Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. However, fully sampled data is often unavailable in a variety of problems, including the recovery of dynamic and high-resolution magnetic resonance imaging (MRI). We introduce a novel variational approach to learn a manifold from undersampled data. The VAE uses a decoder fed by latent vectors, drawn from a conditional density estimated from the fully sampled images using an encoder. Since fully sampled images are not available in our setting, we approximate the conditional density of the latent vectors by a parametric model whose parameters are estimated from the undersampled measurements using back-propagation. We use the framework for the joint alignment and recovery of multi-slice free breathing and ungated cardiac MRI data from highly undersampled measurements. Experimental results demonstrate the utility of the proposed scheme in dynamic imaging alignment and reconstructions.

中文翻译：

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从不完整数据中进行变分流形学习：在多层动态 MRI 中的应用


当前基于深度学习的流形学习算法，例如变分自动编码器（VAE），需要完全采样的数据来学习现实世界数据集的概率密度。然而，在各种问题中通常无法获得完全采样的数据，包括动态和高分辨率磁共振成像 (MRI) 的恢复。我们引入了一种新颖的变分方法来从欠采样数据中学习流形。 VAE 使用由潜在向量馈送的解码器，这些潜在向量是根据使用编码器从完全采样图像估计的条件密度得出的。由于完全采样的图像在我们的设置中不可用，因此我们通过参数模型来近似潜在向量的条件密度，该模型的参数是使用反向传播从欠采样测量中估计的。我们使用该框架对来自高度欠采样测量的多切片自由呼吸和非门控心脏 MRI 数据进行联合对齐和恢复。实验结果证明了该方案在动态成像对准和重建中的实用性。