W. Mean and .. , Weighted Median and Principal Geodesic Analysis (PGA), p.186

A. , P. Of, A. Papers-jian-cheng, R. Ghosh, T. Deriche et al., An Intrinsic Diffeomorphism Invariant Riemannian Framework for Probability Density Function Computing in diffusion MRI, IEEE Transaction on Medical Imaging

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Spherical Polar Fourier Imaging, IEEE transaction on Medical Imaging
URL : https://hal.archives-ouvertes.fr/inria-00615434

N. Zuo, J. Cheng, and T. Jiang, Diffusion magnetic resonance imaging for Brainnetome: A critical review, Neuroscience Bulletin, vol.6, issue.Suppl3, p.2012
DOI : 10.1007/s12264-012-1245-3
URL : https://hal.archives-ouvertes.fr/hal-01485543

C. Papers, J. Cheng, T. Jiang, and R. Deriche, Nonnegative Definite EAP and ODF Estimation via a Unified Multi-Shell HARDI Reconstruction, Proceedings of 15th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI'12), 2012.

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Diffeomorphism Invariant Riemannian Framework for Ensemble Average Propagator Computing, Proceedings of 14th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI'11), 2011.
DOI : 10.1007/s11263-005-3222-z
URL : https://hal.archives-ouvertes.fr/inria-00615431

J. Cheng, T. Jiang, and R. Deriche, Theoretical Analysis and Practical Insights on EAP Estimation via a Unified HARDI Framework " , Computational Diffusion MRI workshop (CDMRI'11), in conjunction with the MIC- CAI'11, 2011.

J. Cheng, S. Merlet, A. Ghosh, E. Caruyer, T. Jiang et al., Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging " , Computational Diffusion MRI workshop (CDMRI'11), in conjunction with the MICCAI, Oral) CHAP. C: PUBLICATIONS OF THE AUTHOR, 2011.

E. Caruyer, J. Cheng, C. Lenglet, G. Sapiro, T. Jiang et al., Optimal Design of Multiple Q-shells experiments for Diffusion MRI " , Computational Diffusion MRI workshop (CDMRI'11), in conjunction with the MICCAI'11, 2011.

S. Merlet, J. Cheng, A. Ghosh, and R. Deriche, Spherical Polar Fourier EAP and odf reconstruction via compressed sensing in diffusion mri, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2011.
DOI : 10.1109/ISBI.2011.5872425
URL : https://hal.archives-ouvertes.fr/inria-00585694

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Model-Free and Analytical EAP Reconstruction via Spherical Polar Fourier Diffusion MRI, Proceedings of 13th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI'10), 2010.
DOI : 10.1007/978-3-642-15705-9_72
URL : https://hal.archives-ouvertes.fr/inria-00496932

J. Cheng, A. Ghosh, R. Deriche, and T. Jiang, Model-Free, Regularized, Fast, and Robust Analytical Orientation Distribution Function Estimation, Proceedings of 13th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI'10), 2010.
DOI : 10.1007/978-3-642-15705-9_79
URL : https://hal.archives-ouvertes.fr/inria-00496929

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, A Riemannian Framework for Orientation Distribution Function Computing, Proceedings of 12th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI'09), 2009.
DOI : 10.1007/978-3-642-04268-3_112
URL : https://hal.archives-ouvertes.fr/inria-00424764

J. Cheng, F. Shi, K. Wang, M. Song, J. Jiang et al., Nonparametric Mean Shift Functional Detection on Functional Space for Task and Resting-state fMRI " , Workshop on fMRI data analysis: statistical modeling and detection issues in intra-and inter-subject functional MRI data analysis, in conjunction with the MICCAI, 2009.

X. Li, W. Hu, Z. Zhang, X. Zhang, M. Zhu et al., Visual tracking via incremental Log-Euclidean Riemannian subspace learning, Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition (CVPR'08), 2008.
URL : https://hal.archives-ouvertes.fr/hal-01485545

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, A Riemannian Framework for Ensemble Average Propagator Computing, 19th Scientific Meeting and Exhibition of the ISMRM, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00615436

J. Cheng, S. Merlet, A. Ghosh, E. Caruyer, T. Jiang et al., Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging, 19th Scientific Meeting and Exhibition of the ISMRM, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00615434

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Fast, modelfree , analytical diffusion PDF profile estimation from the DWI signals, Proceedings of the Sixteenth Annual Meeting of the Organization for Human Brain Mapping (OHBM'10), 2010.
URL : https://hal.archives-ouvertes.fr/inria-00497244

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Fast, Model- Free, Analytical ODF Reconstruction from the Q-Space Signal, Proceedings of the Sixteenth Annual Meeting of the Organization for Human Brain Mapping (OHBM'10), 2010.
URL : https://hal.archives-ouvertes.fr/inria-00497243

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Riemannian Median and Its Applications for Orientation Distribution Function Computing, Proceedings of 18th Scientific Meeting and Exhibition of the ISMRM, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00497246

A. Bibliography and . Rényi, On Measures of Entropy and Information, Proc. Fourth Berkeley Symp. Math., Statistics, and Probability 15, pp.547-561, 1960.

