A PDE-Based Image Dehazing Method via Atmospheric Scattering Theory

TL;DR

This paper presents a PDE-based image dehazing method that integrates atmospheric scattering theory with adaptive regularization, edge-preserving diffusion, and a nonlocal operator to effectively remove haze while maintaining image details.

Contribution

It introduces a novel PDE framework with adaptive regularization guided by the dark channel prior, ensuring effective haze removal and structure preservation.

Findings

Effective haze removal demonstrated in experiments

Preserves local details and global structures

Mathematically well-posed with proven existence and uniqueness

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 $H_0^1(\Omega)$. 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.