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

BMC Medical Imaging

Research Article

Yide Ma¹  Bingxin Yang¹  Kun Zhan¹  Jiuwen Zhang¹  Min Yuan¹ 

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

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

DOI  :  10.1186/s12880-015-0065-0

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

来源: Springer

【 摘 要 】

BackgroundCompressed 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.MethodsIn 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 l1 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.ResultsExperimental 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.ConclusionsThe 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】

Unknown   
© Yang et al.; licensee BioMed Central. 2015. This article is published under license to BioMed Central Ltd. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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