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

详细信息    查看全文

• 作者：Min Yuan ; Bing-xin Yang ; Yi-de Ma…
• 关键词：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) ; TN911
• 刊名：Frontiers of Information Technology & Electronic Engineering
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：16
• 期：12
• 页码：1069-1087
• 全文大小：1,548 KB
• 参考文献：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鈥?95. [doi:10. 1109/TIP.2010.2076294]CrossRef MathSciNet
  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鈥?322. [doi:10.1109/TSP.2006.881199]CrossRef
  Baraniuk, R., 2007. Compressive sensing. IEEE Signal Process. Mag., 24(4):118鈥?21. [doi:10.1109/MSP.2007.4286571]CrossRef
  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鈥?66. [doi:10.1002/cpa.10116]CrossRef MathSciNet MATH
  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鈥?09. [doi:10.1109/TIT.2005.862083]CrossRef MathSciNet MATH
  Candes, E.J., Romberg, J.K., Tao, T., 2006b. Stable signal rcovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math., 59(8):1207鈥?223. [doi:10. 1002/cpa.20124]CrossRef MathSciNet MATH
  Chambolle, A., 2004. An algorithm for total variation minimization and applications. J. Math. Imag. Vis., 20(1-2): 89鈥?7. [doi:10.1023/B:JMIV.0000011325.36760.1e]MathSciNet
  Chen, C., Huang, J., 2014. The benefit of tree sparsity in accelerated MRI. Med. Image Anal., 18(6):834鈥?42. [doi:10. 1016/j.media.2013.12.004]CrossRef
  Combettes, P.L., Wajs, V.R., 2005. Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul., 4(4):1168鈥?200. [doi:10.1137/050626090]CrossRef MathSciNet MATH
  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鈥?2. [doi:10. 1007/s11075-009-9310-3]CrossRef MathSciNet MATH
  Donoho, D.L., 2001. Sparse components of images and optimal atomic decompositions. Constr. Approx., 17(3): 353鈥?82. [doi:10.1007/s003650010032]CrossRef MathSciNet MATH
  Donoho, D.L., 2006. Compressed sensing. IEEE Trans. Inform. Theory, 52(4):1289鈥?306. [doi:10.1109/TIT.2006.871582]CrossRef MathSciNet MATH
  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鈥?18. [doi:10.1007/BF01581204]CrossRef MathSciNet MATH
  Elad, M., 2010. Sparse and Redundant Representations: from Theory to Applications in Signal and Image Processing. Springer, New York, USA. [doi:10.1007/978-1-4419-7011-4]CrossRef
  Elad, M., Aharon, M., 2006. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process., 15(12):3736鈥?745. [doi:10.1109/TIP.2006.881969]CrossRef MathSciNet
  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鈥?0. [doi:10. 1016/0898-1221(76)90003-1]CrossRef MATH
  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鈥?402. [doi:10.1016/j.mri.2010.06.029]CrossRef
  Huang, J., Zhang, S., Metaxas, D., 2011. Efficient MR image reconstruction for compressed MR imaging. Med. Image Anal., 15(5):670鈥?79. [doi:10.1016/j.media.2011.06.001]CrossRef
  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.
  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鈥?108. [doi:10. 1109/TIP.2012.2188807]CrossRef MathSciNet
  Lewicki, M.S., Sejnowski, T.J., 2000. Learning overcomplete representations. Neur. Comput., 12(2):337鈥?65. [doi:10. 1162/089976600300015826]CrossRef
  Lin, L., 1989. A concordance correlation coefficient to evaluate reproducibility. Biometrics, 45(1):255鈥?68. [doi:10. 2307/2532051]CrossRef MATH
  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鈥揺0119584.19. [doi:10.1371/journal.pone.0119584]
  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鈥?195. [doi:10.1002/mrm.21391]CrossRef
