结构保持图拉普拉斯正则的快速图像修复

为了让信息从周围向待修复区域填充时保持图像边缘结构，提出结构保持图拉普拉斯正则的图像修复模型.该模型在信号依赖的图拉普拉斯矩阵基础上，引入梯度图像平滑约束，能够促进目标函数的最优解收敛至分片平面图像；此外，该模型转化为无约束二次规划问题，可以通过共轭梯度法快速求解.实验结果表明，所提的图像修复算法相比于现有图像修复算法不仅速度快，而且可以克服图拉普拉斯正则图像修复算法所产生的块效应，使得复原后的图像更加自然.

Structure-preserving graph Laplacian regularizer for fast image inpainting

Graph Laplacian regularizer can promote the piecewise smoothness of signals and is widely applied to various image restoration tasks in recent years. A structure-preserving graph Laplacian regularizer is proposed for image restoration to improve structure-preserving of image edges while information propagation from the surrounding known regions to the unknown. Based on the signal-dependent graph Laplace matrix, the model introduces gradient image smoothness to promote the objective function to converge to the piecewise planar images. The proposed model is transformed into an unconstrained quadratic programming problem, which can be solved quickly by the conjugate gradient method. The experimental results show that the speed of the proposed algorithm is not only faster than the existing restoration algorithms, but also can restore images which look less blocky and more natural than traditional Laplacian regularizer.