  Pan-sharpening aims to increase the spatial resolution of the low-resolution
multispectral (LrMS) image with the guidance of the corresponding panchromatic
(PAN) image. Although deep learning (DL)-based pan-sharpening methods have
achieved promising performance, most of them have a two-fold deficiency. For
one thing, the universally adopted black box principle limits the model
interpretability. For another thing, existing DL-based methods fail to
efficiently capture local and global dependencies at the same time, inevitably
limiting the overall performance. To address these mentioned issues, we first
formulate the degradation process of the high-resolution multispectral (HrMS)
image as a unified variational optimization problem, and alternately solve its
data and prior subproblems by the designed iterative proximal gradient descent
(PGD) algorithm. Moreover, we customize a Local-Global Transformer (LGT) to
simultaneously model local and global dependencies, and further formulate an
LGT-based prior module for image denoising. Besides the prior module, we also
design a lightweight data module. Finally, by serially integrating the data and
prior modules in each iterative stage, we unfold the iterative algorithm into a
stage-wise unfolding network, Local-Global Transformer Enhanced Unfolding
Network (LGTEUN), for the interpretable MS pan-sharpening. Comprehensive
experimental results on three satellite data sets demonstrate the effectiveness
and efficiency of LGTEUN compared with state-of-the-art (SOTA) methods. The
source code is available at https://github.com/lms-07/LGTEUN.
