Full Text:   <2718>

Summary:  <2124>

CLC number: TN911

On-line Access: 2015-12-07

Received: 2014-12-08

Revision Accepted: 2015-10-09

Crosschecked: 2015-10-12

Cited: 1

Clicked: 7283

Citations:  Bibtex RefMan EndNote GB/T7714


Min Yuan


-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2015 Vol.16 No.12 P.1069-1087


Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm

Author(s):  Min Yuan, Bing-xin Yang, Yi-de Ma, Jiu-wen Zhang, Fu-xiang Lu, Tong-feng Zhang

Affiliation(s):  School of Information Science & Engineering, Lanzhou University, Lanzhou 730000, China

Corresponding email(s):   ydma01@126.com

Key Words:  Compressed sensing (CS), Magnetic resonance imaging (MRI), Uniform discrete curvelet transform (UDCT), Multi-scale dictionary learning (MSDL), Patch-based constraint splitting augmented Lagrangian shrinkage algorithm (PB C-SALSA)

Min Yuan, Bing-xin Yang, Yi-de Ma, Jiu-wen Zhang, Fu-xiang Lu, Tong-feng Zhang. Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(12): 1069-1087.

@article{title="Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm",
author="Min Yuan, Bing-xin Yang, Yi-de Ma, Jiu-wen Zhang, Fu-xiang Lu, Tong-feng Zhang",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm
%A Min Yuan
%A Bing-xin Yang
%A Yi-de Ma
%A Jiu-wen Zhang
%A Fu-xiang Lu
%A Tong-feng Zhang
%J Frontiers of Information Technology & Electronic Engineering
%V 16
%N 12
%P 1069-1087
%@ 2095-9184
%D 2015
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1400423

T1 - Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm
A1 - Min Yuan
A1 - Bing-xin Yang
A1 - Yi-de Ma
A1 - Jiu-wen Zhang
A1 - Fu-xiang Lu
A1 - Tong-feng Zhang
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 16
IS - 12
SP - 1069
EP - 1087
%@ 2095-9184
Y1 - 2015
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1400423

Recently, dictionary learning (DL) based methods have been introduced to compressed sensing magnetic resonance imaging (CS-MRI), which outperforms pre-defined analytic sparse priors. However, single-scale trained dictionary directly from image patches is incapable of representing image features from multi-scale, multi-directional perspective, which influences the reconstruction performance. In this paper, incorporating the superior multi-scale properties of uniform discrete curvelet transform (UDCT) with the data matching adaptability of trained dictionaries, we propose a flexible sparsity framework to allow sparser representation and prominent hierarchical essential features capture for magnetic resonance (MR) images. Multi-scale decomposition is implemented by using UDCT due to its prominent properties of lower redundancy ratio, hierarchical data structure, and ease of implementation. Each sub-dictionary of different sub-bands is trained independently to form the multi-scale dictionaries. Corresponding to this brand-new sparsity model, we modify the constraint splitting augmented Lagrangian shrinkage algorithm (C-SALSA) as patch-based C-SALSA (PB C-SALSA) to solve the constraint optimization problem of regularized image reconstruction. Experimental results demonstrate that the trained sub-dictionaries at different scales, enforcing sparsity at multiple scales, can then be efficiently used for MRI reconstruction to obtain satisfactory results with further reduced undersampling rate. Multi-scale UDCT dictionaries potentially outperform both single-scale trained dictionaries and multi-scale analytic transforms. Our proposed sparsity model achieves sparser representation for reconstructed data, which results in fast convergence of reconstruction exploiting PB C-SALSA. Simulation results demonstrate that the proposed method outperforms conventional CS-MRI methods in maintaining intrinsic properties, eliminating aliasing, reducing unexpected artifacts, and removing noise. It can achieve comparable performance of reconstruction with the state-of-the-art methods even under substantially high undersampling factors.


创新点:改进了基本的字典学习模型,提出了一种基于均匀离散Curvelet变换(Uniform Discrete Curvelet Transform, UDCT)域多尺度字典学习的稀疏化模型,并应用于CS-MRI重构。为适应多尺度分层和分块稀疏化结构,进一步扩展约束型分裂增广拉格朗日收缩方法,并用于模型的数值求解。


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T., 2011. An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans. Image Process., 20(3):681-695.

[2]Aharon, M., Elad, M., Bruckstein, A., 2006. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process., 54(11):4311-4322.

[3]Baraniuk, R., 2007. Compressive sensing. IEEE Signal Process. Mag., 24(4):118-121.

[4]Candes, E.J., Donoho, D.L., 2004. New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities. Commun. Pure Appl. Math., 57(2):219-266.

[5]Candes, E.J., Romberg, J., Tao, T., 2006a. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory, 52(2):489-509.

[6]Candes, E.J., Romberg, J.K., Tao, T., 2006b. Stable signal rcovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math., 59(8):1207-1223.

[7]Chambolle, A., 2004. An algorithm for total variation minimization and applications. J. Math. Imag. Vis., 20(1-2):89-97.

[8]Chen, C., Huang, J., 2014. The benefit of tree sparsity in accelerated MRI. Med. Image Anal., 18(6):834-842.

