MR image reconstruction from highly undersampled k-space data by dictionary learning

IEEE Transactions on Medical Imaging

Volumn 30, Issue 5, 2011, Pages 1028-1041

  Ravishankar, Saiprasad ^a   Bresler, Yoram ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Compressed sensing (CS); dictionary learning; image reconstruction; magnetic resonance imaging (MRI); reduced encoding; sparse representation

Indexed keywords

ALIASING; COMPRESSED SENSING; CURVELETS; DATA SIGNALS; DICTIONARY LEARNING; FINITE DIFFERENCE; K-SPACE; LOCAL STRUCTURE; MR IMAGES; NUMERICAL EXPERIMENTS; ONE STEP; OVERLAPPING IMAGES; PARAMETER-TUNING; RECONSTRUCTION ALGORITHMS; RECONSTRUCTION ERROR; REDUCED ENCODING; SAMPLING SCHEMES; SPARSE REPRESENTATION; UNDER-SAMPLING;

ENCODING (SYMBOLS); IMAGE RECONSTRUCTION; MEDICAL IMAGING; METADATA; RESONANCE; SIGNAL TO NOISE RATIO; WAVELET TRANSFORMS;

MAGNETIC RESONANCE IMAGING;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; BACK; BRAIN; FACTUAL DATABASE; HISTOLOGY; HUMAN; IMAGE PROCESSING; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; THEORETICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; BRAIN; DATABASES, FACTUAL; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; LUMBOSACRAL REGION; MAGNETIC RESONANCE IMAGING; MODELS, THEORETICAL;

EID: 79955633431     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2010.2090538     Document Type: Article

References (61)

