Compressed-sensing MRI with random encoding

IEEE Transactions on Medical Imaging

Volumn 30, Issue 4, 2011, Pages 893-903

  Haldar, Justin P ^a   Hernando, Diego ^a   Liang, Zhi Pei ^a  

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

Author keywords

Compressed sensing; magnetic resonance imaging (MRI); radio frequency encoding

Indexed keywords

COMPRESSED SENSING; ENCODING SCHEMES; EXPERIMENTAL STUDIES; FOURIER; IMAGING PROPERTIES; IMAGING SCHEMES; MATHEMATICAL PROPERTIES; MR IMAGES; RADIO FREQUENCIES; RADIO-FREQUENCY ENCODING; SIGNAL OF INTERESTS; SUFFICIENT CONDITIONS; THEORETICAL PERFORMANCE;

ENCODING (SYMBOLS); IMAGE CODING; RESONANCE; SIGNAL RECONSTRUCTION;

MAGNETIC RESONANCE IMAGING;

ALGORITHM; ARTICLE; BRAIN; FOURIER ANALYSIS; HISTOLOGY; HUMAN; IMAGE QUALITY; METHODOLOGY; MONTE CARLO METHOD; NUCLEAR MAGNETIC RESONANCE IMAGING; REPRODUCIBILITY; SIGNAL PROCESSING;

ALGORITHMS; BRAIN; FOURIER ANALYSIS; HUMANS; MAGNETIC RESONANCE IMAGING; MONTE CARLO METHOD; PHANTOMS, IMAGING; REPRODUCIBILITY OF RESULTS; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 79953740726     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2010.2085084     Document Type: Article

References (57)

