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Highly undersampled MR image reconstruction using an improved dual-dictionary learning method with self-adaptive dictionaries

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Abstract

Dual-dictionary learning (Dual-DL) method utilizes both a low-resolution dictionary and a high-resolution dictionary, which are co-trained for sparse coding and image updating, respectively. It can effectively exploit a priori knowledge regarding the typical structures, specific features, and local details of training sets images. The prior knowledge helps to improve the reconstruction quality greatly. This method has been successfully applied in magnetic resonance (MR) image reconstruction. However, it relies heavily on the training sets, and dictionaries are fixed and nonadaptive. In this research, we improve Dual-DL by using self-adaptive dictionaries. The low- and high-resolution dictionaries are updated correspondingly along with the image updating stage to ensure their self-adaptivity. The updated dictionaries incorporate both the prior information of the training sets and the test image directly. Both dictionaries feature improved adaptability. Experimental results demonstrate that the proposed method can efficiently and significantly improve the quality and robustness of MR image reconstruction.

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References

  1. 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

    Article  Google Scholar 

  2. Awate SP, DiBella EV (2012) Spatiotemporal dictionary learning for undersampled dynamic MRI reconstruction via joint frame-based and dictionary-based sparsity. In: 2012 9th IEEE international symposium on biomedical imaging (ISBI). IEEE, pp 318–321

  3. Bao L, Liu W, Zhu Y, Pu Z, Magnin IE (2008) Sparse representation based MRI denoising with total variation. In: 9th International conference on signal processing, 2008 (ICSP 2008). IEEE, pp 2154–2157

  4. Caballero J, Rueckert D, Hajnal JV (2012) Dictionary learning and time sparsity in dynamic MRI. In: Medical image computing and computer-assisted intervention (MICCAI 2012). Springer, Berlin, pp 256–263

  5. Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509

    Article  Google Scholar 

  6. Chartrand R (2009) Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data. In: IEEE international symposium on biomedical imaging: from nano to macro, 2009 (ISBI’09). IEEE, pp 262–265

  7. Chen SS, Donoho DL, Saunders MA (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20(1):33–61

    Article  CAS  Google Scholar 

  8. Doneva M, Börnert P, Eggers H, Stehning C, Sénégas J, Mertins A (2010) Compressed sensing reconstruction for magnetic resonance parameter mapping. Magn Reson Med 64(4):1114–1120

    Article  PubMed  Google Scholar 

  9. Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  11. Engan K, Aase SO, Hakon Husoy J (1999) Method of optimal directions for frame design. In: Proceedings of the 1999 IEEE international conference on acoustics, speech, and signal processing, vol 5. IEEE, pp 2443–2446

  12. Jung H, Sung K, Nayak KS, Kim EY, Ye JC (2009) k-t FOCUSS: a general compressed sensing framework for high resolution dynamic MRI. Magn Reson Med 61(1):103–116

    Article  PubMed  Google Scholar 

  13. Khormuji MK, Bazrafkan M (2016) A novel sparse coding algorithm for classification of tumors based on gene expression data. Med Biol Eng Comput 54(6):869–876

    Article  Google Scholar 

  14. Kreutz-Delgado K, Murray JF, Rao BD, Engan K, Lee TW, Sejnowski TJ (2003) Dictionary learning algorithms for sparse representation. Neural Comput 15(2):349–396

    Article  PubMed  PubMed Central  Google Scholar 

  15. Li J, Sun J, Song Y, Zhao J (2015) Accelerating MRI reconstruction via three-dimensional dual-dictionary learning using CUDA. J Supercomput 71(7):2381–2396

    Article  Google Scholar 

  16. Lustig M, Donoho D, Pauly JM (2007) Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 58(6):1182–1195

    Article  PubMed  Google Scholar 

  17. Lustig M, Santos JM, Donoho DL, Pauly JM (2006) k-t SPARSE: high frame rate dynamic MRI exploiting spatio-temporal sparsity. In: Proceedings of the 13th annual meeting of ISMRM, Seattle, vol 2420

