A PDE-Based Image Dehazing Method via Atmospheric Scattering Theory

TL;DR

This work tackles single-image dehazing by embedding the atmospheric scattering model into a PDE framework that simultaneously enforces physical fidelity and preserves image structure. The model combines edge-preserving diffusion, a nonlocal Gaussian regularization, and adaptive regularization guided by the dark channel prior, solved via a GPU-accelerated fixed-point method. A rigorous existence-and-uniqueness analysis in the Sobolev space $H_0^1(\Omega)$ guarantees well-posedness through the Lax-Milgram theorem. Experimental results on real-world hazy images show competitive to state-of-the-art performance across NR-IQA metrics and qualitative visual quality, highlighting the practical value of a principled, physically grounded alternative to purely data-driven dehazing methods, with potential for hybrid physics-informed learning.

Abstract

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.

Figures (3)

• Figure 1: Qualitative comparison with state-of-the-art dehazing methods on real-world hazy images.
• Figure 2: Visual results of the ablation study.
• Figure 3: Distribution of best visual quality votes.

Theorems & Definitions (4)

• Lemma 1
• proof
• Theorem 2
• proof