  To accelerate MRI, the field of compressed sensing is traditionally concerned
with optimizing the image quality after a partial undersampling of the
measurable $\textit{k}$-space. In our work, we propose to change the focus from
the quality of the reconstructed image to the quality of the downstream image
analysis outcome. Specifically, we propose to optimize the patterns according
to how well a sought-after pathology could be detected or localized in the
reconstructed images. We find the optimal undersampling patterns in
$\textit{k}$-space that maximize target value functions of interest in
commonplace medical vision problems (reconstruction, segmentation, and
classification) and propose a new iterative gradient sampling routine
universally suitable for these tasks. We validate the proposed MRI acceleration
paradigm on three classical medical datasets, demonstrating a noticeable
improvement of the target metrics at the high acceleration factors (for the
segmentation problem at $\times$16 acceleration, we report up to 12%
improvement in Dice score over the other undersampling patterns).
