  Compressed sensing applied to magnetic resonance imaging (MRI) allows to
reduce the scanning time by enabling images to be reconstructed from highly
undersampled data. In this paper, we tackle the problem of designing a sampling
mask for an arbitrary reconstruction method and a limited acquisition budget.
Namely, we look for an optimal probability distribution from which a mask with
a fixed cardinality is drawn. We demonstrate that this problem admits a
compactly supported solution, which leads to a deterministic optimal sampling
mask. We then propose a stochastic greedy algorithm that (i) provides an
approximate solution to this problem, and (ii) resolves the scaling issues of
[1,2]. We validate its performance on in vivo dynamic MRI with retrospective
undersampling, showing that our method preserves the performance of [1,2] while
reducing the computational burden by a factor close to 200.
