Self-supervised methods have recently proved to be nearly as effective as supervised methods in various imaging inverse problems, paving the way for learning-based methods in scientific and medical imaging applications where ground truth data is hard or expensive to obtain. This is the case in magnetic resonance imaging and computed tomography. These methods critically rely on invariance to translations and/or rotations of the image distribution to learn from incomplete measurement data alone. However, existing approaches fail to obtain competitive performances in the problems of image super-resolution and deblurring, which play a key role in most imaging systems. In this work, we show that invariance to translations and rotations is insufficient to learn from measurements that only contain low-frequency information. Instead, we propose a new self-supervised approach that leverages the fact that many image distributions are approximately scale-invariant, and that enables recovering high-frequency information lost in the measurement process. We demonstrate throughout a series of experiments on real datasets that the proposed method outperforms other self-supervised approaches, and obtains performances on par with fully supervised learning.

翻译：自监督方法近期在多种成像逆问题中已证明与监督方法几乎同样有效，为难以获取或获取成本高昂的地面真值数据的科学和医学成像应用（如磁共振成像和计算机断层扫描）中的基于学习方法奠定了基础。这些方法关键依赖于图像分布对平移和/或旋转的不变性，从而仅从不完整的测量数据中学习。然而，现有方法在图像超分辨率和去模糊问题（这对大多数成像系统至关重要）中未能取得有竞争力的性能。在本工作中，我们表明对平移和旋转的不变性不足以从仅包含低频信息的测量数据中学习。相反，我们提出了一种新的自监督方法，该方法利用许多图像分布近似具有尺度不变性的特性，从而能够恢复测量过程中丢失的高频信息。通过在真实数据集上的一系列实验，我们证明所提方法优于其他自监督方法，并获得了与全监督学习相当的性能。