A central goal of modern magnetic resonance imaging (MRI) is to reduce the time required to produce high-quality images. Efforts have included hardware and software innovations such as parallel imaging, compressed sensing, and deep learning-based reconstruction. Here, we propose and demonstrate a Bayesian method to build statistical libraries of magnetic resonance (MR) images in k-space and use these libraries to identify optimal subsampling paths and reconstruction processes. Specifically, we compute a multivariate normal distribution based upon Gaussian processes using a publicly available library of T1-weighted images of healthy brains. We combine this library with physics-informed envelope functions to only retain meaningful correlations in k-space. This covariance function is then used to select a series of ring-shaped subsampling paths using Bayesian optimization such that they optimally explore space while remaining practically realizable in commercial MRI systems. Combining optimized subsampling paths found for a range of images, we compute a generalized sampling path that, when used for novel images, produces superlative structural similarity and error in comparison to previously reported reconstruction processes (i.e. 96.3% structural similarity and <0.003 normalized mean squared error from sampling only 12.5% of the k-space data). Finally, we use this reconstruction process on pathological data without retraining to show that reconstructed images are clinically useful for stroke identification.

翻译：现代磁共振成像的核心目标之一是缩短生成高质量图像所需的时间。相关努力包括硬件与软件创新，例如并行成像、压缩感知以及基于深度学习的重建方法。本文提出并验证了一种贝叶斯方法，旨在构建k空间磁共振图像的统计库，并利用这些库识别最优子采样路径与重建过程。具体而言，我们基于公开的健康脑部T1加权图像库，通过高斯过程计算多元正态分布，并结合基于物理信息的包络函数，仅保留k空间中具有意义的关联性。随后，利用此协方差函数通过贝叶斯优化选择一系列环形子采样路径，使其在商用MRI系统中兼顾空间探索的最优性与实际可行性。通过整合针对多种图像找到的最优子采样路径，我们计算得到一种广义采样路径。当该路径用于新图像时，在结构相似性与误差指标上均优于此前报道的重建过程（即仅采样12.5%的k空间数据时，达到96.3%的结构相似度与<0.003的归一化均方误差）。最后，我们无需重新训练，直接将此重建过程应用于病理数据，证明重建图像对脑卒中识别具有临床实用价值。