized variational image inpainting model based on compact frame domain is proposed. In contrast to traditional wavelet inpainting model, compact frame system has many excellent characteristics, such as redundancy, time shift invariant and linear phase, which is important in image processing. New model can make constraint on image by introducing lower order and higher order derivative of multi-level tight frame decomposition coefficient, and get the characteristic information of many different directions in the multiscale. The numerical implementation of model adopts an optimization algorithm which connects splitting technique and primal-dual algorithm（PDSBA）, then solves two simple sub problems by alternate iteration, and improves the computational efficiency of image restoration. Compared to the related model, new model can not only reduce staircase effect and produce image edge, but also can restore images that have much detail and texture information. The experiment results show that three restoration performance indexes Peak Signal to Noise Ratio（PSNR）, Mean Square Error（MAE） and Structural Similarity?Index Measure （SSIM） are all significantly improved.

Key words: Total Generalized Variational（TGV） wavelet inpainting, tight frame system, multi-level compact frame decomposition, lower order and higher order derivative, splitting technique, primal-dual algorithm