Sparsity-Enforced Slice-Selective MRI RF Excitation Pulse Design

IEEE Transactions on Medical Imaging

Volumn 27, Issue 9, 2008, Pages 1213-1229

  Zelinski, Adam C ^a   Wald, Lawrence L ^b   Setsompop, Kawin ^a   Goyal, Vivek K ^a   Adalsteinsson, Elfar ^a  

^a USA   (United States)

^b HARVARD MEDICAL SCHOOL   (United States)

Author keywords

B1 inhomogeneity mitigation; high field strength; magnetic resonance imaging (MRI) radio frequency (RF) pulse sequence design; parallel transmission; sparse approximation; threedimensional (3 D) RF excitation

Indexed keywords

ALGORITHM; ARTICLE; BRAIN; COMPUTER ASSISTED DIAGNOSIS; HISTOLOGY; HUMAN; IMAGE ENHANCEMENT; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; SIGNAL PROCESSING; THREE DIMENSIONAL IMAGING;

ALGORITHMS; BRAIN; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; MAGNETIC RESONANCE IMAGING; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 54449094080     PISSN: 02780062     EISSN: 1558254X     Source Type: Journal    
DOI: 10.1109/TMI.2008.920605     Document Type: Article

References (69)

1. X. Hu and T. Parrish, “Reduction of field of viewfor dynamic imaging,” Magn. Reson. Med., vol. 31, pp. 691–694, 1994.
2. G. Glover and S. Lai, “Reduction of susceptibility artifacts in BOLD fMRI using tailored RF pulses,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), 1998, p. 298.
3. S. Saekho, C. Y. Yip, D. C. Noll, F. E. Boada, and V. A. Stenger, “Fast-kz three-dimensional tailored radiofrequency pulse for reduced B1 inhomogeneity,” Magn. Reson. Med., vol. 55, no. 4, pp. 719–724, 2006.
4. J. Ulloa and J. V. Hajnal, “Exploring 3D RF shimming for slice selective imaging,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), Miami Beach, FL, 2005, p. 21.
5. K. Setsompop, L. L. Wald, V. Alagappan, B. A. Gagoski, F. Hebrank, U. Fontius, F. Schmitt, and E. Adalsteinsson, “Parallel RF transmission with 8 channels at 3 Tesla,” Magn. Reson. Med., vol. 56, no. 5, pp. 1163–1171, 2006.
6. J. M. Pauly, D. Nishimura, and A. Macovski, “A Қ-space analysis of small-tip angle excitation,” J. Magn. Reson., vol. 81, pp. 43–56, 1989.
7. A. V. Oppenheim and R. Schafer, Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
8. M. A. Bernstein, K. F. King, and X. J. Zhou, Handbook of MRI Pulse Sequences. New York: Elsevier, 2004.
9. Y. Zhu, “Parallel excitation with an array of transmit coils,” Magn. Reson. Med., vol. 51, no. 4, pp. 775–784, 2004.
10. P. Ullmann, S. Junge, M. Wick, F. Seifert, W. Ruhm, and J. Hennig, “Experimental analysis of parallel excitation using dedicated coil setups and simultaneous RF transmission on multiple channels,” Magn. Reson. Med., vol. 54, no. 4, pp. 994–1001, 2005.
11. Y. Zhu, R. Watkins, R. Gianquinto, C. Hardy, G. Kenwood, S. Mathias, T. Valent, M. Denzin, J. Hopkins, W. Peterson, and B. Mock, “Parallel excitation on an eight transmit channel MRI system,” in Proc. Int. Soc. Magn. Reson. Medicine (ISMRM), Miami Beach, FL, 2005, p. 14.
12. 2-weighted functional magnetic resonance imaging,” Magn. Reson. Med., vol. 56, no. 5, pp. 1050–1059, 2006.
13. P. A. Bottomley and E. R. Andrew, “RF magnetic field penetration, phase shift and power dissipation in biological tissue: Implications for NMR imaging,” Phys. Med. Biol., vol. 23, pp. 630–643, 1978.
