In Magnetic Resonance Imaging typical clinical settings, both low- and high-resolution images of different types are routinarily acquired. In some cases, the acquired low-resolution images have to be upsampled to match with other high-resolution images for posterior analysis or postprocessing such as registration or multimodal segmentation. However, classical interpolation techniques are not able to recover the high-frequency information lost during the acquisition process. In the present paper, a new superresolution method is proposed to reconstruct high-resolution images from the low-resolution ones using information from coplanar high resolution images acquired of the same subject. Furthermore, the reconstruction process is constrained to be physically plausible with the MR acquisition model that allows a meaningful interpretation of the results. Experiments on synthetic and real data are supplied to show the effectiveness of the proposed approach. A comparison with classical state-of-the-art interpolation techniques is presented to demonstrate the improved performance of the proposed methodology.