In magnetic resonance imaging, Fourier coefficients of desired image slices
are acquired through a combination of radiofrequency pulses and magnetic
field gradients. Among the most serious limitations for MRI today is long
scan time (movement artefacts, limited patient tolerance, rapid signal decay
in high fields, overall costs),
which can be shortened substantially by acquiring below the Nyquist limit,
then adopting sparse nonlinear image reconstruction (compressive sensing).
For real anatomical MR images, this works well only if sampling trajectories
are carefully chosen.
We address MRI acquisition optimization by sequential Bayesian experimental
design, driven by a novel variational approximate inference algorithm orders
of magnitude faster than previous approaches. In a first study with brain
scans from a Siemens 3T Trio scanner, optimized designs significantly
outperform trajectories chosen in previously proposed ways.