Recent advances in diffusion MRI modeling: Angular and radial reconstruction

Medical Image Analysis

Volumn 15, Issue 4, 2011, Pages 369-396

  Assemlal, Haz Edine ^a   Tschumperlé, David ^b   Brun, Luc ^b   Siddiqi, Kaleem ^a  

^a MCGILL UNIVERSITY   (Canada)

^b Centre National de la Recherche Scientifique   (France)

Author keywords

Angular sampling; Brain tissue features; Diffusion MRI reconstruction; Local modeling; Radial sampling

Indexed keywords

ANGULAR SAMPLING; BRAIN TISSUE FEATURES; DIFFUSION SIGNALS; FIBROUS TISSUE; LOCAL MODELING; MAGNETIC RESONANCE IMAGES; RADIAL SAMPLING; SPECIALIZED KNOWLEDGE; STATE-OF-THE-ART METHODS; THEORY AND PRACTICE;

MAGNETIC RESONANCE; MAGNETIC RESONANCE IMAGING; SAMPLING; TISSUE;

DIFFUSION;

ALGORITHM; BRAIN TISSUE; DIFFUSION WEIGHTED IMAGING; HUMAN; MATHEMATICAL PARAMETERS; MODEL; NEUROIMAGING; NUCLEAR MAGNETIC RESONANCE SCANNER; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; PRIORITY JOURNAL; RADIOLOGICAL PARAMETERS; REVIEW; SIGNAL PROCESSING;

ALGORITHMS; ANIMALS; BRAIN; COMPUTER SIMULATION; DIFFUSION MAGNETIC RESONANCE IMAGING; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; MODELS, ANATOMIC; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 79958765312     PISSN: 13618415     EISSN: 13618423     Source Type: Journal    
DOI: 10.1016/j.media.2011.02.002     Document Type: Review

References (208)

