Liu Yunsong, Cai Jian-Feng, Zhan Zhifang, Guo Di, Ye Jing, Chen Zhong, Qu Xiaobo
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.
Jian-Feng Cai Department of Mathematics, University of Iowa, Iowa City, Iowa, USA.
PLoS One. 2015 Apr 7;10(4):e0119584. doi: 10.1371/journal.pone.0119584. eCollection 2015.
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).
压缩感知已被证明在加速磁共振成像方面具有前景。在这项新技术中，磁共振图像通常通过在稀疏图像重建模型（包括合成模型和分析模型）中强制其稀疏性来重建。合成模型假设图像是原子信号的稀疏组合，而分析模型假设图像在应用分析算子后是稀疏的。平衡模型是一种新的稀疏模型，它通过在框架系数到分析算子值域的距离上引入惩罚项来弥合分析模型和合成模型之间的差距。在本文中，我们研究了平衡模型在基于紧框架的压缩感知磁共振成像中的性能，并提出了一种新的高效数值算法来解决优化问题。通过调整平衡参数，新模型实现了三种模型的解。结果发现，平衡模型与分析模型具有可比的性能。此外，无论平衡参数取何值，它们都比合成模型取得更好的结果。实验表明，我们提出的用于平衡模型的数值算法——约束分裂增广拉格朗日收缩算法（C-SALSA-B）比先前提出的算法——加速近端算法（APG）和用于平衡模型的交替方向乘子法（ADMM-B）收敛更快。
