# Improved Partial Differential Equation and Fast Approximation Algorithm for Hazy/Underwater/Dust Storm Image Enhancement

arXiv: https://arxiv.org/abs/2502.15986 · HTML: https://mlsanity.com/paper/2502.15986/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 44 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Builds on (most cited first, 2 of 2)

- [Color Image Enhancement In the Framework of Logarithmic Models](https://mlsanity.com/paper/1412.5325/) (2014)
- [A PDE-based log-agnostic illumination correction algorithm](https://mlsanity.com/paper/1801.00098/) (2017)

## Abstract (arXiv)

This paper presents an improved and modified partial differential equation (PDE)-based de-hazing algorithm. The proposed method combines logarithmic image processing models in a PDE formulation refined with linear filter-based operators in either spatial or frequency domain. Additionally, a fast, simplified de-hazing function approximation of the hazy image formation model is developed in combination with fuzzy homomorphic refinement. The proposed algorithm solves the problem of image darkening and over-enhancement of edges in addition to enhancement of dark image regions encountered in previous formulations. This is in addition to avoiding enhancement of sky regions in de-hazed images while avoiding halo effect. Furthermore, the proposed algorithm is utilized for underwater and dust storm image enhancement with the incorporation of a modified global contrast enhancement algorithm. Experimental comparisons indicate that the proposed approach surpasses a majority of the algorithms from the literature based on quantitative image quality metrics.