1. Abraham R., Marsden J., Ratio T. Manifolds, Tensor Analysis, and Applications 1988, Springer.
2. Abramowitz M., Stegun I. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1964, Dover Publications.
3. Aganj I., Lenglet C., Sapiro G. ODF reconstruction in q-ball imaging with solid angle consideration. IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2009 (ISBI'09) 2009, 1398-1401. IEEE.
4. Aganj, I., Lenglet, C., Sapiro, G., Yacoub, E., Ugurbil, K., Harel, N., 2009b. Multiple Q-shell ODF reconstruction in Q-ball imaging. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. Medical Image Computing and Computer-Assisted Intervention (MICCAI), vol. 12, p. 423.
5. Alexander D. Maximum entropy spherical deconvolution for diffusion MRI. Image Processing in Medical Imaging 2005, 76-87.
6. Alexander D., Barker G., Arridge S. Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data. Magnetic Resonance Imaging 2002, 48:331-340.
7. Anderson A. Measurement of fiber orientation distributions using high angular resolution diffusion imaging. Magnetic Resonance in Medicine 2005, 54(5).
8. Anderson, A., Ding, Z., 2002. Sub-voxel measurement of fiber orientation using high angular resolution diffusion tensor imaging. In: Proceedings of the 10th Annual Meeting of ISMRM, p. 440.
9. Andrews G., Askey R., Roy R. Special Functions 1999, Cambridge University Press.
10. Anwander A., Tittgemeyer M., Von Cramon D., Friederici A., Knosche T. Connectivity-based parcellation of Broca's area. Cerebral Cortex 2007, 17(4):816.
11. Arfken G., Weber H., Weber H. Mathematical Methods for Physicists 1985, Academic Press, New York.
12. Arsigny, V., 2006. Processing data in Lie groups: an algebraic approach. application to non-linear registration and diffusion tensor MRI. Ph.D. thesis, École polytechnique.
13. Assaf Y., Basser P.J. Composite hindered and restricted model of diffusion (charmed) mr imaging of the human brain. NeuroImage 2005, 27:48-58.
14. Assaf Y., Cohen Y. In vivo and in vitro bi-exponential diffusion of n-acetyl aspartate (naa) in rat brain: a potential structural probe?. NMR in Biomedicine 1998, 11.
15. Assemlal, H.-E., 2010. Traitement et analyse d'images IRM de diffusion pour l'estimation de l'architecture locale des tissus. Ph.D. thesis, Université de Caen.
16. Assemlal H.-E., Tschumperlé D., Brun L. Efficient and robust computation of pdf features from diffusion mr signal. Medical Image Analysis 2009, 13(5):715-729.
17. Assemlal H.-E., Tschumperlé D., Brun L. Evaluation of q-space sampling strategies for the diffusion magnetic resonance imaging. Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II 2009, 406-414. Springer-Verlag.
18. Aubert G., Kornprobst P. Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations 2006, Springer-Verlag New York Inc.
19. Bao L., Zhu Y., Liu W., Croisille P., Pu Z., Robini M., Magnin I. Denoising of human cardiac diffusion tensor magnetic resonance images using sparse representation combined with segmentation. Physics in Medicine and Biology 2009, 54:1435-1456.
20. Bar-Shir A., Avram L., Özarslan E., Basser P.J., Cohen Y. The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations. Journal of Magnetic Resonance (San Diego, CA: 1997) 2008, 194(2):230-236.
21. Barmpoutis, A., Jian, B., Vemuri, B.C., Shepherd, T.M., 2007. Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI. In: Proceedings of IPMI, pp. 308-319.
22. Basser P. Inferring microstructural features and the physiological state of tissues from diffusion-weighted images. NMR in Biomedicine 1995, 8(7).
23. Basser P. New histological and physiological stains derived from diffusion-tensor MR images. Annals of the New York Academy of Sciences 1997, 820(1 Imaging Brain Structure and Function: Emerging Technologies in the Neurosciences):123-138.
24. Basser P. Relationships between diffusion tensor and q-space MRI. Magnetic Resonance in Medicine 2002, 47(2):392-397.
25. Basser, P., LeBihan, D., 1992. Fiber orientation mapping in an anisotropic medium with nmr diffusion spectroscopy. In: Proceedings of the 11th Society of Magnetic Resonance in Medicine, p. 1221.
26. Basser, P., Mattiello, J., LeBihan, D., 1992. Diagonal and off-diagonal components of the self-diffusion tensor: their relation to and estimation from the nmr spin-echo signal. In: Proceedings of the 11th Society of Magnetic Resonance in Medicine, vol. 1, p. 1222.
27. Basser P., Pajevic S., Pierpaoli C., Duda J., Aldroubi A. In vivo fiber tractography using dt-mri data. Magnetic Resonance in Medicine 2000, 44(4):625-632.
28. Basser P.J., Mattiello J., LeBihan D. Estimation of the effective self-diffusion tensor from the nmr spin echo. Journal of Magnetic Resonance 1994, 103:247-254.
29. Basu, S., Fletcher, T., Whitaker, R., 2006. Rician noise removal in diffusion tensor MRI. In: MICCAI, pp. 117-125.
30. Behrens T., Berg H., Jbabdi S., Rushworth M., Woolrich M. Probabilistic diffusion tractography with multiple fibre orientations: what can we gain?. NeuroImage 2007, 34(1):144-155.
