  Compressive spectral imaging (CSI) has emerged as an alternative spectral
image acquisition technology, which reduces the number of measurements at the
cost of requiring a recovery process. In general, the reconstruction methods
are based on hand-crafted priors used as regularizers in optimization
algorithms or recent deep neural networks employed as an image generator to
learn a non-linear mapping from the low-dimensional compressed measurements to
the image space. However, these data-driven methods need many spectral images
to obtain good performance. In this work, a deep recovery framework for CSI
without training data is presented. The proposed method is based on the fact
that the structure of some deep neural networks and an appropriated
low-dimensional structure are sufficient to impose a structure of the
underlying spectral image from CSI. We analyzed the low-dimension structure via
the Tucker representation, modeled in the first net layer. The proposed scheme
is obtained by minimizing the $\ell_2$-norm distance between the compressive
measurements and the predicted measurements, and the desired recovered spectral
image is formed just before the forward operator. Simulated and experimental
results verify the effectiveness of the proposed method.
