  We present a scalable low dimensional manifold model for the reconstruction
of noisy and incomplete hyperspectral images. The model is based on the
observation that the spatial-spectral blocks of a hyperspectral image typically
lie close to a collection of low dimensional manifolds. To emphasize this, the
dimension of the manifold is directly used as a regularizer in a variational
functional, which is solved efficiently by alternating direction of
minimization and weighted nonlocal Laplacian. Unlike general 3D images, the
same similarity matrix can be shared across all spectral bands for a
hyperspectral image, therefore the resulting algorithm is much more scalable
than that for general 3D data. Numerical experiments on the reconstruction of
hyperspectral images from sparse and noisy sampling demonstrate the superiority
of our proposed algorithm in terms of both speed and accuracy.
