  The challenges in recovering underwater images are the presence of diverse
degradation factors and the lack of ground truth images. Although synthetic
underwater image pairs can be used to overcome the problem of inadequately
observing data, it may result in over-fitting and enhancement degradation. This
paper proposes a model-based deep learning method for restoring clean images
under various underwater scenarios, which exhibits good interpretability and
generalization ability. More specifically, we build up a multi-variable
convolutional neural network model to estimate the clean image, background
light and transmission map, respectively. An efficient loss function is also
designed to closely integrate the variables based on the underwater image
model. The meta-learning strategy is used to obtain a pre-trained model on the
synthetic underwater dataset, which contains different types of degradation to
cover the various underwater environments. The pre-trained model is then
fine-tuned on real underwater datasets to obtain a reliable underwater image
enhancement model, called MetaUE. Numerical experiments demonstrate that the
pre-trained model has good generalization ability, allowing it to remove the
color degradation for various underwater attenuation images such as blue, green
and yellow, etc. The fine-tuning makes the model able to adapt to different
underwater datasets, the enhancement results of which outperform the
state-of-the-art underwater image restoration methods. All our codes and data
are available at \url{https://github.com/Duanlab123/MetaUE}.
