This paper introduces a novel partial differential equation (PDE) framework for single-image dehazing. We embed the atmospheric scattering model into a PDE featuring edge-preserving diffusion and a nonlocal operator to maintain both local details and global structures. A key innovation is an adaptive regularization mechanism guided by the dark channel prior, which adjusts smoothing strength based on haze density. The framework's mathematical well-posedness is rigorously established by proving the existence and uniqueness of its weak solution in H01(Ω). An efficient, GPU-accelerated fixed-point solver is used for implementation. Experiments confirm our method achieves effective haze removal while preserving high image fidelity, offering a principled alternative to purely data-driven techniques.
@article{arxiv.2506.08793,
title = {A PDE-Based Image Dehazing Method via Atmospheric Scattering Theory},
author = {Liubing Hu and Pu Wang and Guangwei Gao and Chunyan Wang and Zhuoran Zheng},
journal= {arXiv preprint arXiv:2506.08793},
year = {2025}
}