title: Local sparsity enhanced compressed sensing magnetic resonance imaging in uniform discrete curvelet domain.
abstract: BACKGROUND
  Compressed sensing(CS) has been well applied to speed up imaging by exploring image sparsity over predefined basis functions or learnt dictionary. Firstly, the sparse representation is generally obtained in a single transform domain by using wavelet-like methods, which cannot produce optimal sparsity considering sparsity, data adaptivity and computational complexity. Secondly, most state-of-the-art reconstruction models seldom consider composite regularization upon the various structural features of images and transform coefficients sub-bands. Therefore, these two points lead to high sampling rates for reconstructing high-quality images.
  
  
  METHODS
  In this paper, an efficient composite sparsity structure is proposed. It learns adaptive dictionary from lowpass uniform discrete curvelet transform sub-band coefficients patches. Consistent with the sparsity structure, a novel composite regularization reconstruction model is developed to improve reconstruction results from highly undersampled k-space data. It is established via minimizing spatial image and lowpass sub-band coefficients total variation regularization, transform sub-bands coefficients l 1 sparse regularization and constraining k-space measurements fidelity. A new augmented Lagrangian method is then introduced to optimize the reconstruction model. It updates representation coefficients of lowpass sub-band coefficients over dictionary, transform sub-bands coefficients and k-space measurements upon the ideas of constrained split augmented Lagrangian shrinkage algorithm.
  
  
  RESULTS
  Experimental results on in vivo data show that the proposed method obtains high-quality reconstructed images. The reconstructed images exhibit the least aliasing artifacts and reconstruction error among current CS MRI methods.
  
  
  CONCLUSIONS
  The proposed sparsity structure can fit and provide hierarchical sparsity for magnetic resonance images simultaneously, bridging the gap between predefined sparse representation methods and explicit dictionary. The new augmented Lagrangian method provides solutions fully complying to the composite regularization reconstruction model with fast convergence speed.
authors.affiliation: School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China. 18919849359@163.com.
authors.forename: Bingxin
authors.initials: B
authors.lastname: Yang
authors.affiliation: School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China. yuanm@lzu.edu.cn.
authors.forename: Min
authors.initials: M
authors.lastname: Yuan
authors.affiliation: School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China. yidema@gmail.com.
authors.forename: Yide
authors.initials: Y
authors.lastname: Ma
authors.affiliation: School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China. zhangjw@lzu.edu.cn.
authors.forename: Jiuwen
authors.initials: J
authors.lastname: Zhang
authors.affiliation: School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China. kzhan@lzu.edu.cn.
authors.forename: Kun
authors.initials: K
authors.lastname: Zhan
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D044962:Data Compression / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D058067:Wavelet Analysis