Near-Optimal Spatial Encoding for Dynamically Adaptive MRI: Mathematical Principles and Computational Methods

International Journal of Imaging Systems and Technology

Volumn 10, Issue 2, 1999, Pages 151-165

  Zientara, Gary P ^a   Panych, Lawrence P ^a   Jolesz, Ferenc A ^a  

^a BRIGHAM AND WOMEN S HOSPITAL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; IMAGE ANALYSIS; IMAGE CODING; MATRIX ALGEBRA;

KRYLOV SUBSPACE METHODS;

MAGNETIC RESONANCE IMAGING;

EID: 0032688188     PISSN: 08999457     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-1098(1999)10:2<151::AID-IMA6>3.0.CO;2-Y     Document Type: Article

References (89)

1. H.C. Andrews and C.L. Patterson, Outer product expansions and their uses in digital image processing, Am Math Monthly 82 (1975), 1-13.
2. H.C. Andrews and W.K. Pratt, "Image transforms," Computer techniques in image processing, H.C. Andrews (Editor), Academic Press, New York, 1970, Chapter 6.
3. W.E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Q Appl Math 9 (1951), 17-29.
4. J.W. Belliveau, D.N. Kennedy, R.C. McKinstry, B.R. Buchbinder, R.M. Weisskoff, M.S. Cohen, J.M. Vevea, T.J. Brady, and B.R. Rosen, Functional mapping of the human visual cortex by magnetic resonance imaging, Science 54 (1991), 716-718.
5. C.H. Bischoff and P.C. Hansen, Structure-preserving and rank-revealing QR-factorization, SIAM J Sci Stat Comput 12 (1991), 1332-1350.
6. A. Bjorck and C. Bowie, An Iterative algorithm for computing the best estimate of an orthogonal matrix, SIAM J Num Anal 8 (1971), 358-364.
7. A. Bjorck and G.H. Golub, Numerical methods for computing angles between linear subspaces, Math Comp 27 (1973), 579-594.
8. L. Bolinger and J.S. Leigh, Hadamard spectroscopoic imaging (HSI): For multivolume localization, J Magn Reson 80 (1988), 162-167.
9. R.P. Brent, F.T. Luk, and C. Van Loan, Computation of the singular value decomposition using mesh-connected processors, J VLSI Comput Systems 1 (1985), 250-260.
10. C. Brezinski, M. Redivo Zaglia, and H. Sadok, A breakdown tree Lanczos-type algorithm for solving linear systems, Numer Math 63 (1992), 29-38.
11. T.F. Chan, Rank revealing QR factorizations, Lin AIg Appl 88/89 (1987), 67-82.
12. T.F. Chan and P.C. Hansen, Some applications of the rank revealing QR factorization, SIAM J Sci Stat Comput 13 (1992), 727-741.
13. J.P. Charlier, M. Vanbegin, and P. Van Dooren, On efficient implementations of Kogbetliantz's algorithm for computing the singular value decomposition, Numer Math 52 (1988), 279-300.
14. P. Comon and G.H. Golub, Tracking a few extreme singular values and vectors in signal processing, Proc IEEE 78 (1990), 1327-1343.
15. J.K. Cullum and R.A. Willoughby, Lanczos algorithms for large symmetric eigenvalue computations, Birkhauser, Boston, 1985.
16. R.R. Edelman, P. Wielopolski, and F. Schmitt, Echo-planar MR imaging, Radiology 192 (1994), 600-612.
17. L.M. Ewerbring and F.T. Luk, "Computing the singular value decomposition on the connection machine," SVD and signal processing, E.F. Deprettre (Editor), Elsevier Science, New York, 1998.
18. K. Fan and A. Hoffman, Some metric inequalities in the space of matrices, Proc Am Math Soc 6 (1955), 11-116.
19. R.D. Fierro and P.C. Hansen, Accuracy of TSVD solutions computed from rank-revealing decompositions, Numer Math 70 (1995), 453-471.
20. L.V. Foster, Rank and null space calculations using matrix decomposition without column interchanges, Lin Alg Appl 74 (1986), 47-71.
