1. A method for producing a series of cardiac gated magnetic resonance images of a subject's heart, the steps comprising: a) administering a contrast agent to the subject; b) producing a gating signal that indicates the start of the subject's cardiac cycle; c) producing a radio frequency (RF) inversion pulse that inverts spin magnetization throughout a field of view a preset time after the gating signal is produced; d) acquiring k-space data as a series of data segments at successive cardiac phases after the RF inversion pulse is produced using a plurality of steady-state free precession (SSFP) pulse sequences during a time period in which the inverted spin magnetization recovers such that some data segments in the series of data segments are acquired when tissue contrast is changing and other data segments in the series of data segments are acquired when tissue contrast is no longer substantially changing; e) repeating steps b) through d) until a desired amount of k-space data is acquired in each data segment; f) reconstructing a series of image frames depicting the heart at a succession of cardiac phases using the k-space data acquired in the series of data segments, and in which images in the series of image frames reconstructed from the data segments acquired when tissue contrast is changing depict a time-varying tissue contrast of the heart, and in which images in the series of image frames reconstructed from the data segments acquired when tissue contrast is no longer substantially changing depict cardiac wall motion; and g) producing a T 1 * map by: i) determining for a given pixel location in the T 1 * map, a T 1 * value by fitting magnitude values from corresponding pixel locations in the series of image frames reconstructed in step f) to a signal model that relates magnitude values to T 1 *; and ii) setting magnitude values for each given pixel location in the T 1 * map to the corresponding T 1 * value determined in step g)i).