31. Behrens T., Woolrich M., Jenkinson M., Johansen-Berg H., Nunes R., Clare S., Matthews P., Brady J., Smith S. Characterization and propagation of uncertainty in diffusion-weighted MR imaging. Magnetic Resonance in Medicine 2003, 50(5):1077-1088.
32. Blackman R., Tukey J. The Measurement of Power Spectra: From the Point of View of Communications Engineering 1959, Dover Publications, New York.
33. Blanco M.A., Flórez M., Bermejo M. Evaluation of the rotation matrices in the basis of real spherical harmonics. Journal of Molecular Structure 1997, 419:19-27.
34. Blees M. The effect of finite duration of gradient pulses on the pulsed-field-gradient NMR method for studying restricted diffusion. Journal of Magnetic Resonance, Series A 1994, 109(2):203-209.
35. Bloy L., Verma R. On computing the underlying fiber directions from the diffusion orientation distribution function. LNCS 2008, vol. 5241:1-8. Springer. D. Metaxas, L. Axel, G. Fichtinger, G. Székely (Eds.).
36. Borisenko A., Tarpov I. Vector and Tensor Analysis with Applications 1980, Dover, New York.
37. Branch M., Coleman T., Li Y. A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems. SIAM Journal on Scientific Computing 2000, 21(1):1-23.
38. Brownstein K.R., Tarr C.E. Importance of classical diffusion in nmr studies of water in biological cells. Physical Review A 1979, 19(6):2446-2453.
39. Burt P., Adelson E. The Laplacian pyramid as a compact code. IEEE Transactions on Communications 1983, 31(4):532-540.
40. Cabral B., Leedom L. Imaging vector fields using line integral convolution. Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques 1993, 263-270. ACM, New York, NY, USA.
41. Callaghan P. Principles of Nuclear Magnetic Resonance Microscopy 1991, Oxford University Press, USA.
42. Callaghan P., Coy A., MacGowan D., Packer K., Zelaya F. Diffraction-like effects in nmr diffusion studies of fluids in porous solids. Nature 1991, 351(6326):467-469.
43. Campbell J., Siddiqi K., Rymar V., Sadikot A., Pike G. Flow-based fiber tracking with diffusion tensor and q-ball data: validation and comparison to principal diffusion direction techniques. NeuroImage 2005, 27(4):725-736.
44. Canales-Rodri{dotless}́guez E., Lin C., Iturria-Medina Y., Yeh C., Cho K., Melie-Garci{dotless}́a L. Diffusion orientation transform revisited. NeuroImage 2010, 49(2):1326-1339.
45. Candès E., Romberg J., Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory 2006, 52(2):489-509.
46. Casimir H.B.G. On onsager's principle of microscopic reversibility. Reviews of Modern Physics 1945, 17(2-3):343-350.
47. Chefd'hotel C., Tschumperlé D., Deriche R., Faugeras O. Constrained flows of matrix-valued functions: application to diffusion tensor regularization. Proceedings of the 7th European Conference on Computer Vision - Part I 2002, 251-265. Springer-Verlag, Copenhaguen, Denmark.
48. Chefd'hotel C., Tschumperlé D., Deriche R., Faugeras O. Regularizing flows for constrained matrix-valued images. Journal of Mathematical Imaging and Vision 2004, 20(1-2):147-162.
49. Chen Y., Guo W., Zeng Q., Yan X., Huang F., Zhang H., He G., Vemuri B., Liu Y. Estimation, smoothing, and characterization of apparent diffusion coefficient profiles from high angular resolution dwi. CVPR 2004, 1:588-593.
50. Chen Y., Guo W., Zeng Q., Yan X., Rao M., Liu Y. Apparent diffusion coefficient approximation and diffusion anisotropy characterization in DWI. Proceedings of the 19th International Conference on Information Processing in Medical Imaging (IPMI) 2005, 246-257. Springer, Glenwood Springs, CO, USA.
51. Cheng J., Ghosh A., Deriche R., Jiang T. Model-free, regularized, fast, and robust analytical orientation distribution function estimation. Lecture Notes in Computer Science 2010, vol. 6361:648-656. Springer, Berlin/Heidelberg. T. Jiang, N. Navab, J. Pluim, M. Viergever (Eds.).
52. Cheng J., Ghosh A., Jiang T., Deriche R. Model-free and analytical EAP reconstruction via spherical polar fourier diffusion MRI. Proceedings of the Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2010, 590-597. Springer.
53. Chung S., Lu Y., Henry R. Comparison of bootstrap approaches for estimation of uncertainties of DTI parameters. NeuroImage 2006, 33(2):531-541.
54. Clark C., Le Bihan D. Water diffusion and anisotropy at high b values in the human brain. Magnetic Resonance in Medicine 2000, 44:852-859.
55. Cohen Y., Assaf Y. High b-value q-space analyzed diffusion-weighted mrs and MRI in neuronal tissues - a technical review. NMR in Biomedicine 2002, 15:516-542.
56. Conturo T., Lori N., Cull T., Akbudak E., Snyder A., Shimony J., McKinstry R., Burton H., Raichle M. Tracking neuronal fiber pathways in the living human brain. Proceedings of the National Academy of Sciences 1999, vol. 96:10422-10427. National Acad Sciences.
57. Cory D., Garroway A. Measurement of translational displacement probabilities by nmr: an indicator of compartmentation. Magnetic Resonance in Medicine 1990, 14(3):435-444.
