title: Sparse Parallel MRI Based on Accelerated Operator Splitting Schemes.
abstract: Recently, the sparsity which is implicit in MR images has been successfully exploited for fast MR imaging with incomplete acquisitions. In this paper, two novel algorithms are proposed to solve the sparse parallel MR imaging problem, which consists ofl1regularization and fidelity terms. The two algorithms combine forward-backward operator splitting and Barzilai-Borwein schemes. Theoretically, the presented algorithms overcome the nondifferentiable property inl1regularization term. Meanwhile, they are able to treat a general matrix operator that may not be diagonalized by fast Fourier transform and to ensure that a well-conditioned optimization system of equations is simply solved. In addition, we build connections between the proposed algorithms and the state-of-the-art existing methods and prove their convergence with a constant stepsize in Appendix. Numerical results and comparisons with the advanced methods demonstrate the efficiency of proposed algorithms.
authors.affiliation: School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China.
authors.forename: Nian
authors.identifier: 0000-0002-7826-5055
authors.initials: N
authors.lastname: Cai
authors.affiliation: Paul C. Lauterbur Research Centre for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Shenzhen, China; Shenzhen Key Laboratory for MRI, Shenzhen, Guangdong, China.
authors.forename: Weisi
authors.initials: W
authors.lastname: Xie
authors.affiliation: School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China; Paul C. Lauterbur Research Centre for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Shenzhen, China; Shenzhen Key Laboratory for MRI, Shenzhen, Guangdong, China.
authors.forename: Zhenghang
authors.initials: Z
authors.lastname: Su
authors.affiliation: Paul C. Lauterbur Research Centre for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Shenzhen, China; Shenzhen Key Laboratory for MRI, Shenzhen, Guangdong, China.
authors.forename: Shanshan
authors.identifier: 0000-0002-0575-6523
authors.initials: S
authors.lastname: Wang
authors.affiliation: Paul C. Lauterbur Research Centre for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Shenzhen, China; Shenzhen Key Laboratory for MRI, Shenzhen, Guangdong, China.
authors.forename: Dong
authors.identifier: 0000-0001-6257-0875
authors.initials: D
authors.lastname: Liang
mesh_terms: D000465:Algorithms; D003952:Diagnostic Imaging; D005583:Fourier Analysis; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging; D015233:Models, Statistical; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D059629:Signal-To-Noise Ratio; D012984:Software