基于非凸矩阵填充模型的图像修复方法研究

Matrix completion based on non-convex low rank approximation

为了减少基于矩阵核范数极小化(NNM)的矩阵填充模型和原始矩阵的秩极小化(RM)矩阵填充模型之间的偏差,提出了一种新的非凸矩阵填充模型。相对于核范数,其能够更好地逼近原始的秩极小化问题。此外,考虑到非凸模型的优化困难,文中结合增广拉格朗日法和迭代重赋权重法去求解提出的矩阵填充模型。为了验证算法的有效性,在人工数据集上进行了大量实验,并将其应用于图像修复这一重要的计算机视觉领域。实验结果表明,提出的算法能够处理不同类型的缺失图像,且其恢复精度明显高于现有的矩阵填充模型。

This paper develops a novel non-convex matrix completion model for reducing the gap between nuclear norm minimization（NNM） and rank minimization（RM） based on matrix completion model,which is more close to the original rank minimization problem compared with NNM. Considering the obstacle arising in solving the non-convex problem,this research combines the augmented Lagrange multiplier and re-weighted methods to optimize the proposed non-convex completion model. To test the performance of our algorithm,we conducts numerous experiments on generated data,and utilizes it to solve the image inpainting problem which is a significant direction in computer version. The experimental results demonstrate that this method can cope with various incomplete images,and provide a high advantage over state-of-the-art methods.