  Undersampling is a common method in Magnetic Resonance Imaging (MRI) to
subsample the number of data points in k-space, reducing acquisition times at
the cost of decreased image quality. A popular approach is to employ
undersampling patterns following various strategies, e.g., variable density
sampling or radial trajectories. In this work, we propose a method that
directly learns the undersampling masks from data points, thereby also
providing task- and domain-specific patterns. To solve the resulting discrete
optimization problem, we propose a general optimization routine called ProM: A
fully probabilistic, differentiable, versatile, and model-free framework for
mask optimization that enforces acceleration factors through a convex
constraint. Analyzing knee, brain, and cardiac MRI datasets with our method, we
discover that different anatomic regions reveal distinct optimal undersampling
masks, demonstrating the benefits of using custom masks, tailored for a
downstream task. For example, ProM can create undersampling masks that maximize
performance in downstream tasks like segmentation with networks trained on
fully-sampled MRIs. Even with extreme acceleration factors, ProM yields
reasonable performance while being more versatile than existing methods, paving
the way for data-driven all-purpose mask generation.