1. K. P. Pruessmann, "Encoding and reconstruction in parallel MRI," NMR Biomed., vol. 19, no. 3, pp. 288-299, 2006. (Pubitemid 43811103)
2. Z. Liang and P. Lauterbur, Principles of Magnetic Resonance Imaging: A Signal Processing Perspective. New York: Wiley-IEEE, 1999.
3. N. Aggarwal and Y. Bresler, "Patient-adapted reconstruction and acquisition dynamic imaging method (PARADIGM) for MRI," Inverse Problems, vol. 24, no. 4, pp. 045015-1-045015-29, 2008.
4. B. Sharif, J. A. Derbyshire, A. Z. Faranesh, and Y. Bresler, "Patient-adaptive reconstruction and acquisition in dynamic imaging with sensitivity encoding (PARADISE),"Magn. Reson. Med., vol. 64, no. 2, pp. 501-513, 2010.
5. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006. (Pubitemid 43174093)
6. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
7. E. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. (Pubitemid 41800353)
8. P. Feng and Y. Bresler, "Spectrum-blind minimum-rate sampling and reconstruction of multiband signals," in ICASSP, May 1996, vol. 3, pp. 1689-1692.
9. Y. Bresler and P. Feng, "Spectrum-blind minimum-rate sampling and reconstruction of 2-D multiband signals," in Proc. 3rd IEEE Int. Conf. Image Process. (ICIP'96), Sep. 1996, pp. 701-704.
10. P. Feng, "Universal spectrum blind minimum rate sampling and reconstruction of multiband signals," Ph.D. dissertation, Univ. Illinois, Urbana-Champaign, Mar. 1997.
11. R. Venkataramani and Y. Bresler, "Further results on spectrum blind sampling of 2D signals," in Proc. IEEE Int. Conf. Image Proc. (ICIP), Oct. 1998, vol. 2, pp. 752-756.
12. Y. Bresler, M. Gastpar, and R. Venkataramani, "Image compression on-the-fly by universal sampling in Fourier imaging systems," in Proc. 1999 IEEE Inf. Theory Workshop Detection, Estimation, Classification, Imag, Feb. 1999, p. 48.
13. M. Gastpar and Y. Bresler, "On the necessary density for spectrum-blind nonuniform sampling subject to quantization," in ICASSP, Jun. 2000, vol. 1, pp. 348-351.
14. J. C. Ye, Y. Bresler, and P. Moulin, "A self-referencing level-set method for image reconstruction from sparse Fourier samples," Int. J. Comput. Vis., vol. 50, no. 3, pp. 253-270, Dec. 2002. (Pubitemid 35377415)
15. Y. Bresler, "Spectrum-blind sampling and compressive sensing for continuous-index signals," in Proc. 2008 Inf. Theory Appl. Workshop Conf, 2008, pp. 547-554.
16. M. Lustig, D. Donoho, and J. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magn. Reson. Med., vol. 58, no. 6, pp. 1182-1195, 2007. (Pubitemid 350234205)
17. M. Lustig, J. M. Santos, D. L. Donoho, and J. M. Pauly, "k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity," in Proc. ISMRM, 2006, p. 2420.
18. R. Chartrand, "Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data," in Proc. IEEE Int. Symp. Biomed. Imag. (ISBI), 2009, pp. 262-265.
19. 0 -minimization," IEEE Trans. Med. Imag, vol. 28, no. 1, pp. 106-121, Jan. 2009.
20. Y. Kim, M. S. Nadar, and A. Bilgin, "Wavelet-based compressed sensing using gaussian scale mixtures," in Proc. ISMRM, 2010, p. 4856.
21. C. Qiu, W. Lu, and N. Vaswani, "Real-time dynamic MR image reconstruction using Kalman filtered compressed sensing," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process., 2009, pp. 393-396.
22. S. Ma, W. Yin, Y. Zhang, and A. Chakraborty, "An efficient algorithm for compressed MR imaging using total variation and wavelets," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit. (CVPR), 2008, pp. 1-8.
23. 2009, American Radiology Services [Online]. Available: http://www3. americanradiology.com/pls/web1/wwimggal.vmg/
24. M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Trans. Signal Process., vol. 54, no. 11, pp. 4311-4322, Nov. 2006. (Pubitemid 44637761)
25. K. Engan, S. Aase, and J. Hakon-Husoy, "Method of optimal directions for frame design," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process., 1999, pp. 2443-2446.
26. M. Elad and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Trans. Image Process., vol. 15, no. 12, pp. 3736-3745, Dec. 2006. (Pubitemid 44811686)
27. J. Mairal, M. Elad, and G. Sapiro, "Sparse representation for color image restoration," IEEE Trans. Image Process., vol. 17, no. 1, pp. 53-69, Jan. 2008.
28. M. Protter and M. Elad, "Image sequence denoising via sparse and redundant representations," IEEE Trans. Image Process., vol. 18, no. 1, pp. 27-36, Jan. 2009.
29. M. Aharon and M. Elad, "Sparse and redundant modeling of image content using an image-signature-dictionary," SIAM J. Imag. Sci., vol. 1, no. 3, pp. 228-247, 2008.
30. J. Mairal, G. Sapiro, and M. Elad, "Learning multiscale sparse representations for image and video restoration," SIAM Multiscale Model. Simulat., vol. 7, no. 1, pp. 214-241, 2008.
31. G. Yu, G. Sapiro, and S. Mallat, "Image modeling and enhancement via structured sparse model selection," in Proc. IEEE Int. Conf. Image Process. (ICIP), Sep., 2010, pp. 1641-1644.
