Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom.
Predictive Analytics Lab, Department of Informatics, University of Sussex, BN1 9RH, United Kingdom.
Phys Med Biol. 2023 Aug 3;68(16). doi: 10.1088/1361-6560/ace49a.
This paper investigates how generative models, trained on ground-truth images, can be used 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.We utilize variational autoencoders 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.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.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.
本文研究了如何将基于真实图像训练的生成模型用作逆问题的先验，惩罚与生成器无法生成的图像相差较大的重建。其目的是，通过学习正则化，为逆问题提供复杂的数据驱动的先验，同时仍然保留变分正则化方法的控制和洞察力。此外，无需配对训练数据的无监督学习允许学习的正则化器能够灵活地适应正向问题的变化，例如 MRI 中的噪声水平、采样模式或线圈灵敏度。我们利用变分自动编码器生成不仅图像，而且为每张图像生成协方差不确定性矩阵。协方差可以对图像中结构引起的变化不确定性依赖性进行建模，例如边缘或物体，并提供从学习图像的流形的新距离度量。我们将这些新颖的生成正则化器评估应用于从 fastMRI 数据集的回顾性欠采样真实值 MRI 测量值。我们将我们提出的学习正则化与其他未学习的正则化方法以及无监督和监督深度学习方法进行了比较。我们的结果表明，所提出的方法与其他最先进的方法具有竞争力，并与变化的采样模式和噪声水平一致。
