In multi-slice magnetic resonance imaging (MRI) the resolution in the slice direction is usually reduced to allow faster acquisition times and to reduce the amount of noise in each 2-D slice. To address this issue a number of super resolution (SR) methods have been proposed to improve the resolution of 3D MRI volumes. These methods typically involve the use of prior models of the MRI data as regularization terms in an ill-conditioned inverse problem. However; an inappropriate choice of these models may reduce the overall performance of the algorithm. In this paper, we propose a novel SR algorithm which utilizes a complex wavelet-based de-noising approach. The proposed algorithm uses a bivariate Laplacian mixture model in a sparseness constraint to regularize the SR inverse problem. Our results show that the 3D MRI volumes reconstructed using this approach have quality superior to volumes produced by the best previously proposed approaches.