Image Restoration with Mean-Reverting Stochastic Differential Equations

TL;DR

This paper introduces a novel mean-reverting stochastic differential equation framework for general image restoration tasks, enabling high-quality image recovery without task-specific priors and achieving state-of-the-art results.

Contribution

The authors develop a mean-reverting SDE with a closed-form solution for image restoration, incorporating a maximum likelihood training objective for improved stability and performance.

Findings

Achieves state-of-the-art results on image deraining datasets.

Demonstrates versatility across multiple restoration tasks like deblurring and denoising.

Provides a unified SDE-based approach for various image restoration problems.

Abstract

This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean state with fixed Gaussian noise. Then, by simulating the corresponding reverse-time SDE, we are able to restore the origin of the low-quality image without relying on any task-specific prior knowledge. Crucially, the proposed mean-reverting SDE has a closed-form solution, allowing us to compute the ground truth time-dependent score and learn it with a neural network. Moreover, we propose a maximum likelihood objective to learn an optimal reverse trajectory that stabilizes the training and improves the restoration results. The experiments show that our proposed method achieves highly competitive performance in quantitative comparisons on image deraining, deblurring, and denoising, setting a new state-of-the-art on two deraining datasets. Finally, the general applicability of our approach is further demonstrated via qualitative results on image super-resolution, inpainting, and dehazing. Code is available at https://github.com/Algolzw/image-restoration-sde.