1. E. J. 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)
2. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
3. E. Candès and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006. (Pubitemid 46445381)
4. E. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. (Pubitemid 41800353)
5. E. J. Candès, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Comm. Pure Appl. Math., vol. 59, pp. 1207-1223, 2006. (Pubitemid 43988295)
6. P. Feng and Y. Bresler, "Spectrum-blind minimum-rate sampling and reconstruction of multiband signals," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 1996, pp. 1688-1691.
7. R. Venkataramani and Y. Bresler, "Further results on spectrum blind sampling of 2D signals," in Proc. IEEE Int. Conf. Image Process., 1998, pp. 752-756.
8. M. Lustig, D. Donoho, and J. M. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magn. Reson. Med., vol. 58, pp. 1182-1195, 2007. (Pubitemid 350234205)
9. 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. Int. Soc. Magn. Reson. Med., 2006, p. 2420.
10. K. T. Block, M. Uecker, and J. Frahm, "Undersampled radial MRI with multiple coils. iterative image reconstruction using a total variation constraint," Magn. Reson. Med., vol. 57, pp. 1086-1098, 2007. (Pubitemid 46911293)
11. H. Jung, J. C. Ye, and E. Y. Kim, "Improved BLAST and SENSE using FOCUSS," Phys. Med. Biol., vol. 52, pp. 3201-3226, 2007. (Pubitemid 46795256)
12. J. C.Ye, S. Tak, Y. Han, and H. W. Park, "Projection reconstructionMR imaging using FOCUSS," Magn. Reson. Med., vol. 57, pp. 764-775, 2007. (Pubitemid 46731802)
13. U. Gamper, P. Boesiger, and S. Kozerke, "Compressed sensing in dynamic MRI," Magn. Reson. Med., vol. 59, pp. 365-373, 2008. (Pubitemid 351220100)
14. S. Hu, M. Lustig, A. P. Chen, J. Crane, A. Kerr, D. A. C. Kelley, R. Hurd, J. Kurhanewicz, S. J. Nelson, J. M. Pauly, and D. B. Vigneron, "Compressed sensing for resolution enhancement of hyperpolarized- flyback 3D-MRSI," J. Magn. Reson., vol. 192, pp. 258-264, 2008.
15. J. Trzasko and A. Manduca, "Highly undersampled magnetic resonance image reconstruction via homotopic -minimization," IEEE Trans. Med. Imag., vol. 28, no. 1, pp. 106-121, Jan. 2009.
16. Y.-C. Kim, S. S. Narayanan, and K. S. Nayak, "Accelerated three-dimensional upper airway MRI using compressed sensing," Magn. Reson. Med., vol. 61, pp. 1434-1440, 2009.
17. C. O. Schirra, S.Weiss, S. Krueger, S. F. Pedersen, R. Razavi, T. Schaeffter, and S.Kozerke, "Toward true 3D visualization of active catheters using compressed sensing," Magn. Reson. Med., vol. 62, pp. 341-347, 2009.
18. D. Liang, B. Liu, J. J.Wang, and L. Ying, "Accelerating SENSE using compressed sensing," Magn. Reson. Med., vol. 62, pp. 1574-1584, 2009.
19. M. Seeger, H. Nickisch, R. Pohmann, and B. Schölkopf, "Optimization of-space trajectories for compressed sensing by Bayesian experimental design," Magn. Reson. Med., vol. 63, pp. 116-126, 2010.
20. S. Ajraoui, K. J. Lee, M. H. Deppe, S. R. Parnell, J. Parra-Robles, and J. M. Wild, "Compressed sensing in hyperpolarized-lung MRI," Magn. Reson. Med., vol. 63, pp. 1059-1069, 2010.
21. E. J. Candès, "The restricted isometry property and its implications for compressed sensing," C. R. Acad. Sci. Paris, Ser. I, vol. 346, pp. 589-592, 2008.
22. M. E. Davies and R. Gribonval, "Restricted isometry constants where-sparse recovery can fail for," IEEE Trans. Inf. Theory, vol. 55, pp. 2203-2214, 2009.
23. D. L. Donoho and M. Elad, "Optimally sparse representation in general (nonorthogonal) dictionaries via-minimization," Proc. Natl. Acad. Sci. USA, vol. 100, pp. 2197-2202, 2003. (Pubitemid 36297476)
24. 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)
25. E. Candès and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Probl., vol. 23, pp. 969-985, 2007. (Pubitemid 46838836)
26. A. Cohen, W. Dahmen, and R. DeVore, "Compressed sensing and best-term approximation," J. Am. Math. Soc., vol. 22, pp. 211-231, 2009.
27. D. L. Donoho and X. Huo, "Uncertainty principles and ideal atomic decomposition," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2845-2862, Nov. 2001. (Pubitemid 33053488)
28. R. Gribonval and M. Nielsen, "Sparse representations in unions of bases," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3320-3325, Dec. 2003.
29. S. Foucart, "A note on guaranteed sparse recovery via-minimization," Appl. Comput. Harmon. Anal., vol. 29, pp. 97-103, 2009.
30. T. T. Cai, L. Wang, and G. Xu, "New bounds for restricted isometry constants," IEEE Trans. Inf. Theory, vol. 56, no. 9, pp. 4388-4394, Sep. 2010.
