Abstract: Using the wavelet tight frame and total variation, a novel image inpainting model is proposed. In this model, the L0 norm is introduced to be the fidelity term; sparsity and total variation are the regularization terms. The  proposed model makes use of the advantages of sparsity and total variation, which approach the piecewise constant and smooth nature images and preserve the structures of images better. Due to the numerical difficulties for the L0 norm, it firstly turns the primal problem into the two subproblems using the alternating direction method, and then gives the corresponding numerical algorithm for the two subproblems respectively. The numerical experiments show that the proposed model can obtain the better inpainting results.

Key words: tight frame, total variation, image inpainting, alternating direction method

摘要： 利用小波紧框架和全变分，提出了一个新的图像修复模型。该模型将稀疏和全变分作为正则项，L0范数作为数据保真项。其充分利用全变分和紧框架各自的优点，即对分片常值和光滑图像有效地逼近，同时保持图像的几何特征不被破坏。由于L0范数不易求解，利用交替方向法将原问题化为两个子问题，并分别对两个子问题给出相应的数值算法。实验结果表明：相比于基于小波紧框架的图像修复方法或基于全变分的图像修的方法，该模型能够获得更好的修复结果。

关键词: 紧框架, 全变分, 图像修复, 交替方向法