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Fast coverage of k-space is a major concern to speed up data acquisition inMagnetic Resonance Imaging (MRI) and limit image distortions due to long echotrain durations. The hardware gradient constraints (magnitude, slew rate) mustbe taken into account to collect a sufficient amount of samples in a minimalamount of time. However, sampling strategies (e.g., Compressed Sensing) andoptimal gradient waveform design have been developed separately so far. Themajor flaw of existing methods is that they do not take the sampling densityinto account, the latter being central in sampling theory. In particular,methods using optimal control tend to agglutinate samples in high curvatureareas. In this paper, we develop an iterative algorithm to project anyparameterization of k-space trajectories onto the set of feasible curves thatfulfills the gradient constraints. We show that our projection algorithmprovides a more efficient alternative than existinf approaches and that it canbe a way of reducing acquisition time while maintaining sampling density forpiece-wise linear trajectories.

Gradient waveform design for variable density sampling in Magnetic Resonance Imaging