  Hyperspectral (HS) and multispectral (MS) image fusion aims at estimating a
high-resolution spectral image from a low-spatial-resolution HS image and a
low-spectral-resolution MS image. Compressive spectral imaging (CSI) has
emerged as an acquisition framework that captures the relevant information of
spectral images using a reduced number of snapshots. Various spectral image
fusion methods from multi-sensor CSI measurements have been proposed.
Nevertheless, these methods exhibit high running times and face the drawback of
choosing a representation transform. In this work, a deep learning architecture
under the algorithm unrolling approach is proposed for solving the fusion
problem from HS and MS 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
forms a deep network. The linearized approach leads to estimate the target
variable without resorting to expensive matrix operations. This approach also
estimates the image high-frequency component included in both the auxiliary
variable and the Lagrange multiplier. 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 data.
