Techniques are disclosed related to the compensation of phase variations introduced into k-space lines, which cause imaging artifacts. The techniques utilize the detection of motion via an encoding plus motion model, which does not require the use of additional prospective or retrospective motion detection techniques. The techniques described herein use the encoding plus motion model to reconstruct an initial image from a set of motion states, and then calculate phase information from images that are projected form the initial reconstructed image using a projection onto convex sets (POCS). The phase information is incorporated into the encoding plus motion model over several iterations to minimize data consistency error, thereby generating a refined image that compensates for patient motion over the set of motion states.