A method for reducing artifacts in magnetic resonance imaging (MRI) data includes acquiring a k-space dataset of an anatomical subject using a MRI scanner. An iterative compressed sensing reconstruction method is used to generate a reconstructed image based on the k-space dataset. This iterative compressed sensing reconstruction method uses (a) L1-norm based total variation constraints applied the temporal and spatial dimensions of the k-space dataset and (b) a low rank constraint. After the reconstructed image is generated, a deep learning network is used to generate an artifact image depicting motion artifacts present in the reconstructed image. The reconstructed image is subtracted from the artifact image to yield a final image with the motion artifacts removed.
