Generalization of the Weighted Nonlocal Laplacian in Low Dimensional Manifold Model
Generalization of the Weighted Nonlocal Laplacian in Low Dimensional Manifold Model
复制标题
低维流形模型中加权非局部拉普拉斯的推广
DOI：
10.1007/s10915-017-0549-x
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发表时间：
2018-05-01
影响因子：
2.5
通讯作者：
Zhu, Wei
中科院分区：
文献类型：
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作者：
Shi, Zuoqiang;Osher, Stanley;Zhu, Wei
在本文中，我们使用加权非局部拉普拉斯算子的思想（Shi等人，J Sci Comput，2017）来处理低维流形模型中的约束（Osher等人，SIAM J Imaging Sci，2017）。在原有的线性多参数模型中，约束是通过点积分法来实现的。点积分法提供了一种正确的处理约束的方法，但由于破坏了原有Laplace-Beltrami算子的对称性，其效率不是很高。WNLL提供了另一种在LDMM中实施约束的方法。在WNLL中，离散系统是对称和稀疏的，因此可以非常快速地求解。我们的实验结果表明，WNLL的帮助下，计算成本显着降低。此外，图像修复和去噪的结果也优于原始LDMM，并与最先进的方法竞争。
In this paper we use the idea of the weighted nonlocal Laplacian (Shi et al. in J Sci Comput, 2017) to deal with the constraints in the low dimensional manifold model (Osher et al. in SIAM J Imaging Sci, 2017). In the original LDMM, the constraints are enforced by the point integral method. The point integral method provides a correct way to deal with the constraints, however it is not very efficient due to the fact that the symmetry of the original Laplace–Beltrami operator is destroyed. WNLL provides another way to enforce the constraints in LDMM. In WNLL, the discretized system is symmetric and sparse and hence it can be solved very fast. Our experimental results show that the computational cost is reduced significantly with the help of WNLL. Moreover, the results in image inpainting and denoising are also better than the original LDMM and competitive with state-of-the-art methods.