21. N. Gelman and M.L. Wood, Wavelet encoding for improved SNR and retrospective slice thickness adjustment, Magn Reson Med 39 (1998), 383-391.
22. G. Goelman, V. Harihara Subramanian, and J.S. Leigh, Transverse Hadamard spectroscopic imaging techniques, J Magn Reson 89 (1990), 437-154.
23. G.H. Golub and G.W. Kahan, Calculating the singular values and pseudo-inverse of a matrix, SIAM J Numer Anal 2 (1965), 205-224.
24. G.H. Golub and C. Reinsch, Singular value decomposition and least squares solutions, Numer Math 14 (1970), 403-420.
25. G.H. Golub and C.F. Van Loan, Matrix computations, 2nd ed., Johns Hopkins University Press, Baltimore, MD, 1989.
26. E.L. Hall, Computer image processing and recognition, Academic, San Diego, 1979, Chapter 3.
27. D.M. Healy and J.B. Weaver, Two applications of wavelet transforms in magnetic resonance imaging, IEEE Trans Inform Theory IT-38 (1992), 840-862.
28. N.J. Higham, Computing the polar decomposition: With applications, SIAM J Sci Stat Comput 7 (1986), 1160-1174.
29. N.J. Higham and R.S. Schreiber, Fast polar decomposition of an arbitrary matrix, SIAM J Sci Stat Comput 11 (1990), 648-655.
30. A.E. Holsinger, R.C. Wright, S.J. Riederer, F. Farzaneh, R.C. Grimm, and J.K. Maier, Real-time interactive magnetic resonance imaging, Magn Reson Med 14 (1990), 547-553.
31. X. Hu and T. Parrish, Reduction of field of view for dynamic imaging, Magn Reson Med 31 (1994), 691-694.
32. E.R. Jessup and D.C. Sorensen, A parallel algorithm for computing the singular value decomposition of a matrix, SIAM J Matrix Anal Appl 15 (1994), 530-548.
33. F.A. Jolesz and S.G. Silverman, Interventional magnetic resonance therapy, Semin Intervent Radiol 12 (1995), 20-27.
34. F.A. Jolesz and G.P. Zientara, "MRI-guided interventions," Clinical magnetic resonance imaging, 2nd edition, R. Edelman (Editor), W.B. Saunders. Philadelphia. 1996.
35. W. Joubert, Lanczos methods for the solution of nonsymmetric systems of linear equations, SIAM J Matrix Anal Appl 13 (1992), 926-943.
36. E. Kogbetliantz, Solution of linear equations by diagonalization of coefficient matrices, Q Appl Math 13 (1955), 123-132.
37. T. Koslowski and W. von Niessen, Linear combination of Lanczos vectors: A storage-efficient algorithm for sparse matrix eigenvector computations, J Comput Chem 14 (1993), 769-774.
38. W.E. Kyriakos and L.P. Panych, Implementation of wavelet encoded MRI with large flip-angle RF pulses, Abstr 5th meeting Int Soc Magn Reson. Vancouver Canada, April 1997, 1990.
39. W. Kyriakos, L.P. Panych, G.P. Zientara, and F.A. Jolesz, Implementation of a reduced field-of-view method for dynamic MR imaging using navigator echoes, J Magn Reson Imaging 7 (1997), 376-381.
40. C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J NBS 45 (1950), 255-282.
41. C. Lanczos, Solution of systems of linear equations by minimized iterations, J NBS 49 (1952), 33-53.
42. A.A. Maudsley, Multiple line-scanning spin density imaging, J Magn Reson 41 (1980), 112-126.
43. G.L. Millhauser, A.A. Carter, D.J. Schneider, J.H. Freed, and R.E. Oswald, Rapid singular value decomposition for time-domain analysis of magnetic resonance signals by use of the Lanczos algorithm, J Magn Reson 82 (1989), 150-155.
44. M. Moonen, P. Van Dooren, and J. Vandewalle, A singular value decomposition updating algorithm for subspace tracking, SIAM J Matrix Anal Appl 13 (1992), 1015-1038.
45. G. Moro and J.H. Freed, Efficient computation of magnetic resonance spectra and related correlation functions from stochastic Liouville equations, J Phys Chem 84 (1980), 2837-2840.
