Various embodiments are described herein for acquiring MRI image data from an object. Various waveforms are provided for producing magnetic field gradients and an RF excitation field such that NMR response signals are sampled according to a spiral-PR k-space trajectory having a plurality of angular sectors. A given angular sector can be defined by a sampling function having a period that defines radial sampling density and an envelope function that defines the angular extent of the angular sector. Various sampling and envelope functions can be used and a variety of values for the parameters for these functions can be used.