  This paper presents several strategies for spectral de-noising of
hyperspectral images and hypercube reconstruction from a limited number of
tomographic measurements. In particular we show that the non-noisy spectral
data, when stacked across the spectral dimension, exhibits low-rank. On the
other hand, under the same representation, the spectral noise exhibits a banded
structure. Motivated by this we show that the de-noised spectral data and the
unknown spectral noise and the respective bands can be simultaneously estimated
through the use of a low-rank and simultaneous sparse minimization operation
without prior knowledge of the noisy bands. This result is novel for for
hyperspectral imaging applications. In addition, we show that imaging for the
Computed Tomography Imaging Systems (CTIS) can be improved under limited angle
tomography by using low-rank penalization. For both of these cases we exploit
the recent results in the theory of low-rank matrix completion using nuclear
norm minimization.
