Model-based MR parameter mapping with sparsity constraints: Parameter estimation and performance bounds

IEEE Transactions on Medical Imaging

Volumn 33, Issue 9, 2014, Pages 1832-1844

  Zhao, Bo ^a   Lam, Fan ^a   Liang, Zhi Pei ^a  

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

Author keywords

Cram r Rao bounds; model based reconstruction; parameter estimation; parameter mapping; quantitative magnetic resonance imaging; sparsity

Indexed keywords

BENCHMARKING; COMPUTER SIMULATION; MAGNETIC RESONANCE IMAGING; PARAMETER ESTIMATION;

CONSTRAINED PARAMETERS; EMPIRICAL PERFORMANCE; MAPPING APPLICATIONS; MODEL BASED RECONSTRUCTION; QUANTITATIVE MAGNETIC RESONANCE IMAGING; SPARSITY; SPARSITY CONSTRAINTS; TISSUE CHARACTERIZATION;

MAPPING;

ALGORITHM; ANATOMY AND HISTOLOGY; BRAIN; COMPUTER SIMULATION; HUMAN; IMAGE PROCESSING; IMAGE QUALITY; NEUROIMAGING; NUCLEAR MAGNETIC RESONANCE IMAGING; PROCEDURES;

ALGORITHMS; BRAIN; COMPUTER SIMULATION; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; NEUROIMAGING; PHANTOMS, IMAGING;

EID: 84906886862     PISSN: 02780062     EISSN: 1558254X     Source Type: Journal    
DOI: 10.1109/TMI.2014.2322815     Document Type: Article

References (67)

