Hybrid Weighted l₁-Total Variation Constrained Reconstruction for MR Image

Compressed sensing based Magnetic resonance (MR) image reconstruction can be done by minimizing the sum of least square data fitting item, the Total variation (TV) and l₁ norm regularizations. In this paper, inspired by the conventional constrained reconstruction model, we propose a hybrid weighted l₁-TV minimization method to reconstruct MR image. We introduce the iterative mechanism to update the weights for l₁ and TV norms adaptively. The weights vary at each element of the image matrix according to the presented weights selection strategy. Experiments on Shepp-Logan phantom and practical MR images demonstrate the proposed method can preserve image details and obtain improved reconstruction quality compared to the traditional CS-MRI method and other weighted methods.