Fig. 1
Comparison of Cartesian phase-encode (PE) schemes. In each row, a Cartesian ky grid with 144 evenly spaced PEs is covered exactly once by a particular PE scheme. In each column, a central-ky region of a specific width is defined as the “navigator zone” (red dashed). Low-PE readouts falling within it are considered “pseudo-projections” (red squares) and used for motion tracking. Row 1: the original integer golden-step scheme provides pseudorandom navigator-zone coverage that is approximately uniform in both time and ky. Row 2 and 3: the golden-step PEs are sorted into temporal segments of 8 and 12, respectively, significantly reducing PE jumps while preserving the pseudorandom coverage of the navigator zone in both time and ky. Row 4 and 5: for comparison, if the “interleaved” PE scheme, a commonly used segmented scheme, were to be used instead of the golden step, there would be large temporal gaps in the navigator zone coverage, i.e., there would be no PE falling inside the central-ky zone (red) to sample the motion for extended periods of time (e.g. row 4 columns 1 and 2, and row 5 column 1). Those that do fall inside would also have be temporally structured (slowly drifting from negative ky to positive in all scenarios in rows 4 and 5), causing slow time-varying bias in motion measurements