  Image fusion aims at estimating a high-resolution spectral image from a
low-spatial-resolution hyperspectral image and a low-spectral-resolution
multispectral image. In this regard, compressive spectral imaging (CSI) has
emerged as an acquisition framework that captures the relevant information of
spectral images using a reduced number of measurements. Recently, various image
fusion methods from CSI measurements have been proposed. However, these methods
exhibit high running times and face the challenging task of choosing
sparsity-inducing bases. In this paper, a deep network under the algorithm
unrolling approach is proposed for fusing spectral images from compressive
measurements. This architecture, dubbed LADMM-Net, casts each iteration of a
linearized version of the alternating direction method of multipliers into a
processing layer whose concatenation deploys a deep network. The linearized
approach enables obtaining fusion estimates without resorting to costly matrix
inversions. Furthermore, this approach exploits the benefits of learnable
transforms to estimate the image details included in both the auxiliary
variable and the Lagrange multiplier. Finally, the performance of the proposed
technique is evaluated on two spectral image databases and one dataset captured
at the laboratory. Extensive simulations show that the proposed method
outperforms the state-of-the-art approaches that fuse spectral images from
compressive measurements.