1. H.-L. Margaret Cheng, N. Stikov, N. R. Ghugre, and G. A. Wright, "Practical medical applications of quantitative MR relaxometry," J. Magn. Reson. Imag., vol. 36, pp. 805-824, 2012.
2. S. Baudrexel, L. Nurnberger, U. Rub, C. Seifried, J. C. Klein, T. Deller, H. Steinmetz, R. Deichmann, and R. Hilker, "Quantitative mapping of and discloses nigral and brainstem pathology in early Parkinson's disease," NeuroImage, vol. 51, pp. 512-520, 2010.
3. J. S. Hankins, M. B. McCarville, R. B. Loeffler, M. P. Smeltzer, M. Onciu, F. A. Hoffer, Li C.-S, W. C. Wang, R. E. Ware, and C. M. Hillenbrand," magnetic resonance imaging of the liver in patients with iron overload," Blood, vol. 113, pp. 4853-4855, 2009.
4. D. R. Messroghli, K. Walters, S. Plein, P. Sparrow, M. G. Friedrich, J. P. Ridgway, and M. U. Sivananthan, "Myocardial mapping: Application to patients with acute and chronic myocardial infarction," Magn. Reson. Med., vol. 58, pp. 34-40, 2007.
5. W. Liu, H. Dahnke, J. Rahmer, E. K. Jordan, and J. A. Frank, "Ultrashort relaxometry for quantitation of highly concentrated su-perparamagnetic iron oxide (SPIO) nanoparticle labeled cells," Magn. Reson. Med., vol. 61, pp. 761-766, 2009.
6. 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.
7. Z.-P. Liang, "Spatiotemporal imaging with partially separable functions," in Proc. IEEE Int. Symp. Biomed. Imag., 2007, pp. 988-991.
8. J. P. Haldar and Z.-P. Liang, "Spatiotemporal imaging with partially separable functions: A matrix recovery approach," in Proc. IEEE Int. Symp. Biomed. Imag., 2010, pp. 716-719.
9. B. Zhao, J. P. Haldar, A. G. Christodoulou, and Z.-P. Liang, "Image reconstruction from highly undersampled-space data with joint partial separability and sparsity constraints," IEEE Trans. Med. Imag., vol. 31, no. 9, pp. 1809-1820, Sep. 2012.
10. S. G. Lingala, Y. Hu, E. Dibella, and M. Jacob, "Accelerated dynamic MRI exploiting sparsity and low-rank structure: SLR," IEEE Trans. Med. Imag., vol. 30, no. 5, pp. 1042-1054, May 2011.
11. M. Doneva, P. Bornert, H. Eggers, C. Stehning, J. Senegas, and A. Mertins, "Compressed sensing reconstruction for magnetic resonance parameter mapping," Magn. Reson. Med., vol. 64, pp. 1114-1120, 2010.
12. L. Feng, R. Otazo, H. Jung, J. H. Jensen, J. C. Ye, D. K. Sodickson, and D. Kim, "Accelerated cardiac mapping using breath-hold multiecho fast spin-echo pulse sequence with k-t FOCUSS," Magn. Reson. Med., vol. 65, pp. 1661-1669, 2011.
13. B. Bilgic, V. K. Goyal, and E. Adalsteinsson, "Multi-contrast reconstruction with Bayesian compressed sensing," Magn. Reson. Med., vol. 66, pp. 1601-1615, 2011.
14. A. Majumdar and R. K. Ward, "Accelerating multi-echo weighted MR imaging: Analysis prior group-sparse optimization," J. Magn. Reson. Imag., vol. 210, pp. 90-97, 2011.
15. F. H. Petzschner, I. P. Ponce, M. Blaimer, P. M. Jakob, and F. A. Breuer, "Fast MR parameter mapping using principal component analysis," Magn. Reson. Med., vol. 66, pp. 706-716, 2011.
16. C. Huang, C. G. Graff, E. W. Clarkson, A. Bilgin, and M. I. Altbach," mapping from highly undersampled data by reconstruction of principal component coefficient maps using compressed sensing," Magn. Reson. Med., vol. 67, pp. 1355-1366, 2012.
17. W. Li, M. Griswold, and X. Yu, "Fast cardiac mapping in mice using a model-based compressed sensing method," Magn. Reson. Med., vol. 68, pp. 1127-1134, 2012.
18. J. Yuan, D. Liang, F. Zhao, Y. Li, Y. X. Xiang, and L. Ying," ISD compressed sensing reconstruction for mapping: A study in rat brains at 3T," in Proc. Int. Symp. Magn. Reson. Med., 2012, pp. 4197-4197.
19. B. Zhao, W. Lu, and Z.-P. Liang, "Highly accelerated parameter mapping with joint partial separability and sparsity constraints," in Proc. Int. Symp. Magn. Reson. Med., 2012, pp. 2233-2233.
20. J. V. Velikina, A. L. Alexander, and A. Samsonov, "Accelerating MR parameter mapping using sparsity-promoting regularization in parametric dimension," Magn. Reson. Med., vol. 70, pp. 1263-1273, 2013.