  18. Mairal J, Sapiro G, Elad M (2008) Learning multiscale sparse representations for image and video restoration. Multiscale Model Simul 7(1):214–241

    Article  Google Scholar 

  19. Mallat SG, Zhang Z (1993) Matching pursuits with time–frequency dictionaries. IEEE Trans Signal Process 41(12):3397–3415

    Article  Google Scholar 

  20. Pati YC, Rezaiifar R, Krishnaprasad P (1993) Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: 1993 Conference record of the twenty-seventh asilomar conference on signals, systems and computers. IEEE, pp 40–44

  21. Qu X, Guo D, Ning B, Hou Y, Lin Y, Cai S, Chen Z (2012) Undersampled MRI reconstruction with patch-based directional wavelets. Magn Reson Imaging 30(7):964–977

    Article  PubMed  Google Scholar 

  22. Qu X, Hou Y, Lam F, Guo D, Zhong J, Chen Z (2014) Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator. Med Image Anal 18(6):843–856

    Article  PubMed  Google Scholar 

  23. Qu X, Zhang W, Guo D, Cai C, Cai S, Chen Z (2010) Iterative thresholding compressed sensing MRI based on contourlet transform. Inverse Probl Sci Eng 18(6):737–758

    Article  Google Scholar 

  24. Ramirez I, Sprechmann P, Sapiro G (2010) Classification and clustering via dictionary learning with structured incoherence and shared features. In: 2010 IEEE conference on computer vision and pattern recognition (CVPR). IEEE, pp 3501–3508

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

    Article  PubMed  Google Scholar 

  26. Rubinstein R, Zibulevsky M, Elad M (2008) Efficient implementation of the K-SVD algorithm using batch orthogonal matching pursuit. CS Tech 40(8):1–15

    Google Scholar 

  27. Song Y, Zhu Z, Lu Y, Liu Q, Zhao J (2014) Reconstruction of magnetic resonance imaging by three-dimensional dual-dictionary learning. Magn Reson Med 71(3):1285–1298

    Article  PubMed  Google Scholar 

  28. Tropp JA (2004) Greed is good: algorithmic results for sparse approximation. IEEE Trans Inf Theory 50(10):2231–2242

    Article  Google Scholar 

  29. Tropp JA, Gilbert AC (2007) Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory 53(12):4655–4666

    Article  Google Scholar 

  30. Trzasko J, Manduca A (2009) Highly undersampled magnetic resonance image reconstruction via homotopic \(l_0\)-minimization. IEEE Trans n Med Imaging 28(1):106–121

    Article  Google Scholar 

  31. van de Gronde J, Vuçini E (2008) Compressed sensing overview. http://www.cg.tuwien.ac.at/research/publications/2008/Gronde_2008/Gronde_2008-report.pdf

  32. Yin XX, Ng BH, Ramamohanarao K, Baghai-Wadji A, Abbott D (2012) Exploiting sparsity and low-rank structure for the recovery of multi-slice breast MRIs with reduced sampling error. Med Biol Eng Comput 50(9):991–1000

    Article  CAS  PubMed  Google Scholar 

  33. Zhan Z, Cai J, Guo D, Liu Y, Chen Z, Qu X (2015) Fast multi-class dictionaries learning with geometrical directions in MRI reconstruction. IEEE Trans Bio-med Eng. doi:10.1109/TMI.2016.2550080

    Google Scholar 

Download references

Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 813716234), National Basic Research Program of China (2010CB834302), and Shanghai Jiao Tong University Medical Engineering Cross Research Funds (YG2013MS30 and YG2014ZD05).

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Correspondence to Jun Zhao.

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All procedures performed in studies were in accordance with the Declaration of Helsinki and approved by our institutional Medical Ethics Review Board.

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Li, J., Song, Y., Zhu, Z. et al. Highly undersampled MR image reconstruction using an improved dual-dictionary learning method with self-adaptive dictionaries. Med Biol Eng Comput 55, 807–822 (2017). https://doi.org/10.1007/s11517-016-1556-z

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  • DOI: https://doi.org/10.1007/s11517-016-1556-z

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