Time-resolved contrast enhanced magnetic resonance angiography (MRA) may suffer from involuntary patient motion. It is noted that while MR signal change associated with motion is large in magnitude and has smooth phase variation in k-phase, signal change associated with vascular enhancement is small in magnitude and has rapid phase variation in k-space. Based upon this observation, a novel projection onto convex sets (POCS) algorithm is developed as an automatic iterative method to remove motion artifacts. The presented POCS algorithm consists of high-pass phase filtering and convex projections in both k-space and image space. Without input of detailed motion knowledge, motion effects are filtered out, while vasculature information is preserved. The proposed method can be effective for a large class of nonrigid motions, including through-plane motion. The algorithm is stable and converges quickly, usually within five iterations. A double-blind evaluation on a set of clinical MRA cases shows that a completely unsupervised version of the algorithm produces significantly better rank scores (P ؍ 0.038) when compared to angiograms produced manually by an experienced radiologist. Time-resolved contrast-enhanced magnetic resonance angiography (MRA) provides temporal flow and anatomic information about vascular conduits (1). In projection 2D MR digital subtraction angiography (MRDSA) (2,3), complex subtraction of precontrast from postcontrast data yields the arteriogram. Clinical evidence (4) indicates that 2D MRDSA is as suitable for infrapopliteal imaging as conventional X-ray angiography. Patient motion can cause spurious changes in contrast-induced dynamic signal, contaminating the integrity of dynamic data relating to vascular evolution. Motion of elongated structures (e.g., bones) can create subtraction artifacts resembling arteries. The radiologist may be forced to discard motion-corrupted frames, causing gaps in the temporal MRA record and possibly misdiagnosis (5). Techniques that can rescue these motion-corrupted frames would be very valuable.A range of motion correction methods have been developed; most of them utilize specific motion modeling. Correction of rigid global motion in single-frame MR images was reported using subspace analysis (6,7) and navigatorbased correction (8 -10). Motion in MRA may be nonglobal (affecting some but not all portions of image space) as well as inter-view motion (i.e., affecting some lines of k-space but not others). Global, rigid inter-view motion was addressed in a model-free manner using projection or entropy maximization (11-15), but these works did not address nonrigid motion typically encountered in MRA. Multisensor techniques for PET images (16) and cardiac gating using EEG (17,18) may be applied to MRA, but require additional instrumentation with questionable effectiveness. Retrospective techniques (18) relying on correlation-based template matching of moving regions are inapplicable for inter-view motion, since motion occurs not only between frames but also within t...