SVD compression for magnetic resonance fingerprinting in the time domain

IEEE Transactions on Medical Imaging

Volumn 33, Issue 12, 2014, Pages 2311-2322

  McGivney, Debra F ^a   Pierre, Eric ^b   Ma, Dan ^b   Jiang, Yun ^b   Saybasili, Haris ^c   Gulani, Vikas ^a   Griswold, Mark A ^a  

^a CASE WESTERN RESERVE UNIVERSITY SCHOOL OF MEDICINE   (United States)

^b Case Western Reserve University   (United States)

^c Siemens Healthcare USA Inc   (United States)

Author keywords

Dimensionality reduction; magnetic resonance imaging; pattern recognition and classification; singular value decomposition

Indexed keywords

ALGORITHM; ANATOMY AND HISTOLOGY; BRAIN; HUMAN; IMAGE PROCESSING; IMAGE QUALITY; INFORMATION PROCESSING; NUCLEAR MAGNETIC RESONANCE IMAGING; PROCEDURES; SIGNAL NOISE RATIO;

ALGORITHMS; BRAIN; DATA COMPRESSION; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; PHANTOMS, IMAGING; SIGNAL-TO-NOISE RATIO;

EID: 84914141938     PISSN: 02780062     EISSN: 1558254X     Source Type: Journal    
DOI: 10.1109/TMI.2014.2337321     Document Type: Article

References (33)

