Of the sources of noise which affect BOLD fMRI, respiration and cardiac fluctuations are responsible for the largest part of the variance, particularly at high and ultra-high field. Existing approaches to removing physiological noise either use external recordings, which can be unwieldy and unreliable, or attempt to identify physiological noise from the magnitude fMRI data. Data-driven approaches are limited by sensitivity, temporal aliasing and the need for user interaction. In the light of the sensitivity of the phase of the MR signal to local changes in the field stemming from physiological processes, we have developed an unsupervised physiological noise correction method which uses the information carried in both the phase and the magnitude of EPI data. Our technique, Physiological Regressor Estimation from Phase and mAgnItude, sub-tR (PREPAIR) derives time series signals which are sampled at the slice TR from both phase and magnitude images. It allows physiological noise to be captured without aliasing, and efficiently removes other sources of signal fluctuations which are not related to physiology, prior to regressor estimation. We demonstrate that the physiological signal time courses identified with PREPAIR not only agree well with those from external devices, but also retrieve challenging cardiac dynamics. The removal of physiological noise was as effective as that achieved with the most commonly used approach based on external recordings, RETROICOR. In comparison with widely used physiological noise correction tools which do not use external signals, PESTICA and FIX, PREPAIR removed more respiratory and cardiac noise and achieved a larger increase in tSNR at both 3 T and 7 T.