58. Courant R., Hilbert D. Methods of Mathematical Physics 1962, Interscience, New York.
59. Coy A., Callaghan P. Pulsed gradient spin echo nuclear magnetic resonance for molecules diffusing between partially reflecting rectangular barriers. The Journal of Chemical Physics 1994, 101:4599.
60. Cramér H. Mathematical Methods of Statistics 1957, Princeton University Press.
61. De Groot S., Mazur P. Non Equilibrium Thermodynamics 1962, North Holland, Amsterdam.
62. Deans S. The Radon Transform and Some of Its Applications 1983, A Wiley-Interscience Publication, New York.
63. Defrise M., De Mol C. A regularized iterative algorithm for limited-angle inverse Radon transform. Journal of Modern Optics 1983, 30(4):403-408.
64. Deriche R., Calder J., Descoteaux M. Optimal real-time q-ball imaging using regularized kalman filtering with incremental orientation sets. Medical Image Analysis 2009, 13(4):564-579.
65. Descoteaux, M., 2008. High angular resolution diffusion MRI: from local estimation to segmentation and tractography. Ph.D. thesis, University of Nice-Sophia Antipolis.
66. Descoteaux M., Angelino E., Fitzgibbons S., Deriche R. Apparent diffusion coefficients from high angular resolution diffusion imaging: estimation and applications. Magnetic Resonance in Medicine 2006, 56(2).
67. Descoteaux M., Angelino E., Fitzgibbons S., Deriche R. Regularized, fast and robust analytical q-ball imaging. Magnetic Resonance in Medicine 2007, 58:497-510.
68. Descoteaux M., Deriche R., Knosche T.R., Anwander A. Deterministic and probabilistic tractography based on complex fibre orientation distributions. IEEE Transactions on Medical Imaging 2009, 28(2):269-286.
69. Descoteaux M., Deriche R., Le Bihan D., Mangin J., Poupon C. Diffusion propagator imaging: using Laplace's equation and multiple shell acquisitions to reconstruct the diffusion propagator. Proceedings of the Information Processing in Medical Imaging 2009, 1-13. Springer.
70. Donoho D. De-noising by soft-thresholding. IEEE Transactions on Information Theory 2002, 41(3):613-627.
71. Einstein A. On the movement of small particles suspended in stationary liquids required by the molecular-kinetic theory of heat. Annalen der Physik 1905, 17:549-560.
72. Fasshauer, G., Schumaker, L., 1998. Scattered data fitting on the sphere. In: Mathematical Methods for Curves and Surfaces II.
73. Fillard P., Pennec X., Arsigny V., Ayache N. Clinical dt-mri estimation, smoothing, and fiber tracking with log-euclidean metrics. IEEE Transactions on Medical Imaging 2007, 26(11):1472-1482.
74. Filler, A., Tsuruda, J.S., Richards, T.L., Howe, F., 1992. Images, apparatus, algorithms and methods. UK Patent Office GB9210810.
75. Frank L. Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magnetic Resonance in Medicine 2002, 47:1083-1099.
76. Freeden W., Gervens T., Schreiner M. Constructive Approximation on the Sphere 1998, Clarendon Press.
77. Frøhlich A., Østergaard L., Kiselev V. Effect of impermeable boundaries on diffusion-attenuated MR signal. Journal of Magnetic Resonance 2006, 179(2):223-233.
78. Ghosh A., Descoteaux M., Deriche R. Riemannian framework for estimating symmetric positive definite 4th order diffusion tensors. LNCS 2008, vol. 5241:858-865. Springer. D. Metaxas, L. Axel, G. Fichtinger, G. Székely (Eds.).
79. Ghosh A., Tsigaridas E., Descoteaux M., Comon P., Mourrain B., Deriche R. A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the orientation distribution function in diffusion MRI. The Workshop on Computational Diffusion MRI (in MICCAI) 2008, 237-248. Citeseer.
80. Grad H. Note on N-dimensional Hermite polynomials. Communications on Pure and Applied Mathematics 1949, 2(4).
81. Grebenkov D. NMR survey of reflected Brownian motion. Reviews of Modern Physics 2007, 79(3):1077-1137.
82. Grebenkov D., Guillot G., Sapoval B. Restricted diffusion in a model acinar labyrinth by NMR: theoretical and numerical results. Journal of Magnetic Resonance 2007, 184(1):143-156.
83. Gudbjartsson H., Patz S. The rician distribution of noisy MRI data. Magnetic Resonance in Medicine 1995, 34:910-914.
84. Hagmann, P., 2005. From diffusion MRI to brain connectomics. Ph.D. thesis, École polytechnique fédérale de Lausanne.
85. Hagmann, P., Reese, T., Tseng, W., Meuli, R., Thiran, J., Wedeen, V., 2004. Diffusion spectrum imaging tractography in complex cerebral white matter: an investigation of the centrum semiovale. In: Proc. Intl. Soc. Mag. Reson. Med., vol. 12, pp. 15-21.
86. Healy D., Hendriks H., Kim P. Spherical deconvolution. Journal of Multivariate Analysis 1998, 67(1):1-22.
87. Hess C., Mukherjee P., Han E., Xu D., Vigneron D. Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis. Magnetic Resonance in Medicine 2006, 56(1):104-117.
88. Hilbert D. Ueber die Darstellung definiter Formen als Summe von formenquadraten. Mathematische Annalen 1888, 32(3):342-350.