21. B. Zhao, T. K. Hitchens, A. G. Christodoulou, F. Lam, Y.-L. Wu, C. Ho, and Z.-P. Liang, "Accelerated 3D UTE relaxometry for quantification of iron-oxide labeled cells," in Proc. Int. Symp. Magn. Reson. Med., 2013, pp. 2455-2455.
22. Y. Zhu, Q. Zhang, Q. Liu, Y.-X. J. Wang, X. Liu, H. Zheng, D. Liang, and J. Yuan, "PANDA-rho: Integrating principal component analysis and dictionary learning for fast rho mapping," Magn. Reson. Med., to be published.
23. T. Zhang, J. M. Pauly, and I. R. Levesque, "Accelerating parameter mapping with a locally low rank constraint," Magn. Reson. Med., to be published.
24. J. P. Haldar, D. Hernando, and Z.-P. Liang, "Super-resolution reconstruction of MR image sequences with contrast modeling," in Proc. IEEE Int. Symp. Biomed. Imag., 2009, pp. 266-269.
25. K. Block, M. Uecker, and J. Frahm, "Model-based iterative reconstruction for radial fast spin-echo MRI," IEEE Trans. Med. Imag., vol. 28, no. 11, pp. 1759-1769, Nov. 2009.
26. T. J. Sumpf, M. Uecker, S. Boretius, and J. Frahm, "Model-based nonlinear inverse reconstruction for mapping using highly undersam-pled spin-echo MRI," J. Magn. Reson. Imag., vol. 34, pp. 420-428, 2011.
27. B. Zhao, F. Lam, W. Lu, and Z.-P. Liang, "Model-based MR parameter mapping with sparsity constraint," in Proc. IEEE Int. Symp. Biomed. Imag., 2013, pp. 1-4.
28. S. C. Deoni, B. K. Rutt, and T. M. Peters, "Rapid combined and mapping using gradient recalled acquisition in the steady state," Magn. Reson. Med., vol. 49, pp. 515-526, 2003.
29. D. P. Bertsekas, Nonlinear Programming, 2nd ed. Belmont, MA: Athena Scientific, 1999.
30. A. Beck and Y. C. Eldar, "Sparsity constrained nonlinear optimization: Optimality conditions and algorithms," SIAM J. Optim., vol. 23, pp. 1480-1509, 2013.
31. T. Blumensath, "Compressed sensing with nonlinear observations and related nonlinear optimization problems," IEEE Trans. Inf. Theory, vol. 59, no. 6, pp. 3466-3474, Jun. 2013.
32. S. Bahmani, B. Raj, and P. Boufounos, "Greedy sparsity-constrained optimization," J. Mach. Learn. Res., vol. 14, pp. 807-841, 2013.
33. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmonic Anal., vol. 26, pp. 301-321, 2009.
34. T. Blumensath, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. Inf. Theory, vol. 55, no. 5, pp. 2230-2249, May 2009.
35. J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. New York, NY: Springer, 2006.
36. J. D. Gorman and A. O. Hero, "Lower bounds for parametric estimation with constraints," IEEE Trans. Inf. Theory, vol. 36, no. 6, pp. 1285-1301, Nov. 1990.
37. P. Stoica and B. Ng, "On the Cramer-Rao bound under parametric constraints," IEEE Signal Process. Lett., vol. 5, no. 7, pp. 177-179, Jul. 1998.
38. Z. Ben-Haim and Y. C. Eldar, "The Cramer-Rao bound for estimating a sparse parameter vector," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3384-3389, Jun. 2010.
39. G. Tang and A. Nehorai, "Lower bounds on the mean-squared error of low-rank matrix reconstruction," IEEE Trans. Signal Process., vol. 59, no. 10, pp. 4559-4571, Oct. 2011.
40. G. Tang and A. Nehorai, "Constrained Cramér-Rao bound on robust principal component analysis," IEEE Trans. Signal Process., vol. 59, no. 10, pp. 5070-5076, Oct. 2011.
41. F. Lam, C. Ma, and Z.-P. Liang, "Performance analysis of denoising with low-rank and sparsity constraints," in Proc. IEEE Int. Symp. Biomed. Imag., 2013, pp. 1211-1214.
42. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Upper Saddle River, NJ: Prentice Hall, 1993.
43. C. A. Rohde, "Generalized inverses of partitioned matrices," J. Soc. Ind. Appl. Math., vol. 13, pp. 1033-1035, 1965.
44. P. Stoica and T. L. Marzetta, "Parameter estimation problems with singular information matrices," IEEE Trans. Signal Process., vol. 49, no. 1, pp. 87-90, Jan. 2001.