31. M. Rudelson and R. Vershynin, "On sparse reconstruction from Fourier and Gaussian measurements," Comm. Pure Appl. Math., vol. 61, pp. 1025-1045, 2008.
32. D. L. Donoho and J. Tanner, "Exponential bounds implying construction of compressed sensing matrices, error-correcting codes, and neighborly polytopes by random sampling," IEEE Trans. Inf. Theory, vol. 56, pp. 2002-2016, 2010.
33. E. J. Candès, Y. C. Eldar, and D. Needell, Compressed sensing with coherent and redundant dictionaries 2010 [Online]. Available: http:// arxiv.org/abs/1005.2613
34. J. P. Haldar, D. Hernando, B. P. Sutton, and Z.-P. Liang, "Data acquisition considerations for compressed sensing in MRI," in Proc. Int. Soc. Magn. Reson. Med., 2007, p. 829.
35. F. M. Sebert, Y. Zou, B. Liu, and L. Ying, "Compressed sensing MRI with random B1 field," in Proc. Int. Soc. Magn. Reson. Med., 2008, p. 1318.
36. D. Liang, G. Xu, H. Wang, K. F. King, D. Xu, and L. Ying, "Toeplitz random encoding MR imaging using compressed sensing," in Proc. IEEE Int. Symp. Biomed. Imag., 2009, pp. 270-273.
37. G. Puy, Y. Wiaux, R. Gruetter, J.-P. Thiran, D. V. de Ville, and P. Vandergheynst, "Spread spectrum for interferometric and magnetic resonance imaging," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2010, pp. 2802-2805.
38. Y.Wiaux, G. Puy, R. Gruetter, J.-P. Thiran, D. V. de Ville, and P. Vandergheynst, "Spread spectrum for compressed sensing techniques in magnetic resonance imaging," in Proc. IEEE Int. Symp. Biomed. Imag., 2010, pp. 756-759.
39. E. C. Wong, "Efficient randomly encoded data acquisition for compressed sensing," in Proc. Int. Soc. Magn. Reson. Med., 2010, p. 4893.
40. X. Pan, E. Y. Sidky, and M.Vannier, "Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?," Inverse Probl., vol. 25, p. 123009, 2009.
41. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, "Single-pixel imaging via compressive sensing," IEEE Signal Process. Mag., vol. 25, pp. 83-91, 2008.
42. R. F. Marcia, Z. T. Harmany, and R. M. Willett, "Compressive coded aperture imaging," in Proc. SPIE, 2009, vol. 7246, p. 72460G.
43. L. P. Panych, G. P. Zientara, and F. A. Jolesz, "MR image encoding by spatially selective RF excitation: An analysis using linear response models," Int. J. Imag. Syst. Tech., vol. 10, pp. 143-150, 1999.
44. G. Johnson, E. X. Wu, and S. K. Hilal, "Optimized phase scrambling for RF phase encoding," J. Magn. Reson. B, vol. 103, pp. 59-63, 1994.
45. C. H. Cunningham, G. A.Wright, and M. L.Wood, "High-order multiband encoding in the heart," Magn. Reson. Med., vol. 48, pp. 689-698, 2002.
46. D. Mitsouras, G. P. Zientara, A. Edelman, and F. J. Rybicki, "Enhancing the acquisition efficiency of fast magnetic resonance imaging via broadband encoding of signal content," Magn. Reson. Imag., vol. 24, pp. 1209-1227, 2006. (Pubitemid 44635066)
47. K. P. Pruessmann, M. Weiger, P. Börnert, and P. Boesiger, "Advances in sensitivity encoding with arbitrary k-space trajectories," Magn. Reson. Med., vol. 46, pp. 638-651, 2001. (Pubitemid 32906132)
48. J. Pauly, D. Nishimura, and A. Macovski, "A k-space analysis of smalltip- angle excitation," J. Magn. Reson., vol. 81, pp. 43-56, 1989.
49. S. T. S. Wong, M. S. Roos, R. D. Newmark, and T. F. Budinger, "Discrete analysis of stochastic NMR. I," J. Magn. Reson., vol. 87, pp. 242-264, 1990.
50. R. D. Peters and M. L. Wood, "Multilevel wavlet-transform encoding in MRI," J. Magn. Reson. Imag., vol. 6, pp. 529-540, 1996.
51. Z. Wang and G. R. Arce, "Variable density compressed image sampling," IEEE Trans. Image Process., vol. 19, no. 1, pp. 264-270, Jan. 2010.
52. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, vol. 60, pp. 259-268, 1992.
53. S. Becker, J. Bobin, and E. J. Candès, NESTA: A fast and accurate first-order method for sparse recovery California Inst. Technol., Tech. Rep., 2009 [Online]. Available: http://www.acm.caltech.edu/nesta/
54. M. A. Herman and T. Strohmer, "General deviants: An analysis of perturbations in compressed sensing," IEEE J. Sel. Topics Signal Process., vol. 4, pp. 342-349, 2010.
55. A. Edelman, "Eigenvalues and condition numbers of random matrices," SIAM J. Matrix Anal. Appl., vol. 9, pp. 543-560, 1988.
56. M. Elad, "Optimized projections for compressed sensing," IEEE Trans. Signal Process., vol. 55, no. 12, pp. 5695-5702, Dec. 2007. (Pubitemid 350201203)
57. T. T. Cai, L. Wang, and G. Xu, "Stable recovery of sparse signals and an oracle inequality," IEEE Trans. Inf. Theory, vol. 56, no. 7, pp. 3516-3522, Jul. 2010.