46. G. Moro and J.H. Freed, Calculation of ESR spectra and related Fokker-Planck forms by the use of the Lanczos algorithm, J Chem Phys 74 (1981), 3757-3773.
47. S. Ogawa, T.M. Lee, A.S. Nayak, and P. Glynn, Oxygenation-sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields, Magn Reson Med 14 (1990), 68-78.
48. S. Ogawa, R.S. Menon, D.W. Tank, S.G. Kim, H. Merkle, J.M. Ellermann, and K. Ugurbil, Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging, Biophys J 64 (1993), 803-812.
49. C.H. Oh, H.W. Park, and Z.H. Cho, Line-integral projection reconstruction (LPR) with slice encoding techniques: Multislice regional imaging in NMR tomography, IEEE Trans Med Imaging MI-3 (1984), 170-178.
50. C.C. Paige, Bidiagonalization of matrices and solution of linear equations, SIAM J Numer Anal 11 (1974), 197-209.
51. L.P. Panych, Adaptive magnetic resonance imaging by wavelet transform PhD thesis, Massachusetts Institute of Technology, 1993.
52. L.P. Panych, P.D. Jakab, and F.A. Jolesz, An implementation of wavelet encoded MRI, J Magn Reson Imaging 3 (1993), 649-655.
53. L.P. Panych and F.A. Jolesz, A dynamically adaptive imaging algorithm for wavelet-encoded MRI, Magn Reson Med 32 (1994), 738-748.
54. L.P. Panych, R.V. Mulkern, P. Saiviroonporn, G.P. Zientara, and F.A. Jolesz, Non-Fourier encoding with multiple spin echoes, Magn Reson Med 38 (1997), 964-973.
55. L.P. Panych, C. Oesterle, G.P. Zientara, and J. Hennig, Implementation of a fast gradient-echo SVD encoding technique for dynamic imaging, Magn Reson Med 35 (1996), 554-562.
56. 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 Imaging Syst Tech 1999 (this issue).
57. L.P. Panych, G.P. Zientara, P. Saiviroonporn, S.-S. Yoo, and F.A. Jolesz, Digital wavelet encoded MRI: A new wavelet encoding methodology, J Magn Reson Imaging 8 (1998), 1135-1144.
58. B.N. Parlett, D.R. Taylor, and Z.A. Liu, A look-ahead Lanczos algorithm for unsymmetric matrices, Math Comp 44 (1985), 105-124.
59. J. Pauly, D. Nishimura, A. Macovski, A linear class of large-tip-angle selective excitation pulses, J Magn Reson 82 (1989), 571-587.
60. W.K. Pratt, Digital image processing, Wiley-Interscience, New York, 1978. Chapter 10.
61. S.J. Riederer, MR Fluoroscopy, Proc ISMRM Fast MRI Workshop: Methodological Perspectives and Advances in Cardiac, Neuro, Angiography and Abdominal Imaging, Monterey, CA, October 1997, pp. 135-137.
62. Y. Saad, Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices, Lin Alg Appl 34 (1980), 269-295.
63. P. Saiviroonporn, L.P. Panych, G.P. Zientara, R. Kikinis, and F.A. Jolesz, Human brain imaging with multiple-echo SVD encoded MRI, Abstr 5th meeting Int Soc Magn Reson, Vancouver, Canada, April 1997a, p. 1829.
64. P. Saiviroonporn, L.P. Panych, G.P. Zientara, R. Kikinis, and F.A. Jolesz, Transient artifacts in SVD encoded MRI, Abstr 5th meeting Int Soc Magn Reson Med, Vancouver, Canada, April 1997b, p. 1915.
65. G.W. Stewart, Introduction to matrix computations, Academic Press, New York, 1973.
66. G.W. Stewart, Simultaneous iteration for computing invariant subspaces of non-Hermitean matrices, Numer Math 25 (1976), 123-126.
67. G.W. Stewart, An updating algorithm for subspace tracking, IEEE Trans Signal Proc 40 (1992), 1535-1541.
68. G.W. Stewart, "Determining rank in the presence of error," Linear algebra for large scale and real-time applications, M.S. Moonen, G.H. Golub, and B.L.R. de Moor (Editors), NATO ASI Series, Kluwer Academic, Dordrecht, 1993.