89. Hosey T., Williams G., Ansorge R. Inference of multiple fiber orientations in high angular resolution diffusion imaging. Magnetic Resonance in Medicine 2005, 54(6):1480-1489.
90. Hyslop W., Lauterbur P. Effects of restricted diffusion on microscopic NMR imaging. Journal of Magnetic Resonance 1991, 94(3):501-510.
91. Jansons K., Alexander D. Persistent angular structure: new insights from diffusion magnetic resonance imaging data. Inverse Problems 2003, 19(5):1031-1046.
92. Jensen J., Helpern J., Ramani A., Lu H., Kaczynski K. Diffusional kurtosis imaging: the quantification of non-Gaussian water diffusion by means of magnetic resonance imaging. Magnetic Resonance in Medicine 2005, 53(6):1432-1440.
93. Jian B., Vemuri B.C. A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted MRI. IEEE Transactions on Medical Imaging 2007, 26(11):1464-1471.
94. Jian B., Vemuri B.C., Özarslan E., Carney P.R., Mareci T.H. A novel tensor distribution model for the diffusion-weighted mr signal. NeuroImage 2007, 37:164-176.
95. Johansen-Berg H., Behrens T. Diffusion MRI: From Quantitative Measurement to In Vivo Neuroanatomy 2009, Academic Press, Elsevier.
96. Johnston T.W. Cartesian tensor scalar product and spherical harmonic expansions in Boltzmann's equation. Physical Review 1960, 120(4):1103-1111.
97. Jones D., Horsfield M., Simmons A. Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging. Magnetic Resonance in Medicine 1999, 42(3):515-525.
98. Jones D., Simmons A., Williams S., Horsfield M. Non-invasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magnetic Resonance in Medicine 1999, 42(1).
99. Kaden E., Knösche T., Anwander A. Parametric spherical deconvolution: inferring anatomical connectivity using diffusion MR imaging. NeuroImage 2007, 37(2):474-488.
100. Kärger J., Heink W. The propagator representation of molecular transport in microporous crystallites. Journal of Magnetic Resonance 1969, 51(1):1-7.
101. Kendall M., Stuart A. The Advanced Theory of Statistics. Distribution Theory 1977, vol. 1. Griffin, London. furth ed.
102. Kezele, I., Descoteaux, M., Poupon, C., Abrial, P., Poupon, F., Mangin, J., 2008. Multiresolution decomposition of HARDI and ODF profiles using spherical wavelets. In: The Computational Diffusion MRI Workshop (CDMRI'08), New York, pp. 225-234.
103. Khachaturian M., Wisco J., Tuch D. Boosting the sampling efficiency of q-ball imaging using multiple wavevector fusion. Magnetic Resonance in Medicine 2007, 57:289-296.
104. Köpf M., Corinth C., Haferkamp O., Nonnenmacher T. Anomalous diffusion of water in biological tissues. Biophysical Journal 1996, 70(6):2950-2958.
105. Köpf M., Metzler R., Haferkamp O., Nonnenmacher T. NMR studies of anomalous diffusion in biological tissues: experimental observation of Lévy stable processes. Fractals in Biology and Medicine 1998, 2:354-364.
106. Kuchel P., Coy A., Stilbs P. NMR diffusion-diffraction of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics. Magnetic Resonance in Medicine 1997, 37(5):637-643.
107. Kuo L.-W., Chen J.-H., Wedeen V.J., Tseng W.-Y.I. Optimization of diffusion spectrum imaging and q-ball imaging on clinical MRI system. NeuroImage 2008, 41(1):7-18.
108. Landman, B.A., Wan, H., Bogovic, J.A., Bazin, P.-L., Prince, J.L., 2010. Resolution of crossing fibers with constrained compressed sensing using traditional diffusion tensor MRI. In: Proceedings of SPIE, vol. 7623, p. 76231H.
109. Le Bihan D. Molecular diffusion nuclear magnetic resonance imaging. Magnetic Resonance Quarterly 1991, 7(1):1-30.
110. Le Bihan D., van Zijl P. from the diffusion coefficient to the diffusion tensor. NMR in Biomedicine 2002, 15(7-8):431-434.
111. LeBihan D., Poupon C., Amadon A., Lethimonnier F. Artifacts and pitfalls in diffusion MRI. Journal of Magnetic Resonance Imaging 2006, 24:478-488.
112. Lee, N., Singh, M., 2010. Compressed sensing based diffusion spectrum imaging. In: Proceedings of the ISMRM, Stockholm, Sweden, pp. 1-8.
113. Lenglet, C., 2006. Geometric and variational methods for diffusion tensor MRI processing. Ph.D. thesis, University Nice Sophia-Antipolis.
114. Lenglet C., Campbell J., Descoteaux M., Haro G., Savadjiev P., Wassermann D., Anwander A., Deriche R., Pike G., Sapiro G., Siddiqi K., Thompson P. Mathematical methods for diffusion MRI processing. NeuroImage 2009, 45(1, Suppl. 1):S111-S122.
115. Li H., Manjunath B., Mitra S. Multisensor image fusion using the wavelet transform. Graphical Models and Image Processing 1995, 57(3):235-245.
116. Lin C., Tseng W., Cheng H., Chen J. Validation of diffusion tensor magnetic resonance axonal fiber imaging with registered manganese-enhanced optic tracts. NeuroImage 2001, 14(5):1035-1047.
117. Lin C.-P., Wedeen V.J., Chen J.-H., Yao C., Tseng W.-Y.I. Validation of diffusion spectrum magnetic resonance imaging with manganese-enhanced rat optic tracts and ex vivo phantoms. NeuroImage 2003, 19(3):482-495.