14. H. Bomsdorf, T. Helzel, D. Kunz, P. Roschmann, O. Tschendel, and J. Wieland, “Spectroscopy and imaging with a 4 Tesla whole-body MR system,” NMR Biomed., vol. 1, no. 3, pp. 151–158, 1988.
15. J. T. Vaughan, M. Garwood, C. M. Collins, W. Liu, L. DelaBarre, G. Adriany, P. Anderson, H. Merkle, R. Goebel, M. B. Smith, and K. Ugurbil, “7T vs. 4T: RF power, homogeneity, and signal-to-noise comparison in head images,” Magn. Reson. Med., vol. 46, no. 1, pp. 24–30, 2001.
16. 1 destructive interference and spatial phase patterns at 7T with a head transceiver array coil,” Magn. Reson. Med., vol. 54, pp. 1503–1518, 2005.
17. C. M. Collins, L. Wanzhan, W. Schreiber, Q.X.Yang, and M. B. Smith, “Central brightening due to constructive interference with, without, and despite dielectric resonance,” J. Magn. Reson. Imag., vol. 21, no. 2, pp. 192–196, 2005.
18. J. Jin and J. Chen, “On the SAR and field inhomogeneity of birdcage coils loaded with the human head,” Magn. Reson. Med., vol. 21, pp. 192–196, 1997.
19. C. M. Collins, S. Li, and M. B. Smith, “SAR and B1 field distributions in a heterogeneous human head model within a birdcage coil,” Magn. Res. Med., vol. 40, pp. 847–856, 1998.
20. T. S. Ibrahim, R. Lee, B. A. Baertlein, and P.-M.L. Robitaille, “B1 field homogeneity and SAR calculations in the high pass birdcage coil,” Phys. Med. Biol., vol. 46, pp. 609–619, 2001.
21. C. Y. Yip, J. A. Fessler, and D. C. Noll, “A novel, fast and adaptive trajectory in three-dimensional excitation k-space,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), Miami, FL, 2005, p. 2350.
22. G. Davis, “Adaptive nonlinear approximations,” Ph.D. dissertation, New York Univ., Sep. 1994.
23. B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput., vol. 24, no. 2, pp. 227–234, 1995.
24. I. F. Gorodnitsky and B. D. Rao, “Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm,” IEEE Trans Signal Process., vol. 45, no. 3, pp. 600–616, Mar. 1997.
25. S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33–61, 1999.
26. 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.
27. J. A. Tropp, “Topics in sparse approximation,” Ph.D. dissertation, Univ. Texas, Austin, 2004.
28. U. Katscher, P. Bornert, C. Leussler, and J. S. van den Brink, “Transmit SENSE,” Magn. Reson. Med., vol. 49, no. 1, pp. 144–150, Jan. 2003.
29. I. Graesslin, P. Vernickel, J. Schmidt, C. Findeklee, P. Roschmann, C. Leussler, P. Haaker, H. Laudan, K. M. Luedeke, J. Scholz, S. Buller, J. Keupp, P. Bornert, H. Dingemans, G. Mens, G. Vissers, K. Blom, N. Swennen, J. vd Heijden, L. Mollevanger, P. Harvey, and U. Katscher, “Whole body 3T MRI system with eight parallel RF transmission channels,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), Seattle, WA, 2006, p. 129.
30. D. M. Malioutov, M. Cetin, and A. S. Willsky, “A sparse signal reconstruction perspective for source localization with sensor arrays,” IEEE Trans. Signal Process., vol. 53, no. 8, pp. 3010–3022, Aug. 2005.
31. J. A. Tropp, “Just relax: Convex programming methods for identifying sparse signals,” IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1030–1051, Mar. 2006.
32. J. A. Tropp, “Algorithms for simultaneous sparse approximation: Part II: Convex relaxation,” Signal Process., vol. 86, no. 3, pp. 589–602, 2006.
