基于低秩矩阵优化的纹理图像修复

Low rank texture repairing by convex optimization

提出了1种新的低秩纹理图像修复算法,该算法将低秩纹理图像修复问题建模成低秩矩阵优化问题进行求解。由于单纯使用低秩假设不足以描述自然图像的性质,因此除了纹理的低秩性以外,算法还使用了自然图像的连续性假设:在优化目标函数中加入了总变分算子。结合纹理的低秩性和连续性假设,提出了基于凸优化的纹理图像修复算法,可以在不知道图像损毁区域的情况下自动检测损毁区域并修复纹理图像。通过结合图像的低秩性假设和连续性假设,此算法有效弥补了单纯使用低秩假设的不足之处。该算法可以有效修复低秩纹理图像,且无论是在主观视觉效果还是客观量化指标上全面优于现有同类算法。

A new low rank texture image repairing algorithm is proposed. It models texture image repairing as solving a low rank matrix optimization problem. The continuity assumption of natural images is also used in the algorithm, by adding the total varia-tion operator to the optimization objective function, since only low rank assumption is insufficient for describing the properties of natural images,and large corruption will lead to unsatisfactory repairing results or serious loss of image details,in addition to the low rank assumption Our low rankness based algorithm can automatically and correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. Via combining the low rank assumption and the con-tinuity assumption, the proposed algorithm can make up for the deficiency of the simple use of low rank assumption The algo-rithm can effectively fill in the missing part in low rank texture images, and presents better performance than existing algorithms in both subjective visual effect and objective quantitative measures.