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We present a scalable low dimensional manifold model for the reconstructionof noisy and incomplete hyperspectral images. The model is based on theobservation that the spatial-spectral blocks of a hyperspectral image typicallylie close to a collection of low dimensional manifolds. To emphasize this, thedimension of the manifold is directly used as a regularizer in a variationalfunctional, which is solved efficiently by alternating direction ofminimization and weighted nonlocal Laplacian. Unlike general 3D images, thesame similarity matrix can be shared across all spectral bands for ahyperspectral image, therefore the resulting algorithm is much more scalablethan that for general 3D data. Numerical experiments on the reconstruction ofhyperspectral images from sparse and noisy sampling demonstrate the superiorityof our proposed algorithm in terms of both speed and accuracy.

Scalable low dimensional manifold model in the reconstruction of noisy and incomplete hyperspectral images