33. A. Nemirovski and A. Ben-Tal, Lectures on Modern Convex Optimization. Analysis, Algorithms and Engineering Applications. Philadelphia, PA: SIAM, 2001.
34. A. C. Zelinski, K. Setsompop, V. K. Goyal, V. Alagappan, U. Fontius, F. Schmitt, L. L. Wald, and E. Adalsteinsson, “Designing fast 3D RF excitations by optimizing the number, placement, and weighting of spokes in k-space via a sparsity-enforcement algorithm,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), Berlin, Germany, 2007, p. 1691.
35. K. Setsompop, A. C. Zelinski, V. K. Goyal, L. L. Wald, and E. Adalsteinsson, “Sparse spokes slice-selective design for B1-inhomogeneity correction at 7T,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), Berlin, Germany, 2007, p. 356.
36. C. Y. Yip, W. A. Grissom, J. A. Fessler, and D. C. Noll, “Joint design of trajectory and RF pulses for parallel excitation,” Magn. Reson. Med., vol. 58, no. 3, pp. 598–604, 2007.
37. D. K. Sodickson and W. J. Manning, “Simultaneous acquisition of spatial harmonics (SMASH): Fast imaging with radio frequency coil arrays,” Magn. Reson. Med., vol. 38, no. 4, pp. 591–603, Oct. 1997.
38. K. P. Pruessmann, M. Weiger, M. B. Scheidegger, and P. Boesiger, “SENSE: Sensitivity encoding for fast MRI,” Magn. Reson. Med., vol. 42, pp. 952–962, Nov. 1999.
39. W. A. Grissom, C. Y. Yip, Z. Zhang, V. A. Stenger, J. A. Fessler, and D. C. Noll, “Spatial domain method for the design of RF pulses in multicoil parallel excitation,” Magn. Reson. Med., vol. 56, no. 3, pp. 620–629, 2006.
40. C. Y. Yip, J. A. Fessler, and D. C. Noll, “Iterative RF pulse design for multidimensional, small-tip-angle selective excitation,” Magn. Reson. Med., vol. 54, no. 4, pp. 908–917, 2005.
41. U. Katscher, I. Graesslin, H. Dingemans, and G. Mens, “Experimental verification of over- and underdetermined transmit SENSE,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), 2006, p. 600.
42. A. C. Zelinski, L. L. Wald, K. Setsompop, V. Alagappan, B. A. Gagoski, V. K. Goyal, F. Hebrank, U. Fontius, F. Schmitt, and E. Adalsteinsson, “Comparison of three algorithms for solving linearized systems of parallel excitation RF waveform design equations: Experiments on an eight-channel system at 3 Tesla,” Concepts Magn. Reson. Part B: Magn. Reson. Eng., vol. 31B, no. 3, pp. 176–190, Aug. 2007.
43. A. N. Tikhonov, “On the solution of incorrectly stated problems and a method of regularization,” Dokl. Acad. Nauk SSSR, vol. 151, pp. 501–504, 1963.
44. U. Katscher, P. Bornert, and J. S. van den Brink, “Theoretical and numerical aspects of transmit SENSE,” IEEE Trans. Med. Imag., vol. 23, no. 4, pp. 520–525, Apr. 2004.
45. C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Software, vol. 8, no. 1, pp. 43–71, Mar. 1982.
46. R. R. Ernst and W. A. Anderson, “Applications of Fourier transform spectroscopy to magnetic resonance,” Rev. Sci. Instrum., vol. 37, pp. 93–102, 1966.
47. J.Wang, M. Qiu, Q. X. Yang, M. B. Smith, and R. T. Constable, “Measurement and correction of transmitter and receivers induced nonuniformities in vivo,” Magn. Reson. Med., vol. 53, pp. 408–417, 2005.
48. A. B. Kerr, C. H. Cunningham, J. M. Pauly, R. O. Gianquinto, R. D. Watkins, and Y. Zhu, “Self-calibrated transmit SENSE,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), Seattle, WA, 2006, p. 14.
49. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, Mar. 2004.
50. 1-norm near-solution approximates the sparsest near-solution,” Commun. Pure Appl. Math, vol. 59, no. 7, pp. 907–934, Jul. 2006.
51. R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. Roy. Statist. Soc., ser. B, vol. B 58, no. 1, pp. 267–288, Nov. 1996.
52. J. A. Tropp, A. C. Gilbert, and M. J. Strauss, “Algorithms for simultaneous sparse approximation: Part I: Greedy pursuit,” Signal Process., vol. 86, no. 3, pp. 572–588, 2006.
53. J. Sturm, “Using sedumi 1.02, a MATLAB toolbox for optimization over symmetric cones,” Optimizat. Methods Software, vol. 11–12, pp. 625–653, 1999.
54. K. C. Toh, M. J. Todd, and R. H. Tutuncu, “SDPT3—A matlab software package for semidefinite programming,” Optimizat. Methods Software, vol. 11, no. 12, pp. 545–581, 1999.
55. D. G. Luenberger, Optimization by Vector Space Methods. New York: Wiley, 1969.
56. P. Ullmann, S. Junge, F. Seifert, W. Ruhm, and J. Hennig, “Parallel excitation experiments using a novel direct calibration technique for RF-pulse determination,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), Berlin, Germany, 2007, p. 672.
57. J. Tropp, “The hybrid bird cage resonator,” in Proc. Soc. Magn. Reson. Med. (SMRM), Berlin, Germany, 1992, p. 4009.
58. E. A. Barberi, J. S. Gati, B. K. Rutt, and R. S. Menon, “A transmitonly/ receive-only (TORO) RF system for high-field MRI/MRS applications,” Magn Reson Med, vol. 43, pp. 284–289, 2000.
59. V. Alagappan, G. C. Wiggins, A. Potthast, K. Setsompop, E. Adalsteinsson, and L. L. Wald, “An 8 channel transmit coil for transmit sense at 3T,” in Proc. Int. Soc. Magn. Reson. Med. (ISMRM), Seattle, WA, 2006, p. 121.
60. M. J. D. Powell, “A fast algorithm for nonlinearly constrained optimization calculations,” Lecture Notes Math., vol. 630, pp. 144–157, 1978.
61. C. L. Dumoulin and H. R. Hart, “Magnetic resonance angiography,” Radiology, vol. 161, pp. 717–720, 1986.
62. S. P. Souza and C. L. Dumoulin, “Phase-contrast magnetic resonance angiography,” in Proc. 11th Annu. Int. Conf. Eng. Med. Biol. Soc., 1989, vol. 2, pp. 514–515.
63. P. C. Hansen, “Regularization tools: A matlab package for analysis and solution of discrete ill-posed problems,” Numer. Algor., vol. 6, pp. 1–35, 1994.
64. D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrica, vol. 81, no. 3, pp. 425–455, Aug. 1994.
65. I. M. Johnstone, “On minimax estimation of a sparse normal mean vector,” Ann. Stat., vol. 22, no. 1, pp. 271–289, Mar. 1994.
66. I. Daubechies, M. Defrise, and C. D. Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math., vol. 57, no. 11, pp. 1413–1457, 2004.
67. M. Elad, B. Matalon, and M. Zibulevsky, “Image denoising with shrinkage and redundant representations,” in Proc. IEEE Comput. Vis. Pattern Recognit., 2006, vol. 2, pp. 1924–1931.
68. M. A. Saunders and B. Kim, PDCO: Primal-dual interior method for convex objectives [Online]. Available: http://www.stanford.edu/group/SOL/software/pdco.html
69. S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, A method for large-scale-regularized least squares problems with applications in signal processing and statistics Stanford Univ., Stanford, CA, 2007 [Online]. Available: http://www.stanford.edu/~boyd/reports/l1_ls.pdf