We propose an algorithm for dMRI reconstruction from highly under-sampled k-space data acquired during free breathing. Stack-of-star GRE radial sequence with self-navigator is used to acquire the data. We explore spatial and temporal redundancy for the reconstruction by using weighted group sparsity, weighted sparsity, and low-rank tensor. Additionally, a tensor total variation is used to ensure spatial and temporal smoothness. By applying a weighting function to the sparsity and group sparsity, the subtle structural sparsity features in the sparse domain can be better utilized. The proposed algorithm has the potential to be used in clinical applications such as MR-guided surgery.
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