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Compressed sensing(CS)is a promising technique to accelerate magnetic resonance imaging(MRI).The goal of CS-MRI is to reconstruct MRI images of high quality as fast as possible.For CS-MRI,there are two main challenges: sparsity and compuation.In this talk,we will summarize our work on how to train the semi-adaptive sparse representation of MRI images to reduce reconstruction error and design fast and compatible algorithms to solve analysis sparse models for tight frames.Main contents include: 1)Semi-adaptive sparse representations,e.g.sparsifying transforms exploiting geometric direction and self-similarity information of MR images,are shown better in preserving the abundant features of MR images than those general representations,e.g.DCT and wavelets,in CS-MRI; 2)A projected FISTA(pFISTA)is proposed by introducing the canonical dual frame to construct the orthogonal projection operator on the range of the analysis sparsity operator to solve sparse MRI reconstruction with analysis models and proved its theoretically prove that pISTA converges to the minimum of a function with a balanced tight frame sparsity.Ref: 14.Liu,Y.,Zhan Z.,Cai J.F.,Guo D.,Chen Z.,Qu X..arXiv:1504.07786,2015.