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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.

No abstract uploaded!

No abstract uploaded!

We prove rigidity results for a class of non-uniformly hyperbolic holomorphic maps. If a holomorphic Collet-Eckmann map$f$is topologically conjugate to a holomorphic map$g$, then the conjugacy can be improved to be quasiconformal. If there is only one critical point in the repeller, then$g$is Collet-Eckmann, too.