  Lustig, M., Donoho, D.L., Santos, J.M., et al., 2008. Compressed sensing MRI. IEEE Signal Process. Mag., 25(2):72鈥?2. [doi:10.1109/MSP.2007.914728]CrossRef
  Mallat, S., 2008. A Wavelet Tour of Signal Processing: the Sparse Way (3rd Ed.). Academic Press, USA.
  Nguyen, T.T., Chauris, H., 2010. Uniform discrete curvelet transform. IEEE Trans. Signal Process., 58(7):3618鈥?634. [doi:10.1109/TSP.2010.2047666]CrossRef MathSciNet
  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鈥?622. [doi:10.1016/j.mri.2013.07.010]CrossRef
  Ophir, B., Lustig, M., Elad, M., 2011. Multi-scale dictionary learning using wavelets. IEEE J. Sel. Topics Signal Process., 5(5):1014鈥?024. [doi:10.1109/JSTSP.2011.2155032]CrossRef
  Qu, G., Zhang, D., Yan, P., 2002. Information measure for performance of image fusion. Electron. Lett., 38(7): 313鈥?15. [doi:10.1049/el:20020212]CrossRef
  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鈥?58. [doi:10.1080/17415977.2010.492509]CrossRef MathSciNet MATH
  Qu, X., Guo, D., Ning, B., et al., 2012. Undersampled MRI reconstruction with patch-based directional wavelets. Magn. Reson. Imag., 30(7):964鈥?77. [doi:10.1016/j.mri. 2012.02.019]CrossRef
  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鈥?56. [doi:10.1016/j.media.2013.09.007]CrossRef
  Rauhut, H., Schnass, K., Vandergheynst, P., 2008. Compressed sensing and redundant dictionaries. IEEE Trans. Inform. Theory, 54(5):2210鈥?219. [doi:10.1109/TIT.2008. 920190]CrossRef MathSciNet MATH
  Ravishankar, S., Bresler, Y., 2011. MR image reconstruction from highly undersampled k-space data by dictionary learning. IEEE Trans. Med. Imag., 30(5):1028鈥?041. [doi:10.1109/TMI.2010.2090538]CrossRef
  Rubinstein, R., Zibulevsky, M., Elad, M., 2010. Double sparsity: learning sparse dictionaries for sparse signal approximation. IEEE Trans. Signal Process., 58(3): 1553鈥?564. [doi:10.1109/TSP.2009.2036477]CrossRef MathSciNet
  Rudin, L.I., Osher, S., Fatemi, E., 1992. Nonlinear total variation based noise removal algorithms. Phys. D, 60(1-4): 259鈥?68. [doi:10.1016/0167-2789(92)90242-F]CrossRef MATH
  Trzasko, J., Manduca, A., 2009. Highly undersampled magnetic resonance image reconstruction via homotopic l 0-minimization. IEEE Trans. Med. Imag., 28(1):106鈥?21. [doi:10.1109/TMI.2008.927346]CrossRef
  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鈥?12. [doi:10.1109/TIP.2003.819861]CrossRef
  Xydeas, C.S., Petrovic, V., 2000. Objective image fusion performance measure. Electron. Lett., 36(4):308鈥?09. [doi:10.1049/el:20000267]CrossRef
  Zhu, Z., Wahid, K., Babyn, P., et al., 2013. Compressed sensing-based MRI reconstruction using complex doubledensity dual-tree DWT. Int. J. Biomed. Imag., 2013. 907501.1鈥?07501.12. [doi:10.1155/2013/907501]CrossRef
  
• 作者单位：Min Yuan (1)
  Bing-xin Yang (1)
  Yi-de Ma (1)
  Jiu-wen Zhang (1)
  Fu-xiang Lu (1)
  Tong-feng Zhang (1)
  
  1. School of Information Science & Engineering, Lanzhou University, Lanzhou, 730000, China
  
• 刊物类别：Computer Science, general; Electrical Engineering; Computer Hardware; Computer Systems Organization
• 刊物主题：Computer Science, general; Electrical Engineering; Computer Hardware; Computer Systems Organization and Communication Networks; Electronics and Microelectronics, Instrumentation; Communications Engine
• 出版者：Zhejiang University Press
• ISSN：2095-9230

文摘

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. Keywords 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)