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：在图像处理应用中，从嘈杂和不完整的测量结果中重建图像是一项核心任务。近年来，基于深度学习的先进重建方法已被开发并应用。特别是对于高度欠定的问题，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随后的网络重建投影来实现。然而，对于这样的方法在医学成像等安全关键领域的使用，网络重建不仅应该提供用户重建出的图像，还要提供有关重建的一定信心水平。为了满足这两个关键要求，本文将深度零空间网络与不确定性量化相结合。该方法的评估包括通过玩具CT数据集的欠采样Radon测量来进行图像重建以及通过fastMRI数据集的加速MRI重建。该工作是通过估算输入相关的比例图来估计数据依赖的不确定性，从而提供了有关重建质量的稳健评估而解决了反问题的第一种方法。