  Pan-sharpening is an important technique for remote sensing imaging systems
to obtain high resolution multispectral images. Recently, deep learning has
become the most popular tool for pan-sharpening. This paper develops a
model-based deep pan-sharpening approach. Specifically, two optimization
problems regularized by the deep prior are formulated, and they are separately
responsible for the generative models for panchromatic images and low
resolution multispectral images. Then, the two problems are solved by a
gradient projection algorithm, and the iterative steps are generalized into two
network blocks. By alternatively stacking the two blocks, a novel network,
called gradient projection based pan-sharpening neural network, is constructed.
The experimental results on different kinds of satellite datasets demonstrate
that the new network outperforms state-of-the-art methods both visually and
quantitatively. The codes are available at https://github.com/xsxjtu/GPPNN.
