The invention provides for a magnetic resonance imaging system (100, 200) comprising a memory (148) for storing machine executable instructions (150) and pulse sequence commands (152). The pulse sequence commands are configured for acquiring a four dimensional magnetic resonance data set (162) from an imaging region of interest (109). The four dimensional magnetic resonance data set is at least divided into three dimensional data magnetic resonance data sets (400, 402, 404, 406, 408) indexed by a repetitive motion phase of the subject. The three dimensional data magnetic resonance data sets are further at least divided into and indexed by k-space portions (410, 412, 414, 416, 418, 420, 422, 424, 426, 428, 430, 432, 434, 436). The magnetic resonance imaging system further comprises a processor (144) for controlling the magnetic resonance imaging system. Execution of the machine executable instructions causes the processor during a first operational portion (310) to iteratively: receive (300) a motion signal (156) descriptive of the repetitive motion phase; acquire (302) an initial k-space portion using the pulse sequence commands, wherein the initial k-space portion is selected from the k-space portions; store (304) the motion signal and the initial k-space portion in a buffer (158) for each iteration of the first operational portion; at least partially construct (306) a motion phase mapping (160) between the motion signal and the repetitive motion phase; and continue (308) the first operational portion until the motion phase mapping is complete. Execution of the machine executable instructions causes the processor to assign (312) the initial k-space portion for each iteration of the first operational portion in the temporary buffer to the four dimensional magnetic resonance data set using the motion phase mapping. Execution of the machine executable instructions causes the processor during a second operational portion (332) to iteratively: receive (314) the motion signal; determine (316) a predicted next motion phase using the motion signal and the motion phase mapping; select (318) a subsequent k-space portion (154) from the k-space portions of the four dimensional magnetic resonance data set using the predicted next motion phase; acquire (320) the subsequent k-space portion using the pulse sequence commands; rereceive (322) the motion signal; determine (324) a current motion phase using the re-received motion signal and the motion phase mapping; assign (326) the subsequent k-space portion to the four dimensional magnetic resonance data set using the current motion phase; and repeat (328) the second operational portion until the k-space portions for each repetitive motion phase has been assigned.