Recovery of perfusion data with (I) inconsistent gating and shallow breathing and (II) ungated data. Few spatial frames and the image time profiles are shown. In (I), the first row shows the fully sampled data. The motion due to breathing and improper gating are shown by the green arrows. In (II), we consider applying the reconstructions to a single slice; the motion here is due to the cardiac dynamics. Here, we note that the proposed scheme robustly recovers the data in the presence of motion, while sliding window and the gridding reconstructions respectively show temporal blur and streak artifacts. Specifically, for the ungated data, we note that if the motion is not compensated, it could lead to misinterpreting the cardiac phase at a particular time frame. For instance in (II a), it is clear that the systolic phase is being imaged, while sliding window in (II b) depicts this as a phase which looks like diastolic. The proposed scheme recovers the appropriate phase in (II c).