An Iterative PDE Based Illumination Restoration Scheme for Image Enhancement

TL;DR

This paper introduces an iterative PDE-based method for restoring uneven illumination in grayscale images, improving image quality metrics through a novel mathematical framework and demonstrating its effectiveness on standard tests.

Contribution

The paper proposes a new iterative PDE scheme for illumination correction, with proven convergence and superior performance over classical methods.

Findings

Reported PSNR and SSIM improvements on test images.

Proven existence and uniqueness of the solution.

Demonstrated convergence of the iterative scheme.

Abstract

We present a novel iterative scheme for restoring uneven illumination in grayscale images. Our approach solves, at each global iteration, a nonlinear elliptic equation for an auxiliary field $u$ and then updates the illumination via an explicit time-marching step driven by the logarithmic potential of $u$. We establish existence and uniqueness of the discrete subproblems, analyze convergence of the fixed point iteration, and demonstrate performance on standard test images, reporting PSNR and SSIM gains over classical methods. Future work will address color coupling and GPU acceleration.