基于物理模型的图像去雾方法，兼顾细节保留与全局结构。
A PDE-Based Image Dehazing Method via Atmospheric Scattering Theory
- 用偏微分方程融合散射模型，结合边缘保持与非局部算子。
- 自适应正则化根据雾霾密度调节平滑强度，提升去雾效果。
- 数学上证明解的存在唯一性，适合追求可解释性的研究者。
本文提出一种基于偏微分方程（PDE）的单幅图像去雾新框架。将大气散射模型嵌入具有边缘保持扩散和非局部算子的PDE中，以同时保留局部细节与全局结构。关键创新在于引入由暗通道先验引导的自适应正则化机制，根据雾霾密度动态调整平滑强度。该框架在 $H_0^1(Ω)$ 空间中严格证明了弱解的存在性与唯一性。采用高效的GPU加速定点迭代求解器实现。实验表明，该方法能有效去除雾霾，同时保持高图像保真度，为纯数据驱动方法提供了一种有理论依据的替代方案。
原文摘要 · Abstract (English)
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 $H_0^1(Ω)$. 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.
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