title: Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging.
abstract: Compressed sensing has shown to be promising to accelerate magnetic resonance imaging. In this new technology, magnetic resonance images are usually reconstructed by enforcing its sparsity in sparse image reconstruction models, including both synthesis and analysis models. The synthesis model assumes that an image is a sparse combination of atom signals while the analysis model assumes that an image is sparse after the application of an analysis operator. Balanced model is a new sparse model that bridges analysis and synthesis models by introducing a penalty term on the distance of frame coefficients to the range of the analysis operator. In this paper, we study the performance of the balanced model in tight frame based compressed sensing magnetic resonance imaging and propose a new efficient numerical algorithm to solve the optimization problem. By tuning the balancing parameter, the new model achieves solutions of three models. It is found that the balanced model has a comparable performance with the analysis model. Besides, both of them achieve better results than the synthesis model no matter what value the balancing parameter is. Experiment shows that our proposed numerical algorithm constrained split augmented Lagrangian shrinkage algorithm for balanced model (C-SALSA-B) converges faster than previously proposed algorithms accelerated proximal algorithm (APG) and alternating directional method of multipliers for balanced model (ADMM-B).
authors: Yunsong Liu, Zhifang Zhan, Jing Ye, Zhong Chen, Xiaobo Qu Department of Electronic Science/Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen, China.
authors: Yunsong
authors: Y
authors: Liu
authors: Jian-Feng Cai Department of Mathematics, University of Iowa, Iowa City, Iowa, USA.
authors: Jian-Feng
authors: JF
authors: Cai
authors: Yunsong Liu, Zhifang Zhan, Jing Ye, Zhong Chen, Xiaobo Qu Department of Electronic Science/Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen, China.
authors: Zhifang
authors: Z
authors: Zhan
authors: Di Guo School of Computer and Information Engineering, Xiamen University of Technology, Xiamen, China.
authors: Di
authors: D
authors: Guo
authors: Yunsong Liu, Zhifang Zhan, Jing Ye, Zhong Chen, Xiaobo Qu Department of Electronic Science/Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen, China.
authors: Jing
authors: J
authors: Ye
authors: Yunsong Liu, Zhifang Zhan, Jing Ye, Zhong Chen, Xiaobo Qu Department of Electronic Science/Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen, China.
authors: Zhong
authors: Z
authors: Chen
authors: Yunsong Liu, Zhifang Zhan, Jing Ye, Zhong Chen, Xiaobo Qu Department of Electronic Science/Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen, China.
authors: Xiaobo
authors: X
authors: Qu
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology* / Q000502:physiology; D003198:Computer Simulation; D064368:Healthy Volunteers; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008962:Models, Theoretical; D012815:Signal Processing, Computer-Assisted