Reconstructing an image from noisy and incomplete measurements is a central task in several image processing applications. In recent years, state-of-the-art reconstruction methods have been developed based on recent advances in deep learning. Especially for highly underdetermined problems, maintaining data consistency is a key goal. This can be achieved either by iterative network architectures or by a subsequent projection of the network reconstruction. However, for such approaches to be used in safety-critical domains such as medical imaging, the network reconstruction should not only provide the user with a reconstructed image, but also with some level of confidence in the reconstruction. In order to meet these two key requirements, this paper combines deep null-space networks with uncertainty quantification. Evaluation of the proposed method includes image reconstruction from undersampled Radon measurements on a toy CT dataset and accelerated MRI reconstruction on the fastMRI dataset. This work is the first approach to solving inverse problems that additionally models data-dependent uncertainty by estimating an input-dependent scale map, providing a robust assessment of reconstruction quality.

翻译：从含噪且不完整的测量值中重建图像是多个图像处理应用中的核心任务。近年来，基于深度学习的最新进展，人们开发了多种最先进的重建方法。尤其是在高度欠定问题中，保持数据一致性是一个关键目标。这可以通过迭代网络架构或对网络重建结果进行后续投影来实现。然而，对于此类方法在医学成像等安全关键领域的应用，网络重建不仅应向用户提供重建图像，还应提供一定程度的置信度评估。为同时满足这两个关键要求，本文结合了深度零空间网络与不确定性量化方法。所提方法的评估包括在玩具CT数据集上对欠采样Radon测量的图像重建，以及在fastMRI数据集上的加速MRI重建。本研究是首个通过估计输入依赖的尺度图来额外建模数据相关不确定性以解决逆问题的方法，从而提供了对重建质量的稳健评估。