Motion artifacts are a dominant cause of magnetic resonance image quality degradation. Periodic or nearly periodic motion results in image replicates of the moving structures in spin-warp Fourier imaging. The replicates, or ghosts, propagate in the image in the phase-encoding, or y, direction. These ghosted images can be considered to consist of the time-averaged spin density I0 and a ghost mask g. A set of j ghosted images Ij may be acquired in which the ghost mask is intentionally phase shifted by varying amounts relative to I0 with interleaved acquisitions that have shifted phase-encoding orders or by acquiring multiple images during a single readout period in the presence of an oscillating phase-encoding gradient. The resulting complex images Ij have the same time-averaged spin density I0 but have ghost contributions gj that, on a pixel-by-pixel basis, trace part of a circle around I0. The source images Ij can then be used to estimate I0. Simulations and experiments with the phase-encoding gradient modulation method show good general ghost suppression for a variety of quasi-periodic motion sources including both respiratory-type artifacts and flow artifacts. The primary limitation of the method is the need for rapid gradient switching.