Low Dimensional Manifold Model in Hyperspectral Image Reconstruction

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

Information Theory Numerical Analysis and Scientific Computing mathscidoc:1709.25001

We present the application of a low dimensional manifold model (LDMM) on hyperspectral image (HSI) reconstruction. An important property of hyperspectral images is that the patch manifold, which is sampled by the three-dimensional blocks in the data cube, is generally of a low dimensional nature. This is a generalization of low-rank models in that hyperspectral images with nonlinear mixing terms can also fit in this framework. The point integral method (PIM) is used to solve a Laplace-Beltrami equation over a point cloud sampling the patch manifold in LDMM. Both numerical simulations and theoretical analysis show that the sample points constraint is correctly enforced by PIM. The framework is demonstrated by experiments on the reconstruction of both linear and nonlinear mixed hyperspectral images with a significant number of missing voxels and several entirely missing spectral bands.
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@inproceedings{zuoqianglow,
  title={Low Dimensional  Manifold  Model in  Hyperspectral Image Reconstruction},
  author={Zuoqiang Shi, Wei Zhu, and Stanley Osher},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170925160054638898817},
}
Zuoqiang Shi, Wei Zhu, and Stanley Osher. Low Dimensional Manifold Model in Hyperspectral Image Reconstruction. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170925160054638898817.
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