  In the area of magnetic resonance imaging (MRI), an extensive range of
non-linear reconstruction algorithms have been proposed that can be used with
general Fourier subsampling patterns. However, the design of these subsampling
patterns has typically been considered in isolation from the reconstruction
rule and the anatomy under consideration. In this paper, we propose a
learning-based framework for optimizing MRI subsampling patterns for a specific
reconstruction rule and anatomy, considering both the noiseless and noisy
settings. Our learning algorithm has access to a representative set of training
signals, and searches for a sampling pattern that performs well on average for
the signals in this set. We present a novel parameter-free greedy mask
selection method, and show it to be effective for a variety of reconstruction
rules and performance metrics. Moreover we also support our numerical findings
by providing a rigorous justification of our framework via statistical learning
theory.
