  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.