118. Liu C., Bammer R., Acar B., Moseley M. Characterizing non-Gaussian diffusion by using generalized diffusion tensors. Magnetic Resonance in Medicine 2004, 51:924-937.
119. Ljunggren S. A simple graphical representation of fourier-based imaging methods. Journal of Magnetic Resonance 1983, 54:338-343.
120. Luo J., Zhu Y., Magnin I. Denoising by averaging reconstructed images: application to magnetic resonance images. IEEE Transactions on Biomedical Engineering 2009, 56(3):666-674.
121. Lustig M., Donoho D., Pauly J. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine 2007, 58(6):1182-1195.
122. Lythgoe M., Busza A., Calamante F., Sotak C., King M., Bingham A., Williams S., Gadian D. Effects of diffusion anisotropy on lesion delineation in a rat model of cerebral ischemia. Magnetic Resonance in Medicine 1997, 38(4):662-668.
123. Maier S., Vajapeyam S., Mamata H., Westin C., Jolesz F., Mulkern R. Biexponential diffusion tensor analysis of human brain diffusion data. Magnetic Resonance in Medicine 2004, 51(2):321-330.
124. Mair R., Sen P., Hürlimann M., Patz S., Cory D., Walsworth R. The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media. Journal of Magnetic Resonance 2002, 156(2):202-212.
125. Malcolm J.G., Shenton M.E., Rathi Y. Filtered multi-tensor tractography. IEEE Transactions on Medical Imaging 2010, 29:1664-1675.
126. Mangin J., Poupon C., Clark C., Le Bihan D., Bloch I. Distortion correction and robust tensor estimation for MR diffusion imaging. Medical Image Analysis 2002, 6(3):191-198.
127. Marquardt D. An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics 1963, 11(2):431-441.
128. McCullagh P. Tensor Methods in Statistics 1987, Chapman and Hall, London.
129. Mendelson K. Percolation model of nuclear magnetic relaxation in porous media. Physical Review B 1990, 41(1):562-567.
130. Menzel, M.I., Khare, K., King, K.F., Tao, X., Hardy, C.J., Marinelli, L., 2010. Accelerated diffusion spectrum imaging in the humain brain using compressed sensing. In: Proceedings of the ISMRM, Stockholm, Sweden, pp. 1-8.
131. Merlet, S., Deriche, R., 2010. Compressed Sensing for Accelerated EAP Recovery in Diffusion MRI. In: MICCAI, Beijing, China, p. 14. http://hal.inria.fr/inria-00536278/en/.
132. Michailovich O., Rathi Y. Fast and accurate reconstruction of hardi data using compressed sensing. Lecture Notes in Computer Science 2010, vol. 6361:607-614. Springer, Berlin/Heidelberg. T. Jiang, N. Navab, J. Pluim, M. Viergever (Eds.).
133. Michailovich, O., Rathi, Y., Shenton, M., 2008. On approximation of orientation distributions by means of spherical ridgelets. In: Proceedings of the Int. Symp. on Biomedical Imaging, pp. 939-942.
134. Michailovich, O.V., Rathi, Y., Dolui, S., 2010. Spatially regularized compressed sensing of diffusion MRI data. CoRR abs/1009.1889.
135. Mitra P., Halperin B. Effects of finite gradient-pulse widths in pulsed-field-gradient diffusion measurements. Journal of Magnetic Resonance, Series A 1995, 113(1):94-101.
136. Mitra P.P., Sen P.N. Effects of microgeometry and surface relaxation on nmr pulsed-field-gradient experiments: simple pore geometries. Physical Review B 1992, 45(1):143-156.
137. Mori S., Crain B., Chacko V., Van Zijl P. Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals of Neurology 1999, 45(2).
138. Moritani T., Ekholm S., Westesson P. Diffusion-Weighted MR Imaging of the Brain 2004, Springer-Verlag.
139. Moseley M.E., Cohen Y., Kucharczyk J., Mintorovitch J., Asgari H.S., Wendland M.F., Tsuruda J., Norman D. Diffusion-weighted MR imaging of anisotropic water diffusion in cat central nervous system. Radiology 1990, 176(2):439-445.
140. Neji R., Azzabou N., Paragios N., Fleury G. A Convex Semi-definite Positive Framework for DTI Estimation and Regularization. Lecture Notes in Computer Science 2007, 4841:220.
141. Neuman C. Spin echo of spins diffusing in a bounded medium. The Journal of Chemical Physics 1974, 60:4508.
142. Niendorf T., Dijkhuizen R., D.G.N., van Lookeren C.M., Nicolay K. Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magnetic Resonance in Medicine 1996, 36:847-857.
143. Onsager L. Reciprocal relations in irreversible processes: I. Physical Review 1931, 37(4):405-426.
144. Onsager L. Reciprocal relations in irreversible processes: II. Physical Review 1931, 38(12):2265-2279.
145. Özarslan, E., Koay, C., Basser, P., 2008. Simple harmonic oscillator based estimation and reconstruction for one-dimensional q-space. In: Proc. Intl. Soc. Mag. Reson. Med., vol. 16, p. 35.
146. Özarslan E., Mareci T. Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. Magnetic Resonance in Medicine 2003, 50(5):955-965.
147. Özarslan E., Sherperd T.M., Vemuri B.C., Blackband S.J., Mareci T.H. Resolution of complex tissue microarchitecture using the diffusion orientation transform (dot). NeuroImage 2006, 31:1086-1103.
148. Özarslan E., Vemuri B., Mareci T. Generalized scalar measures for diffusion MRI using trace, variance, and entropy. Magnetic Resonance in Medicine 2005, 53(4).
