Image restoration, or inverse problems in image processing, has long been an extensively studied topic. In recent years supervised learning approaches have become a popular strategy attempting to tackle this task. Unfortunately, most supervised learning-based methods are highly demanding in terms of computational resources and training data (sample complexity). In addition, trained models are sensitive to domain changes, such as varying acquisition systems, signal sampling rates, resolution and contrast. In this work, we try to answer a fundamental question: Can supervised learning models generalize well solely by learning from one image or even part of an image? If so, then what is the minimal amount of patches required to achieve acceptable generalization? To this end, we focus on an efficient patch-based learning framework that requires a single image input-output pair for training. Experimental results demonstrate the applicability, robustness and computational efficiency of the proposed approach for supervised image deblurring and super-resolution. Our results showcase significant improvement of learning models' sample efficiency, generalization and time complexity, that can hopefully be leveraged for future real-time applications, and applied to other signals and modalities.

翻译：图像复原，即图像处理中的逆问题，长期以来一直是广泛研究的课题。近年来，有监督学习方法已成为应对这一任务的流行策略。然而，大多数基于有监督学习的方法在计算资源和训练数据（样本复杂度）方面要求极高。此外，训练模型对领域变化（如不同的采集系统、信号采样率、分辨率和对比度）较为敏感。本文试图回答一个基本问题：有监督学习模型能否仅通过学习单张图像甚至图像的一部分就能实现良好的泛化？若能，那么为达到可接受的泛化效果所需的最小图像块数量是多少？为此，我们聚焦于一个高效的基于图像块的学习框架，该框架仅需一对输入-输出图像进行训练。实验结果表明，所提方法在有监督图像去模糊和超分辨率任务中具有适用性、鲁棒性和计算效率。我们的结果展示了学习模型在样本效率、泛化能力和时间复杂度方面的显著提升，有望应用于未来的实时场景，并拓展至其他信号与模态。