The present disclosure is intended to describe embodiments for improving image data acquisition and processing in accelerated dynamic magnetic resonance imaging sequences. One embodiment is described where a method includes an acquisition sequence configured to acquire an undersampled set of magnetic resonance data. The undersampled set of magnetic resonance data has a pseudo-random sampling pattern within a data space acquired at a first time, the pseudo-random sampling pattern being influenced by other pseudo-random sampling patterns within the data space arising from the acquisition of additional undersampled sets of magnetic resonance data at respective times. In some embodiments, the pseudo-random sampling patterns of the undersampled sets of magnetic resonance data interleave to yield a desired sampling pattern.