149. Pajevic S., Pierpaoli C. Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain. Magnetic Resonance in Medicine 1999, 42(3):526-540.
150. Papadakis N., Xing D., Houston G., Smith J., Smith M., James M., Parsons A., Huang C., Hall L., Carpenter T. A study of rotationally invariant and symmetric indices of diffusion anisotropy. Magnetic Resonance Imaging 1999, 17(6):881.
151. Parker G., Alexander D. Probabilistic Monte Carlo based mapping of cerebral connections utilising whole-brain crossing fibre information. Lecture Notes in Computer Science 2003, 684-696.
152. Peled S., Friman O., Jolesz F., Westin C. Geometrically constrained two-tensor model for crossing tracts in DWI. Magnetic Resonance Imaging 2006, 24(9):1263-1270.
153. Pennec X., Fillard P., Ayache N. A Riemannian framework for tensor computing. International Journal of Computer Vision 2006, 66(1):41-66.
154. Perrin M., Poupon C., Rieul B., Leroux P., Constantinesco A., Mangin J., LeBihan D. Validation of q-ball imaging with a diffusion fibre-crossing phantom on a clinical scanner. Philosophical Transactions of the Royal Society B: Biological Sciences 2005, 360(1457):881.
155. Pickalov, V., Basser, P.J., 2006. 3D tomographic reconstruction of the average propagator from MRI data. In: Proceedings of the ISBI, p. 710-713.
156. Pierpaoli C., Basser P.J. Toward a quantitative assessment of diffusion anisotropy. Magnetic Resonance Medicine 1996, 36(6):893-906.
157. Pipe J. Diffusion MRI: From Quantitative Measurement to In Vivo Neuroanatomy 2009, Academic Press, Elsevier, Chapter: Pulse Sequences for Diffusion-weighted MRI, pp. 11-35.
158. Poupon, C., 1999. Détection des faisceaux de fibres de la substance blanche pour l'étude de la connectivité anatomique cérébrale. Ph.D. thesis, École nationale supérieure des télécommunications.
159. Poupon C., Roche A., Dubois J., Mangin J.-F., Poupon F. Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering. Medical Image Analysis 2008, 12(5):527-534.
160. Putz B., Barsky D., Schulten K. Edge enhancement by diffusion in microscopic magnetic resonance imaging. Journal of Magnetic Resonance 1992, 97:27-53.
161. Radon J. Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte Sächsische Akademie der Wissenschaften, Leipzig, Mathematisch-Physikalische Klasse 1917, 69:262-277.
162. Ramirez-Manzanares A., Cook P., Gee J. A comparison of methods for recovering intra-voxel white matter fiber architecture from clinical diffusion imaging scans. Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention - Part I 2008, 305-312. Springer.
163. Rathi Y., Michailovich O., Shenton M., Bouix S. Directional functions for orientation distribution estimation. Medical Image Analysis 2009, 13(3):432-444.
164. Regan D., Kuchel P. NMR studies of diffusion-coherence phenomena in red cell suspensions: current status. Israel Journal of Chemistry 2003, 43(1):45-54.
165. Ritchie, D., September 1998. Parametric protein shape recognition. Ph.D. thesis, University of Aberdeen, UK.
166. Robertson B. Spin-echo decay of spins diffusing in a bounded region. Physical Review 1966, 151(1):273-277.
167. Disorders of Brain and Mind 2003, Cambridge University Press. M. Ron, T. Robbins (Eds.).
168. Savadjiev P., Campbell J., Descoteaux M., Deriche R., Pike G., Siddiqi K. Labeling of ambiguous subvoxel fibre bundle configurations in high angular resolution diffusion MRI. NeuroImage 2008, 41(1):58-68.
169. Savadjiev P., Campbell J., Pike G., Siddiqi K. 3D curve inference for diffusion MRI regularization and fibre tractography. Medical Image Analysis 2006, 10(5):799-813.
170. Sen P., Hürlimann M., de Swiet T. Debye-Porod law of diffraction for diffusion in porous media. Physical Review B 1995, 51(1):601-604.
171. Seunarine, K., Alexander, D., 2006. Linear persistent angular structure MRI and non-linear spherical deconvolution for diffusion MRI. In: Proceedings of the ISMRM, p. 2726.
172. Smoluchowski M.V. Drei vortrage uber diffusion, brownsche bewegung und koagulation von kolloidteilchen. Zeitschrift fur Physik 1916, 17:557-585.
173. Stalling D., Hege H. Fast and resolution independent line integral convolution. Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques 1995, 249-256. ACM, New York, NY, USA.
174. Stejskal E. Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow. The Journal of Chemical Physics 1965, 43(10):3597-3603.
175. Stejskal E., Tanner J. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. Journal of Chemical Physics 1965, 42:288-292.
176. Stepisnik J. Analysis of NMR self-diffusion measurements by a density matrix calculation. Physica B 1981, 104:350-364.
177. Stewart G., Stewart G. Introduction to Matrix Computations 1973, Academic press, New York.
178. Su Z., Coppens P. Rotation of real spherical harmonics. Foundations of Crystallography 1994, 50(5):7673.
179. Tanner J. Transient diffusion in a system partitioned by permeable barriers. application to nmr measurements with a pulsed field gradient. The Journal of Chemical Physics 1978, 69(4):1748-1754.
