An apparatus and method are provided to correct motion artifacts in magnetic resonance imaging (MRI) data by finding and removing motion-corrupted encodes. The MRI data non-uniformly sample k-space using a series of shots, each including one or more encodes. The motion-corrupted encodes/shots are identified by omitting respective encodes/shots from the MRI data when reconstructing respective images using a compressed-sensing (CS) method. The image quality is improved for those reconstructed images in which the motion-corrupted encodes are omitted, whereas all other images include the motion-corrupted encodes and exhibit the motion artifact. Assuming a minority of encodes/shots are corrupted by motion, the images improved by omitting the motion-corrupted encodes can be identified as outliers. Once, the motion-corrupted encodes are identified and excluded from the final MRI dataset, a final, high-resolution image is reconstructed using the final MRI dataset.