Abstract: In a method and magnetic resonance (MR) apparatus for MR image reconstruction, an image reconstruction algorithm is used that operates on one calibration matrix that is formed by reorganizing a number of individual, undersampled k-space data sets respectively acquired by multiple reception coils in a parallel MR data acquisition from a subject exhibiting motion. The motion causes the k-space data sets to exhibit errors. In order to use the calibration matrix in the reconstruction algorithm, it is subjected to an iterative rank reduction procedure in which, in each iteration, a residual is calculated for each data point that represents how poorly, due to motion-induced corruptions, that data point satisfies the low rank constraint, and non-satisfying data points are removed from the data point for the next iteration. The resulting low rank matrix at the end of the iterations is then used to produce images with fewer motion-induced errors.