[9]Combettes, P.L., Wajs, V.R., 2005. Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul., 4(4):1168-1200.

[10]Dahl, J., Hansen, P.C., Jensen, S.H., et al., 2010. Algorithms and software for total variation image reconstruction via first-order methods. Numer. Algor., 53(1):67-92.

[11]Donoho, D.L., 2001. Sparse components of images and optimal atomic decompositions. Constr. Approx., 17(3):353-382.

[12]Donoho, D.L., 2006. Compressed sensing. IEEE Trans. Inform. Theory, 52(4):1289-1306.

[13]Eckstein, J., Bertsekas, D.P., 1992. On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program., 55(1):293-318.

[14]Elad, M., 2010. Sparse and Redundant Representations: from Theory to Applications in Signal and Image Processing. Springer, New York, USA.

[15]Elad, M., Aharon, M., 2006. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process., 15(12):3736-3745.

[16]Gabay, D., Mercier, B., 1976. A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. Appl., 2(1):17-40.

[17]Gho, S.M., Nam, Y., Zho, S.Y., et al., 2010. Three dimension double inversion recovery gray matter imaging using compressed sensing. Magn. Reson. Imag., 28(10):1395-1402.

[18]Huang, J., Zhang, S., Metaxas, D., 2011. Efficient MR image reconstruction for compressed MR imaging. Med. Image Anal., 15(5):670-679.

[19]Kim, Y., Altbach, M.I., Trouard, T.P., et al., 2009. Compressed sensing using dual-tree complex wavelet transform. Proc. Int. Soc. Mag. Reson. Med., 17:2814.

[20]Kim, Y., Nadar, M.S., Bilgin, A., 2012. Wavelet-based compressed sensing using a Gaussian scale mixture model. IEEE Trans. Image Process., 21(6):3102-3108.

[21]Lewicki, M.S., Sejnowski, T.J., 2000. Learning overcomplete representations. Neur. Comput., 12(2):337-365.

[22]Lin, L., 1989. A concordance correlation coefficient to evaluate reproducibility. Biometrics, 45(1):255-268.

[23]Liu, Y., Cai, J., Zhan, Z., et al., 2015. Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging. PLoS ONE, 10(4):e0119584.1-e0119584.19.

[24]Lustig, M., Donoho, D., Pauly, J.M., 2007. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med., 58(6):1182-1195.

[25]Lustig, M., Donoho, D.L., Santos, J.M., et al., 2008. Compressed sensing MRI. IEEE Signal Process. Mag., 25(2):72-82.

[26]Mallat, S., 2008. A Wavelet Tour of Signal Processing: the Sparse Way (3rd Ed.). Academic Press, USA.

[27]Nguyen, T.T., Chauris, H., 2010. Uniform discrete curvelet transform. IEEE Trans. Signal Process., 58(7):3618-3634.

[28]Ning, B., Qu, X., Guo, D., et al., 2013. Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization. Magn. Reson. Imag., 31(9):1611-1622.

[29]Ophir, B., Lustig, M., Elad, M., 2011. Multi-scale dictionary learning using wavelets. IEEE J. Sel. Topics Signal Process., 5(5):1014-1024.

[30]Qu, G., Zhang, D., Yan, P., 2002. Information measure for performance of image fusion. Electron. Lett., 38(7):313-315.

[31]Qu, X., Zhang, W., Guo, D., et al., 2010. Iterative thresholding compressed sensing MRI based on contourlet transform. Inv. Probl. Sci. Eng., 18(6):737-758.

[32]Qu, X., Guo, D., Ning, B., et al., 2012. Undersampled MRI reconstruction with patch-based directional wavelets. Magn. Reson. Imag., 30(7):964-977.

[33]Qu, X., Hou, Y., Lam, F., et al., 2014. Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator. Med. Image Anal., 18(6):843-856.

[34]Rauhut, H., Schnass, K., Vandergheynst, P., 2008. Compressed sensing and redundant dictionaries. IEEE Trans. Inform. Theory, 54(5):2210-2219.

[35]Ravishankar, S., Bresler, Y., 2011. MR image reconstruction from highly undersampled k-space data by dictionary learning. IEEE Trans. Med. Imag., 30(5):1028-1041.

[36]Rubinstein, R., Zibulevsky, M., Elad, M., 2010. Double sparsity: learning sparse dictionaries for sparse signal approximation. IEEE Trans. Signal Process., 58(3):1553-1564.

[37]Rudin, L.I., Osher, S., Fatemi, E., 1992. Nonlinear total variation based noise removal algorithms. Phys. D, 60(1-4):259-268.

[38]Trzasko, J., Manduca, A., 2009. Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization. IEEE Trans. Med. Imag., 28(1):106-121.

[39]Wang, Z., Bovik, A.C., Sheikh, H.R., et al., 2004. Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process., 13(4):600-612.

[40]Xydeas, C.S., Petrović, V., 2000. Objective image fusion performance measure. Electron. Lett., 36(4):308-309.

[41]Zhu, Z., Wahid, K., Babyn, P., et al., 2013. Compressed sensing-based MRI reconstruction using complex double-density dual-tree DWT. Int. J. Biomed. Imag., 2013:907501.1-907501.12.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE