  Performing k-space variable density sampling is a popular way of reducing
scanning time in Magnetic Resonance Imaging (MRI). Unfortunately, given a
sampling trajectory, it is not clear how to traverse it using gradient
waveforms. In this paper, we actually show that existing methods [1, 2] can
yield large traversal time if the trajectory contains high curvature areas.
Therefore, we consider here a new method for gradient waveform design which is
based on the projection of unrealistic initial trajectory onto the set of
hardware constraints. Next, we show on realistic simulations that this
algorithm allows implementing variable density trajectories resulting from the
piecewise linear solution of the Travelling Salesman Problem in a reasonable
time. Finally, we demonstrate the application of this approach to 2D MRI
reconstruction and 3D angiography in the mouse brain.