B. Afsari, Riemannian Lp center of mass: Existence, uniqueness, and convexity, Proceedings of the American Mathematical Society, pp.655-673, 2011.

I. Aganj, C. Lenglet, and G. Sapiro, ODF reconstruction in q-ball imaging with solid angle consideration, 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, p.89, 2009.
DOI : 10.1109/ISBI.2009.5193327

I. Aganj, C. Lenglet, and G. , Sapiro: 2010a, 'ODF maxima extraction in spherical harmonic representation via analytical search space reduction'. Medical Image Computing and Computer-Assisted Intervention?MICCAI, pp.84-91, 2010.

I. Aganj, C. Lenglet, G. Sapiro, E. Yacoub, K. Ugurbil et al., Reconstruction of the orientation distribution function in single- and multiple-shell q-ball imaging within constant solid angle, Magnetic Resonance in Medicine, vol.27, issue.119, pp.554-566, 0198.
DOI : 10.1002/mrm.22365

D. Alexander and G. Barker, Optimal imaging parameters for fiber-orientation estimation in diffusion MRI, NeuroImage, vol.27, issue.2, pp.357-367, 2005.
DOI : 10.1016/j.neuroimage.2005.04.008

D. Alexander, G. Barker, and S. Arridge, Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data, Magnetic Resonance in Medicine, vol.46, issue.2, pp.331-340, 2002.
DOI : 10.1002/mrm.10209

D. C. Alexander, C. Pierpaoli, P. J. Basser, and J. C. Gee, Spatial transformations of diffusion tensor magnetic resonance images, IEEE Transactions on Medical Imaging, vol.20, issue.11, pp.1131-1139, 2001.
DOI : 10.1109/42.963816

S. Amari, Differential-geometrical methods in statistic, p.57, 1985.
DOI : 10.1007/978-1-4612-5056-2

A. Anderson, Measurement of fiber orientation distributions using high angular resolution diffusion imaging, Magnetic Resonance in Medicine, vol.77, issue.5, pp.1194-1206, 2005.
DOI : 10.1002/mrm.20667

G. Andrews, R. Askey, and R. Roy, Special functions, p.25, 1999.

G. Arfken, H. Weber, and H. Weber, Mathematical methods for physicists, pp.24-25, 2005.

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, Log-Euclidean metrics for fast and simple calculus on diffusion tensors, Magnetic Resonance in Medicine, vol.52, issue.2, pp.411-421, 2006.
DOI : 10.1002/mrm.20965
URL : https://hal.archives-ouvertes.fr/inria-00502678

R. Askey and J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Memoirs of the American Mathematical Society, vol.54, issue.319, p.12, 1985.
DOI : 10.1090/memo/0319

Y. Assaf, R. Freidlin, G. Rohde, and P. Basser, New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter, Magnetic Resonance in Medicine, vol.121, issue.204, pp.965-978, 2004.
DOI : 10.1002/mrm.20274

H. Assemlal, D. Tschumperlé, and L. Brun, Efficient computation of pdf-based characteristics from diffusion mr signal'. Medical Image Computing and Computer- Assisted Intervention?MICCAI, pp.70-78, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00329239

H. Assemlal, D. Tschumperlé, L. Brun, and K. Siddiqi, Recent advances in diffusion MRI modeling: Angular and radial reconstruction'. Medical Image Analysis, p.62, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00927445

H. Assemlal, Diffusion MR image analysis for the estimation of tissues local architecture, pp.115-123, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00554969

H. Assemlal, D. Tschumperlé, and L. Brun, Efficient and robust computation of PDF features from diffusion MR signal, Medical Image Analysis, vol.13, issue.5, pp.715-729, 0193.
DOI : 10.1016/j.media.2009.06.004
URL : https://hal.archives-ouvertes.fr/hal-00410615

H. Assemlal, D. Tschumperlé, and L. Brun, Evaluation of q-Space Sampling Strategies for the Diffusion Magnetic Resonance Imaging, Medical Image Computing and Computer Assisted Intervention (MICCAI), p.227, 2009.
DOI : 10.1007/978-3-642-04271-3_50
URL : https://hal.archives-ouvertes.fr/hal-00814007

C. Atkinson and A. Mitchell, Rao's distance measure'. Sankhy ¯ a: The Indian Journal of Statistics, Series A, vol.43, issue.99, pp.345-365, 1981.

