Example systems, methods, and apparatus control a pMRI apparatus to produce a pulse sequence having an extended acquisition window, and overlapping phase-encoding gradients and read gradients. One example method controls a pMRI apparatus to produce a trajectory having Cartesian and non-Cartesian segments that sample in a manner that satisfies the Nyquist criterion in at least one region of a volume to be imaged. The pMRI apparatus is controlled to apply radio frequency energy to the volume according to the pulse sequence and following the trajectory and to acquire MR signal from the volume in response to the application of the RF energy. The MR signal includes a first component associated with the Cartesian segment of the trajectory and a second component associated with the non-Cartesian segment of the trajectory. The example method includes calibrating a reconstruction process using Nyquist-satisfying data from the second component.