69. G.W. Stewart, "UTV decompositions," Numerical analysis 1993, D.F. Griffiths and G.A. Watson (Editors), Longman, New York, 1994.
70. G. Strang, Linear algebra and its applications, 2nd edition, Academic Press, New York, 1980.
71. A. Van Der Veen, E.F. Deprettere, and A.L. Swindlehurst, Subspace-based signal analysis using singular value decomposition, Proc IEEE 81 (1993), 1277-1308.
72. K.V. Vasavada and J.H. Freed, Application of Lanczos and conjugate gradient methods to a class of computational problems in physics, Comp Phys 3 (1989), 61-64.
73. K.V. Vasavada, D.J. Schneider, and J.H. Freed, Calculation of ESR spectra and related Fokker-Planck forms by the use of the Lanczos algorithm, II. Criteria for truncation of basis sets and recursive steps utilizing conjugate gradients, J Chem Phys 86 (1987), 647-661.
74. Y.V. Vorobyev, Method of moments in applied mathematics, Gordon and Breach, New York, 1965.
75. J.B. Weaver, Y. Xu, D.M. Healy, and J.R. Driscoll, Wavelet-encoded MR imaging, Magn Reson Med 24 (1992), 275-287.
76. J.H. Wilkinson, The algebraic eigenvalue problem, Claredon Press, Oxford, England, 1965.
77. R.C. Wright, S.J. Riederer, F. Farzaneh, P.J. Rossman, and Y. Liu, Real-time MR fluoroscopic data acquisition and image reconstruction, Magn Reson Med 12 (1989), 407-415.
78. Q. Ye, A breakdown-free variation of the nonsymmetric Lanczos algorithms, Math Comp 62 (1994), 79-206.
79. G.P. Zientara, SVD encoded MRI: Dynamically adaptive imaging, Proc SMR Workshop Interventional MRI, 1994, p. 8.
80. G.P. Zientara, Advanced non-Fourier imaging, Proc ISMRM Fast MRI Workshop: Methodological Perspectives and Advances in Cardiac, Neuro, Angiography and Abdominal Imaging, Monterey, CA, October 1997, pp. 149-152.
81. G.P. Zientara, L.P. Panych, and F.A. Jolesz, Dynamically adaptive MRI with encoding by singular value decomposition, Magn Reson Med 32 (1994), 268-274.
82. G.P. Zientara, L.P. Panych, and F.A. Jolesz, Lanczos spatial encodings for dynamically adaptive MRI, Abstr 3rd meeting Soc Magn Reson, Nice, France, August 1995.
83. G.P. Zientara, L.P. Panych, and F.A. Jolesz, Methods for rapid computation of near-optimal spatial encodings for dynamically adaptive MRI, Abstr 5th meeting Int Soc Magn Reson, Vancouver, Canada, April 1997a, p. 1829.
84. G.P. Zientara, L.P. Panych, and F.A. Jolesz, Principal angles analysis of the applicability and efficiency of near-optimal spatial encoding for dynamically adaptive MRI, Abstr 5th meeting Int Soc Magn Reson, Vancouver, Canada, April 1997b, p. 1830.
85. G.P. Zientara, L.P. Panych, and F.A. Jolesz, Applicability and efficiency of near-optimal spatial encoding for dynamically adaptive MRI, Magn Reson Med, 39 (1998), 204-213.
86. G.P. Zientara, L.P. Panych, P. Saiviroonporn, and F.A. Jolesz, MR fluoroscopy using near-optimal adaptive spatial encoding, Abstr 4th meeting Soc Magn Reson, New York, April 1996, p. 1495.
87. G.P. Zientara, P. Saiviroonporn, L.P. Panych, and F.A. Jolesz, Interventional MR application of MR fluoroscopy with near-optimal adaptive spatial encodings, Abstr 5th meeting Int Soc Magn Reson, Vancouver, Canada, April 1997c, p. 781.
88. G.P. Zientara, P. Saiviroonporn, L.P. Panych, and F.A. Jolesz, Implementation of Lanczos spatial encodings for MRI, Abstr 5th meeting Int Soc Magn Reson, Vancouver, Canada, April 1997d, p. 1826.
89. G.P. Zientara, P. Saiviroonporn, L.P. Panych, and F.A. Jolesz, Interventional MR application of MR fluoroscopy with near-optimal adaptive spatial encodings, Abstr 5th meeting Int Soc Magn Reson, Vancouver, Canada, April 1997e, p. 781.