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 which stabilizes the training and improves the restoration results. In the experiments, we 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.

翻译：本文提出了一种基于随机微分方程的通用图像恢复方法。关键构造在于一个均值回归随机微分方程，该方程将高质量图像转化为带有固定高斯噪声的退化状态作为均值状态。通过模拟相应的逆向时间随机微分方程，我们无需依赖任何任务特定先验知识即可恢复低质量图像的原始状态。值得注意的是，所提出的均值回归随机微分方程具有闭式解，这使得我们能够计算真实的时间依赖得分函数，并通过神经网络进行学习。此外，我们提出了最大化似然目标来学习最优逆向轨迹，从而稳定训练过程并提升恢复效果。实验表明，所提方法在图像去雨、去模糊和去噪任务中取得了极具竞争力的定量性能，并在两个去雨数据集上创造了新的最先进水平。最后，通过图像超分辨率、修复和去雾的定性结果进一步证明了该方法的广泛适用性。代码已开源至：https://github.com/Algolzw/image-restoration-sde。