A. Bar-shir, L. Avram, E. Ozarslan, P. Basser, and Y. Cohen, 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, vol.194, issue.2, pp.230-236, 2008.
DOI : 10.1016/j.jmr.2008.07.009

A. Barmpoutis, M. Hwang, D. Howland, J. Forder, and B. Vemuri, Regularized positive-definite fourth order tensor field estimation from DW-MRI, NeuroImage, vol.45, issue.1, pp.153-162, 2009.
DOI : 10.1016/j.neuroimage.2008.10.056

A. Barmpoutis, B. Jian, and B. C. Vemuri, Symmetric Positive 4th Order Tensor & Their Estimation from Diffusion Weighted MRI', In: IPMI, vol.66, pp.308-319, 2007.

P. J. Basser, J. Mattiello, D. Lebihan, B. Batchelor, P. et al., MR diffusion tensor spectroscopy and imaging, Biophysical Journal, vol.66, issue.1, pp.259-267, 1994.
DOI : 10.1016/S0006-3495(94)80775-1
URL : https://hal.archives-ouvertes.fr/hal-00349721

T. Behrens, H. Berg, S. Jbabdi, M. Rushworth, and M. Woolrich, Probabilistic diffusion tractography with multiple fibre orientations: What can we gain?, NeuroImage, vol.34, issue.1, pp.144-155, 2007.
DOI : 10.1016/j.neuroimage.2006.09.018

M. A. Bernstein, K. F. King, and X. , Handbook of MRI Pulse Sequences, p.67, 2004.

A. Bhattacharyya, On a measure of divergence between two statistical populations defined by their probability distributions, Bull. Calcutta Math. Soc, vol.35, pp.99-109, 1943.

D. L. Bihan, E. Breton, D. Lallemand, P. Grenier, E. Cabanis et al., MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders., Radiology, vol.161, issue.2, pp.401-407, 1986.
DOI : 10.1148/radiology.161.2.3763909
URL : https://hal.archives-ouvertes.fr/hal-00349714

S. Blinnikov and R. Moessner, Expansions for nearly Gaussian distributions, Astronomy and Astrophysics Supplement Series, vol.130, issue.1, pp.193-205, 1998.
DOI : 10.1051/aas:1998221

W. Boothby, An introduction to differentiable manifolds and Riemannian geometry, p.36, 1986.

S. Braunstein and C. Caves, Statistical distance and the geometry of quantum states'. Physical review letters, pp.3439-3443, 1994.

D. Brody and L. Hughston, Statistical geometry in quantum mechanics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.454, issue.1977, pp.2445-53, 1977.
DOI : 10.1098/rspa.1998.0266

S. R. Buss and J. P. Fillmore, Spherical averages and applications to spherical splines and interpolation, ACM Transactions on Graphics, vol.20, issue.2, pp.95-126, 0198.
DOI : 10.1145/502122.502124

F. Byron and R. Fuller, Mathematics of classical and quantum physics, p.23, 1992.

P. Callaghan, Principles of nuclear magnetic resonance microscopy, p.80, 1991.

E. J. Canales-rodr?guez, L. Melie-garc?a, and Y. Iturria-medina, Mathematical description of q-space in spherical coordinates: Exact q-ball imaging, Magnetic Resonance in Medicine, vol.LXIX, issue.6, pp.1350-1367, 0198.
DOI : 10.1002/mrm.21917

E. Caruyer, J. Cheng, C. Lenglet, G. Sapiro, T. Jiang et al., Optimal Design of Multiple Q-shells experiments for Diffusion MRI'. In: Computational Diffusion MRI -MICCAI Workshop, p.227, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00617663

C. Chefd-'hotel, D. Tschumperlé, R. Deriche, and O. Faugeras, Regularizing Flows for Constrained Matrix-Valued Images, Journal of Mathematical Imaging and Vision, vol.20, issue.1/2, pp.147-162, 2004.
DOI : 10.1023/B:JMIV.0000011324.14508.fb

Y. Chen, W. Guo, Q. Zeng, X. Yan, F. Huang et al., Estimation, smoothing, and characterization of apparent diffusion coefficient profiles from high angular resolution DWI, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., pp.588-79, 2004.
DOI : 10.1109/CVPR.2004.1315085