32. C. Kervrann and J. Boulanger, "Local adaptivity to variable smoothness for exemplar-based image regularization and representation," Int. J. Comput. Vis., vol. 79, no. 1, pp. 45-69, 2008.
33. J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
34. D. L.Donoho, "For most large underdetermined systems of linear equations the minimal l1-norm solution isalso the sparsest solution," Comm. Pure Appl. Math, vol. 59, pp. 797-829, 2004.
35. D. L. Donoho, M. Elad, and V. N. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 6-18, Jan. 2006. (Pubitemid 43263116)
36. I. F. Gorodnitsky, J. George, and B. D. Rao, "Neuromagnetic source imaging with FOCUSS: A recursive weighted minimum norm algorithm," Electrocephalogr. Clin. Neurophysiol., vol. 95, pp. 231-251, 1995.
37. G. Harikumar and Y. Bresler, "A new algorithm for computing sparse solutions to linear inverse problems," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process., May 1996, pp. 1331-1334.
38. Y. Bresler, C. Couvreur, and G. Harikumar, "Fast optimal and sub-optimal algorithms for sparse solutions to linear inverse problems," in Proc. IEEE Int. Conf. Acoust. Speech, Sig. Proc., Apr. 1998, vol. 3, pp. 1877-1880.
39. G. Harikumar, "Blind image deconvolution from multiple blurs, and sparse approximation," Ph.D. dissertation, Univ.Illinois, Ur-bana-Champaign, Mar. 1997.
40. R. Chartrand, "Exact reconstruction of sparse signals via nonconvex minimization," IEEE Signal Process. Lett., vol. 14, no. 10, pp. 707-710, Oct. 2007. (Pubitemid 47434090)
41. U. Gamper, P. Boesiger, and S. Kozerke, "Compressed sensing in dynamic MRI," Magn. Reson. Med., vol. 59, no. 2, pp. 365-373, 2008. (Pubitemid 351220100)
42. H. Jung, K. Sung, K. S. Nayak, E. Y. Kim, and J. C. Ye, "k-t FOCUSS: A general compressed sensing framework for high resolution dynamic MRI," Magn. Reson. Med., vol. 61, no. 1, pp. 103-116, 2009.
43. B. Wu, R. Watts, R. Millane, and P. Bones, "An improved approach in applying compressed sensing in parallel MR imaging," in Proc. ISMRM, 2009, p. 4595.
44. B. Liu, F. M. Sebert, Y. Zou, and L. Ying, "SparseSENSE: Randomly-sampled parallel imaging using compressed sensing," in Proc. ISMRM, 2008, p. 3154.
45. G. Adluru and E. V. R. DiBella, "Reordering for improved constrained reconstruction from undersampled k-space data," J. Biomed. Imag., vol. 2008, pp. 1-12, 2008.
46. Y. Kim, M. I. Altbach, T. P. Trouard, and A. Bilgin, "Compressed sensing using dual-tree complex wavelet transform," in Proc. ISMRM, 2009, p. 2814.
47. X. Qu, D. Guo, Z. Chen, and C. Cai, "Compressed sensing MRI based on nonsubsampled contourlet transform," in Proc. IEEE Int. Symp. IT Med. Edu., 2008, pp. 693-696.
48. X. Qu, X. Cao, D. Guo, C. Hu, and Z. Chen, "Combined sparsifying transforms for compressed sensing MRI," Electron. Lett., vol. 46, no. 2, pp. 121-123, 2010.
49. X. Qu, W. Zhang, D. Guo, C. Cai, S. Cai, and Z. Chen, "Iterative thresholding compressed sensing MRI based on contourlet transform," Inverse Problems Sci. Eng., Jun. 2010.
50. J. Trzasko, A. Manduca, and E. Borisch, "Robust kernel methods for sparse MR image reconstruction," in Proc. Med. Image Comput. Computer-Assist. Intervent. (MICCAI2007), 2007, pp. 809-816.
51. 0 -continuation," in Proc. IEEE/SP 14th Workshop Stat. Signal Process., 2007, pp. 176-180.
52. M. Yaghoobi, T. Blumensath, and M. Davies, "Dictionary learning for sparse approximations with the majorization method," IEEE Trans. Signal Process., vol. 57, no. 6, pp. 2178-2191, Jun. 2009.
53. B. A. Olshausen and D. J. Field, "Emergence of simple-cell receptive field properties by learning a sparse code for natural images," Nature, vol. 381, no. 6583, pp. 607-609, 1996. (Pubitemid 26177476)
54. R. Rubinstein, A. M. Bruckstein, and M. Elad, "Dictionaries for sparse representation modeling," Proc. IEEE, vol. 98, no. 6, pp. 1045-1057, 2010.
55. I. Tosic, I. Jovanovic, P. Frossard, M. Vetterli, and N. Duric, "Ultrasound tomography with learned dictionaries," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., 2010, pp. 5502-5505.
56. A. Bilgin, Y. Kim, F. Liu, and M. S. Nadar, "Dictionary design for compressed sensing MRI," in Proc. ISMRM, 2010, p. 4887.
57. Y. Chen, X. Ye, and F. Huang, "A novel method and fast algorithm for MR image reconstruction with significantly under-sampled data," Inverse Problems Imag., vol. 4, no. 2, pp. 223-240, 2010.
58. R. Otazo and D. K. Sodickson, "Adaptive compressed sensing MRI," in Proc. ISMRM, 2010, p. 4867.
59. R. Gribonval and K. Schnass, "Dictionary identification-Sparse matrix-factorisation via 11 -minimisation," IEEE Trans. Inf. Theory vol. 56, no. 7, pp. 3523-3539, Jul. 2010.
60. J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski, "Selection of a convolution function for Fourier inversion using gridding," IEEE Trans. Med. Imag., vol. 10, no. 3, pp. 473-478, Sep. 1991.
61. M. Lustig, 2006 [Online]. Available: http://www.stanford.edu/ ~mlustig/