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.

翻译：全色锐化旨在以对应全色（PAN）图像为指导，提升低分辨率多光谱（LrMS）图像的空间分辨率。尽管基于深度学习（DL）的全色锐化方法已取得显著性能，但多数方法存在双重缺陷：其一，普遍采用的黑箱原理限制了模型可解释性；其二，现有基于DL的方法无法同时高效捕获局部与全局依赖关系，不可避免地制约了整体性能。针对上述问题，我们首先将高分辨率多光谱（HrMS）图像的退化过程构建为统一变分优化问题，并通过设计的迭代近端梯度下降（PGD）算法交替求解其数据子问题与先验子问题。进而定制局部-全局Transformer（LGT）以同步建模局部与全局依赖关系，并据此构建基于LGT的先验模块用于图像去噪。除先验模块外，我们还设计了轻量级数据模块。最后，通过在每次迭代阶段中串联集成数据模块与先验模块，将迭代算法展开为阶段式展开网络——局部-全局Transformer增强展开网络（LGTEUN），以实现可解释的多光谱全色锐化。在三个卫星数据集上的全面实验结果表明，相较于最先进（SOTA）方法，LGTEUN在有效性与效率方面均具优势。源代码已开源至https://github.com/lms-07/LGTEUN。