Low dimensional manifold model with semi-local patches

Zuoqiang Shi Tsinghua University Stanley Osher University of California, Los Angeles Wei Zhu University of California, Los Angeles

Information Theory Numerical Analysis and Scientific Computing mathscidoc:1609.19001

Journal of Scientific Computing
In this paper we integrate semi-local patches and the weighted graph Laplacian into the framework of the low dimensional manifold model. This approach is much faster than the original LDMM algorithm. The number of iterations is typically reduced from 100 to 10 and the equations in each step are much easier to solve. This new approach is tested in image inpainting and denoising and the results are better than the original LDMM and competitive with state-of-the-art methods.
low dimensional manifold model; point integral method; semi-local patch; weighted graph Laplacian
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@inproceedings{zuoqianglow,
  title={Low dimensional manifold model with semi-local patches},
  author={Zuoqiang Shi, Stanley Osher, and Wei Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160902101936656263605},
  booktitle={Journal of Scientific Computing},
}
Zuoqiang Shi, Stanley Osher, and Wei Zhu. Low dimensional manifold model with semi-local patches. In Journal of Scientific Computing. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160902101936656263605.
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