Objective: This paper investigates how generative models, trained on ground-truth images, can be used \changes{as} priors for inverse problems, penalizing reconstructions far from images the generator can produce. The aim is that learned regularization will provide complex data-driven priors to inverse problems while still retaining the control and insight of a variational regularization method. Moreover, unsupervised learning, without paired training data, allows the learned regularizer to remain flexible to changes in the forward problem such as noise level, sampling pattern or coil sensitivities in MRI. Approach: We utilize variational autoencoders (VAEs) that generate not only an image but also a covariance uncertainty matrix for each image. The covariance can model changing uncertainty dependencies caused by structure in the image, such as edges or objects, and provides a new distance metric from the manifold of learned images. Main results: We evaluate these novel generative regularizers on retrospectively sub-sampled real-valued MRI measurements from the fastMRI dataset. We compare our proposed learned regularization against other unlearned regularization approaches and unsupervised and supervised deep learning methods. Significance: Our results show that the proposed method is competitive with other state-of-the-art methods and behaves consistently with changing sampling patterns and noise levels.

翻译：目标：本文研究如何将基于真实图像训练生成模型用作逆问题的先验知识，以惩罚远离生成器所能生成图像的图像重建结果。旨在利用学习正则化方法为逆问题提供复杂的数据驱动先验，同时保留变分正则化方法的可控性与洞察力。此外，非成对训练数据的无监督学习策略使学习正则化器能够灵活适应前向问题（如MRI中的噪声水平、采样模式或线圈灵敏度）的变化。方法：我们采用变分自编码器（VAE），该类模型不仅可生成图像，还可同时生成每幅图像的协方差不确定性矩阵。该协方差能够模拟由图像结构（如边缘或物体）引发的动态不确定性依赖关系，并为从学习到的图像流形中测量距离提供新的度量标准。主要结果：基于fastMRI数据集的回顾性子采样实值MRI测量数据，我们评估了这些新型生成式正则化器的性能，并将其与未学习正则化方法及无监督/监督深度学习方法进行对比。意义：实验结果表明，所提方法与现有最优方法性能相当，且在采样模式与噪声水平变化时保持稳定表现。