In this paper, we address the multi-frame superresolution MRI problem. We formulate the reconstruction problem as a coupled tensor multilinear approximation. We prove that exact recovery of the high-resolution 3D isotropic image is achievable for a variety of multilinear ranks. We propose a simple algorithm based on Tikhonov regularization to perform the reconstruction. Our simulations on real datasets illustrates the good performance of the proposed approach, with a lower computation time than state-of-the-art methods.