  Currently, most single image dehazing models cannot run an
ultra-high-resolution (UHD) image with a single GPU shader in real-time. To
address the problem, we introduce the principle of infinite approximation of
Taylor's theorem with the Laplace pyramid pattern to build a model which is
capable of handling 4K hazy images in real-time. The N branch networks of the
pyramid network correspond to the N constraint terms in Taylor's theorem.
Low-order polynomials reconstruct the low-frequency information of the image
(e.g. color, illumination). High-order polynomials regress the high-frequency
information of the image (e.g. texture). In addition, we propose a Tucker
reconstruction-based regularization term that acts on each branch network of
the pyramid model. It further constrains the generation of anomalous signals in
the feature space. Extensive experimental results demonstrate that our approach
can not only run 4K images with haze in real-time on a single GPU (80FPS) but
also has unparalleled interpretability.
  The developed method achieves state-of-the-art (SOTA) performance on two
benchmarks (O/I-HAZE) and our updated 4KID dataset while providing the reliable
groundwork for subsequent optimization schemes.
