  Pan-sharpening aims to generate a high-resolution multispectral (HRMS) image
by integrating the spectral information of a low-resolution multispectral
(LRMS) image with the texture details of a high-resolution panchromatic (PAN)
image. It essentially inherits the ill-posed nature of the super-resolution
(SR) task that diverse HRMS images can degrade into an LRMS image. However,
existing deep learning-based methods recover only one HRMS image from the LRMS
image and PAN image using a deterministic mapping, thus ignoring the diversity
of the HRMS image. In this paper, to alleviate this ill-posed issue, we propose
a flow-based pan-sharpening network (PanFlowNet) to directly learn the
conditional distribution of HRMS image given LRMS image and PAN image instead
of learning a deterministic mapping. Specifically, we first transform this
unknown conditional distribution into a given Gaussian distribution by an
invertible network, and the conditional distribution can thus be explicitly
defined. Then, we design an invertible Conditional Affine Coupling Block (CACB)
and further build the architecture of PanFlowNet by stacking a series of CACBs.
Finally, the PanFlowNet is trained by maximizing the log-likelihood of the
conditional distribution given a training set and can then be used to predict
diverse HRMS images. The experimental results verify that the proposed
PanFlowNet can generate various HRMS images given an LRMS image and a PAN
image. Additionally, the experimental results on different kinds of satellite
datasets also demonstrate the superiority of our PanFlowNet compared with other
state-of-the-art methods both visually and quantitatively.