1. D. Ma, V. Gulani, N. Seiberlich, K. Liu, J. L. Sunshine, J. L. Duerk, andM. A. Griswold, "Magnetic resonance fingerprinting," Nature, vol. 495, pp. 187-192, 2013.
2. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1996.
3. G. H. Golub and C. Reinsch, "Singular value decomposition and least squares solutions," Numer. Math., vol. 14, pp. 403-420, 1970.
4. I. T. Jolliffe, Principal Component Analysis. NewYork:Springer, 2002.
5. J. Cadima and I. Jolliffe, "On relationships between uncentred and column-centred principal component analysis," Pakistan J. Stat., vol. 25, pp. 473-503, 2009.
6. J.-J.Wei, C.-J. Chang, N.-K. Chou, and G.-J. Jan, "ECG data compression using truncated singular value decomposition," IEEE Trans. Inf. Technol. Biomed., vol. 5, no. 4, pp. 290-299, Dec. 2001.
7. H. C. Andrews and C. L. Patterson, III, "Singular value decomposition (SVD) image coding," IEEE Trans. Commun., vol. 24, no. 4, pp. 425-432, Apr. 1976.
8. M. Tian, S.-W. Luo, and L.-Z. Liao, "An investigation into using singular value decomposition as a method of image compression," in Proc. 4th Int. Conf. Mach. Learn. Cybern., 2005, vol. 8, pp. 5200-5204.
9. T. Tan and R. Liu, "An SVD-based watermarking scheme for protecting rightful ownership," IEEE Trans. Multimedia, vol. 4, no. 1, pp. 121-128, Mar. 2002.
10. C.-C. Lai and C.-C. Tsai, "Digital image watermarking using discrete wavelet transform and singular value decomposition," IEEE Trans. Instrum. Meas., vol. 59, no. 11, pp. 3060-3063, Nov. 2010.
11. S. Deerwester, S. T. Dumais, G. W. Furnas, T. K. Landauer, and R. Harshman, "Indexing by latent semantic analysis," J.Am. Soc. Inf. Sci., vol. 41, pp. 391-407, 1990.
12. T. A. Letsche andM.W. Berry, "Large-scale information retrieval with latent semantic indexing," Inf. Sci., vol. 100, pp. 105-137, 1997.
13. O. Alter, P. O. Brown, and D. Botstein, "Singular value decomposition for genome-wide expression data processing andmodeling," Proc. Nat. Acad. Sci. USA, vol. 97, pp. 10 101-10 106, 2000.
14. O. Alter and G. H. Golub, "Singular value decomposition of genomescale mRNA lengths distribution reveals asymmetry in RNA gel electrophoresis band broadening," Proc. Nat. Acad. Sci. USA, vol. 103, pp. 11 828-11 833, 2006.
15. M. Turk and A. Pentland, "Eigenfaces for recognition," J. Cognitive Neurosci., vol. 3, pp. 71-86, 1991.
16. G. P. Zientara, L. P. Panych, and F. A. Jolesz, "Dynamically adaptive MRI with encoding by singular value decomposition," Magn. Reson. Med., vol. 32, pp. 268-274, 1994.
17. 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., vol. 35, pp. 554-562, 1996.
18. J. M. Hanson, Z.-P. Liang, R. L. Magin, J. L. Duerk, and P. C. Lauterbur, "A comparison of RIGR and SVD dynamic imaging methods," Magn. Reson. Med., vol. 38, pp. 161-167, 1997.
19. Y. Cao and D. N. Levin, "On the relationship between feature-recognizing MRI and MRI encoded by singular value decomposition," Magn. Reson. Med., vol. 33, pp. 140-142, 1995.
20. H. Moriguchi and J. L. Duerk, "Modified block uniform resampling (BURS) algorithm using truncated singular value decomposition: Fast accurate gridding with noise and artifact reduction," Magn. Reson. Med., vol. 46, pp. 1189-1201, 2001.
21. M. Lustig, P. Lai, M. Murphy, S. S. Vasanawala, M. Elad, J. Zhang, and J. M. Pauly, "An eigen-vector approach to autocalibrating parallel MRI, where SENSE meets GRAPPA," in Proc. 19th Annu. Meet. ISMRM, Montreal, Canada, 2011, p. 479.
22. M. Uecker, P. Lai, M. J. Murphy, P. Virtue, M. Elad, J. M. Pauly, S. S. Vasanawala, and M. Lustig, "ESPIRiT-An eigenvalue apporach to autocalibrating parallel MRI: Where SENSE meets GRAPPA," Magn. Reson. Med., vol. 71, pp. 990-1001, 2013.
23. A. Sbrizzi, A. J. E. Raaijmakers, H. Hoogduin, J. J. W. Lagendijk, P. R. Luijten, and C. A. T. van den Berg, "Transmit and receive RF fields determination from a single low-tip-angle gradient-echo scan by scaling of SVD data," Magn. Reson. Med., vol. 72, pp. 248-259, 2014.
24. P. Schmitt, M. A. Griswold, V. Gulani, A. Haase, M. Flentje, and P. M. Jakob, "A simple geometrical description of the TrueFISP ideal transient and steady-state signal," Magn. Reson. Med., vol. 55, pp. 177-186, 2006.
25. Y. Jiang, D. Ma, N. Seiberlich, V. Gulani, and M. A. Griswold, "MR fingerprinting using FISP," in Proc. 22nd Annu. Meet. ISMRM, Milan, Italy, 2014, p. 4290.
26. C. Eckart and G. Young, "The approximation of one matrix by another of lower rank," Psychometrika, vol. 1, pp. 211-218, 1936.
27. J. A. Fessler and B. P. Sutton, "Nonuniform fast Fourier transforms using min-max interpolation," IEEE Trans. Signal Process., vol. 51, no. 2, pp. 560-574, Feb. 2003.
28. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems. Philadelphia, PA: SIAM, 1998.
29. E. Liberty, F. Woolfe, P.-G. Martinsson, V. Rokhlin, and M. Tygert, "Randomized algorithms for the low-rank approximation of matrices," Proc. Nat. Acad. Sci. USA, vol. 104, pp. 20 167-20 172, 2007.
30. N. Halko, P.-G. Martinsson, and J. A. Tropp, "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions," SIAM Rev., vol. 53, pp. 217-288, 2011.
31. N. Halko, P.-G. Martinsson, Y. Shkolnisky, and M. Tygert, "An algorithm for the principal component analysis of large data sets," SIAM J. Sci. Comput., vol. 33, pp. 2580-2594, 2011.
32. J. Zhang, J. Erway, X. Hu, Q. Zhang, and R. Plemmons, "Randomized SVD methods in hyperspectral imaging," J. Elect. Comput. Eng., 2012.
33. P. C. Hansen, "Analysis of discrete ill-posed problems by means of the L-curve," SIAM Rev., vol. 34, pp. 561-580, 1992.