180. Tanner J., Stejskal E. Restricted self-diffusion of protons in colloidal systems by the pulsed-gradient, spin-echo method. Journal of Chemical Physics 1968, 49:1768-1777.
181. Torrey H.C. Bloch equations with diffusion terms. Physical Review 1956, 104(3):563-565.
182. Tournier J., Calamante F., Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. NeuroImage 2007, 35(4):1459-1472.
183. Tournier J., Calamante F., Gadian D., Connely A. Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. NeuroImage 2004, 23:1179-1185.
184. Tournier J., Yeh C., Calamante F., Cho K., Connelly A., Lin C. Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data. NeuroImage 2008, 42(2):617-625.
185. Tristan-Vega A., Westin C.-F., Aja-Fernandez S. Estimation of fiber orientation probability density functions in high angular resolution diffusion imaging. NeuroImage 2009, 47(2):638-650.
186. Tschumperlé, D., 2002. Pde's based regularization of multivalued images and applications. Ph.D. thesis, Université de Nice-Sophia-Antipolis, UFR Sciences.
187. Tschumperlé, D., Deriche, R., 2003a. Tensor field visualization with pde's and application to dt-mri fiber visualization. In: Proceedings of the VLSM, Nice, France, pp. 255-262.
188. Tschumperlé, D., Deriche, R., 2003b. Variational frameworks for DT-MRI estimation, regularization and visualization. In: Proceedings of the Ninth IEEE International Conference on Computer Vision, vol. 2, pp. 116-121.
189. Tschumperlé D., Deriche R. Vector-valued image regularization with PDEs: A common framework for different applications. IEEE Transactions on Pattern Analysis and Machine Intelligence 2005, 506-517.
190. Tuch, D., 2002. Diffusion MRI of complex tissue structure. Ph.D. thesis, Harvard University - MIT Division of Health Sciences and Technology.
191. Tuch D. Q-ball imaging. Magnetic Resonance in Medicine 2004, 52:1358-1372.
192. Tuch D., Reese T., Wiegell M., Makris N., Belliveau J., Wedeen V. High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magnetic Resonance in Medicine 2002, 48(4).
193. Tuch, D., Weisskoff, R., Belliveau, J., Wedeen, V., 1999. High angular resolution diffusion imaging of the human brain. In: Proceedings of the ISMRM, p. 321.
194. Veretennikov V., Koshevoi M., Panferov N., Pikalov V., Rupasov A., Semenov O., Shikanov A. Emission tomography of a micropinch discharge plasma. Soviet Journal of Plasma Physics 1992, 18(2).
195. von dem Hagen E., Henkelman R. Orientational diffusion reflects fiber structure within a voxel. Magnetic Resonance in Medicine 2002, 48(3).
196. Wayne R., Cotts R. Nuclear-magnetic-resonance study of self-diffusion in a bounded medium. Physical Review 1966, 151(1):264-272.
197. Wedeen V., Hagmann P., Tseng W., Reese T., Weisskoff R. Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magnetic Resonance in Medicine 2005, 54(6).
198. Wedeen, V., Reese, T., Tuch, D., Weigl, M., Dou, J.-G., Weiskoff, R., Chesler, D., 2000. Mapping fiber orientation spectra in cerebral white matter with fourier transform diffusion MRI. In: Proceedings of the ISMRM, p. 82.
199. Wedeen V., Wang R., Schmahmann J., Benner T., Tseng W., Dai G., Pandya D., Hagmann P., D'Arceuil H., de Crespigny A. Diffusion spectrum magnetic resonance imaging (DSI) tractography of crossing fibers. NeuroImage 2008, 41(4):1267-1277.
200. Weickert J., Hagen H. Visualization and Image Processing of Tensor Fields 2006, Springer, Heidelberg.
201. Weng J.-C., Chen J.-H., Kuo L.-W., Wedeen V.J., Tseng W.-Y.I. Maturation-dependent microstructure length scale in the corpus callosum of fixed rat brains by magnetic resonance diffusion-diffraction. Magnetic Resonance Imaging 2007, 25(1):78-86.
202. Westin, C., Peled, S., Gudbjartsson, H., Kikinis, R., Jolesz, F., 1997. Geometrical diffusion measures for MRI from tensor basis analysis. In: Proceedings of the ISMRM, p. 1742.
203. Wishart J. The generalised product moment distribution in samples from a normal multivariate population. Biometrika 1928, 20(1):32-52.
204. Wu Y., Field A., Alexander A. Computation of diffusion function measures in q-space using magnetic resonance hybrid diffusion imaging. IEEE Transactions on Medical Imaging 2008, 27(6):858-865.
205. Wu Y.-C., Alexander A.L. Hybrid diffusion imaging. NeuroImage 2007, 36.
206. Yin W., Osher S., Goldfarb D., Darbon J. Bregman iterative algorithm for l-1 minimization with application to compressed sensing. SIAM Journal Imaging Sciences 2008, 1(1):143-168.
207. Zhan W., Gu H., Xu S., Silbersweig D., Stern E., Yang Y. Circular spectrum mapping for intravoxel fiber structures based on high angular resolution apparent diffusion coefficients. Magnetic Resonance in Medicine 2003, 49(6):1077-1088.
208. Zielinski L., Sen P. Relaxation of nuclear magnetization in a nonuniform magnetic field gradient and in a restricted geometry. Journal of Magnetic Resonance 2000, 147(1):95-103.