Local sparsity enhanced compressed sensing magnetic resonance imaging in uniform discrete curvelet domain

BMC Medical Imaging

Kun Zhan¹  Jiuwen Zhang¹  Yide Ma¹  Min Yuan¹  Bingxin Yang¹ 

[1] School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou 730000, China

关键词: Augmented Lagrangian;    Dictionary learning;    Uniform discrete curvelet transform;    Magnetic resonance imaging;    Compressed sensing;   

Others  :  1222836
DOI  :  10.1186/s12880-015-0065-0

 received in 2014-12-27, accepted in 2015-06-16,  发布年份 2015

【 摘 要 】

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 l₁sparse 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.

【 授权许可】

   
2015 Yang et al.; licensee BioMed Central.

【 图 表 】

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