Image restoration has experienced significant advancements due to the development of deep learning. Nevertheless, it encounters challenges related to ill-posed problems, resulting in deviations between single model predictions and ground-truths. Ensemble learning, as a powerful machine learning technique, aims to address these deviations by combining the predictions of multiple base models. Most existing works adopt ensemble learning during the design of restoration models, while only limited research focuses on the inference-stage ensemble of pre-trained restoration models. Regression-based methods fail to enable efficient inference, leading researchers in academia and industry to prefer averaging as their choice for post-training ensemble. To address this, we reformulate the ensemble problem of image restoration into Gaussian mixture models (GMMs) and employ an expectation maximization (EM)-based algorithm to estimate ensemble weights for aggregating prediction candidates. We estimate the range-wise ensemble weights on a reference set and store them in a lookup table (LUT) for efficient ensemble inference on the test set. Our algorithm is model-agnostic and training-free, allowing seamless integration and enhancement of various pre-trained image restoration models. It consistently outperforms regression based methods and averaging ensemble approaches on 14 benchmarks across 3 image restoration tasks, including super-resolution, deblurring and deraining. The codes and all estimated weights have been released in Github.

翻译：得益于深度学习的发展，图像复原领域已取得显著进展。然而，该任务仍面临不适定问题带来的挑战，导致单一模型的预测结果与真实值之间存在偏差。集成学习作为一种强大的机器学习技术，旨在通过结合多个基模型的预测来缓解此类偏差。现有研究大多在复原模型设计阶段采用集成学习，而针对预训练复原模型在推理阶段进行集成的研究则相对有限。基于回归的方法难以实现高效推理，使得学界与工业界更倾向于采用均值融合作为训练后集成方案。为此，我们将图像复原的集成问题重新表述为高斯混合模型，并采用基于期望最大化的算法来估计用于聚合候选预测的集成权重。我们在参考集上估计范围化集成权重，并将其存储于查找表中，以实现测试集上的高效集成推理。本算法具有模型无关性与免训练特性，可无缝集成并增强各类预训练图像复原模型。在超分辨率、去模糊和去雨三种图像复原任务的14个基准测试中，本方法持续优于基于回归的方法与均值集成策略。相关代码及全部估计权重已在GitHub平台开源。