1. A method for reconstructing an image of a subject with a magnetic resonance imaging (MRI) system that includes a radio frequency (RF) coil array having multiple coil channels, the steps of the method comprising: a) acquiring, with the MRI system and from the subject, undersampled scan data defining a set of k-space lines including sampled k-space lines and unsampled k-space lines; b) acquiring, with the MRI system and from the subject, auto-calibration scan (ACS) data; c) estimating k-space line data for the unsampled k-space lines from an under-determined linear system that includes the ACS data and the undersampled scan data to produce a set of synthesized k-space lines corresponding to the unsampled k-space lines; and d) reconstructing an image of the subject using the synthesized k-space lines and the acquired scan data.