45. Z. Ben-Haim and Y. C. Eldar, "On the constrained Cramér-Rao bound with a singular Fisher information matrix," IEEE Signal Process. Lett., vol. 16, pp. 453-456, Jun. 2009.
46. Y. C. Eldar, "Rethinking biased estimation: Improving maximum likelihood and the Cramér-Rao bound," Foundat. Trends Signal Process., vol. 1, pp. 305-449, 2008.
47. D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, "Design and construction of a realistic digital brain phantom," IEEE Trans. Med. Imag., vol. 17, no. 3, pp. 463-468, Jun. 1998.
48. A. MacKay, C. Laule, I. Vavasour, T. Bjarnason, S. Kolind, and B. Madler, "Insights into brain microstructure from the distribution," Magn. Reson. Imag., vol. 24, pp. 515-525, 2006.
49. C. R. McCreary, T. A. Bjarnason, V. Skihar, J. R. Mitchell, V. W. Yong, and J. F. Dunn, "Multiexponential and magnetization transfer MRI of demyelination and remyelination in murine spinal cord," NeuroImage, vol. 45, pp. 1173-1182, 2008.
50. D. Reiter, R. Roque, P. Lin, T. Bjarnason, S. Kolind, and B. Madler, "Mapping proteoglycan-bound water in cartilage: improved specificity of matrix assessment using multiexponential transverse relaxation analysis," Magn. Reson. Med., vol. 65, pp. 377-384, 2011.
51. A. K. Funai, "Regularized estimation of main and RF field inho-mogeneity and longitudinal relaxation rate in magnetic resonance imaging," Ph.D. dissertation, Univ. Michigan, Ann Arbor, MI, 2011.
52. L. Sorber, M. Barel, and L. Lathauwer, "Unconstrained optimization of real functions in complex variables," SIAM J. Optimizat., vol. 22, pp. 879-898, 2012.
53. A. Van Den Bos, "A Cramer-Rao lower bound for complex parameters," IEEE Trans. Signal Process., vol. 42, no. 10, pp. 2859-2859, Oct. 1994.
54. A. Jagannatham and B. Rao, "Cramer-Rao lower bound for constrained complex parameters," IEEE Signal Process. Lett., vol. 11, no. 11, pp. 875-878, Nov. 2004.
55. B. Zhao, F. Lam, W. Lu, and Z.-P. Liang, "Model-based MR parameter mapping with sparsity constraint," in Proc. Int. Symp. Magn. Reson. Med., 2013, pp. 2459-2459.
56. R. Baraniuk, V. Cevher, M. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Trans. Inf. Theory, vol. 56, no. 4, pp. 1982-2001, Apr. 2010.
57. D. R. Hunter and K. Lange, "A tutorial on MM algorithms," Am. Statist., vol. 58, pp. 30-37, 2004.
58. G. Golub and V. Pereyra, "Separable nonlinear least squares: the variable projection method and its applications," Inverse Probl., vol. 19, pp. R1-R26, 2003.
59. R. Gribonval, V. Cevher, and M. Davies, "Compressible distributions for high-dimensional statistics," IEEE Trans. Inf. Theory, vol. 58, no. 8, pp. 5016-5034, Aug. 2012.
60. H. L. Van Trees and K. L. Bell, Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking. New York: Wiley-IEEE Press, 2007.
61. P. Chatterjee and P. Milanfar, "Is denoising dead?," IEEE Trans. Image Process., vol. 19, no. 4, pp. 895-911, Apr. 2010.
62. R. Prasad and C. Murthy, "Cramér-Rao-type bounds for sparse Bayesian learning," IEEE Trans. Signal Process., vol. 61, pp. 622-632, 2013.
63. C. Baker, K. King, D. Liang, and L. Ying, "Translational-invariant dictionaries for compressed sensing in magnetic resonance imaging," in Proc. IEEE Int. Symp. Biomed. Imag., 2011, pp. 1602-1605.
64. S. Ravishankar and Y. Bresler, "MR image reconstruction from highly undersampled-space data by dictionary learning," IEEE Trans. Med. Imag., vol. 30, no. 5, pp. 1028-1041, May 2011.
65. X. Qu, Y. Hou, F. Lam, D. Guo, J. Zhong, and Z. Chen, "Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator," Med. Image Anal., vol. 18, no. 6, pp. 843-856, Aug. 2014.
66. J. D. Trzasko, P. M. Mostardi, S. J. Riederer, and A. Manduca, "Estimating from multichannel variable flip angle SPGR sequences," Magn. Reson. Med., vol. 69, pp. 1787-1794, 2013.
67. R. M. Lebel and A. H. Wilman, "Transverse relaxometry with stimulated echo compensation," Magn. Reson. Med., vol. 64, pp. 1005-1014, 2010.