Y. Chen, W. Guo, Q. Zeng, X. Yan, M. Rao et al., Apparent Diffusion Coefficient Approximation and Diffusion Anisotropy Characterization in DWI, Information Processing in Medical Imaging, pp.246-257, 2005.
DOI : 10.1007/11505730_21

J. Cheng, A. Ghosh, R. Deriche, and T. Jiang, Model-Free, Regularized, Fast, and Robust Analytical Orientation Distribution Function Estimation, Medical Image Computing and Computer-Assisted Intervention -MICCAI, vol.6361, issue.212, pp.648-656, 2010.
DOI : 10.1007/978-3-642-15705-9_79
URL : https://hal.archives-ouvertes.fr/inria-00496929

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, A Riemannian Framework for Orientation Distribution Function Computing, Medical Image Computing and Computer-Assisted Intervention -MICCAI, pp.911-918, 0190.
DOI : 10.1007/978-3-642-04268-3_112
URL : https://hal.archives-ouvertes.fr/inria-00424764

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Model-Free and Analytical EAP Reconstruction via Spherical Polar Fourier Diffusion MRI, Medical Image Computing and Computer-Assisted Intervention -MICCAI, vol.6361, issue.212, pp.590-597, 2010.
DOI : 10.1007/978-3-642-15705-9_72
URL : https://hal.archives-ouvertes.fr/inria-00496932

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Riemannian Median and Its Applications for Orientation Distribution Function Computing, p.226, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00497246

J. Cheng, A. Ghosh, T. Jiang, and R. Deriche, Diffeomorphism Invariant Riemannian Framework for Ensemble Average Propagator Computing, Medical Image Computing and Computer-Assisted Intervention -MICCAI, pp.98-106, 0190.
DOI : 10.1007/s11263-005-3222-z
URL : https://hal.archives-ouvertes.fr/inria-00615431

J. Cheng, T. Jiang, and R. Deriche, Theoretical Analysis and Practical Insights on EAP Estimation via a Unified HARDI Framework'. In: Computational Diffusion MRI -MICCAI Workshop, p.226, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00615430

J. Cheng, S. Merlet, E. Caruyer, A. Ghosh, T. Jiang et al., Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging'. In: Computational Diffusion MRI -MICCAI Workshop, pp.181-233, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00615434

J. Cheng, F. Shi, K. Wang, M. Song, J. Jiang et al., Nonparametric Mean Shift Functional Detection in the Functional Space for Task and Resting-state fMRI'. In: Workshop on fMRI data analysis: statistical modeling and detection issues in intra-and inter-subject functional MRI data analysis in conjunction with the MICCAI, p.226, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00424765

M. Descoteaux, High Angular Resolution Diffusion MRI: from Local Estimation to Segmentation and Tractograpghy, pp.72-234, 2008.

M. Descoteaux, E. Angelino, S. Fitzgibbons, and R. Deriche, Apparent diffusion coefficients from high angular resolution diffusion imaging: Estimation and applications, Magnetic Resonance in Medicine, vol.50, issue.2, pp.395-410, 2006.
DOI : 10.1002/mrm.20948

M. Descoteaux, E. Angelino, S. Fitzgibbons, and R. Deriche, Regularized, fast, and robust analytical Q-ball imaging, Magnetic Resonance in Medicine, vol.17, issue.3, pp.497-510, 0206.
DOI : 10.1002/mrm.21277

M. Descoteaux and R. Deriche, High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution, Journal of Mathematical Imaging and Vision, vol.12, issue.1, pp.239-252, 2009.
DOI : 10.1007/s10851-008-0071-8
URL : https://hal.archives-ouvertes.fr/inria-00423393

M. Descoteaux, R. Deriche, D. Bihan, J. Mangin, and C. Poupon, Multiple q- Shell Diffusion Propagator Imaging'. Medical Image Analysis, pp.141-142, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00531473

M. Descoteaux, R. Deriche, D. L. Bihan, J. Mangin, and C. Poupon, Diffusion Propagator Imaging: Using Laplace???s Equation and Multiple Shell Acquisitions to Reconstruct the Diffusion Propagator, IPMI. 94, p.138, 2009.
DOI : 10.1002/mrm.21277

M. Descoteaux, R. Deriche, T. R. Knösche, and A. Anwander, Deterministic and Probabilistic Tractography Based on Complex Fibre Orientation Distributions, IEEE Transactions on Medical Imaging, vol.28, issue.2, pp.269-286, 2008.
DOI : 10.1109/TMI.2008.2004424

M. Descoteaux, N. Wiest-daessle, S. Prima, C. Barillot, and R. Deriche, Impact of Rician Adapted Non-Local Means Filtering on HARDI, p.126, 2008.
DOI : 10.1007/978-3-540-85990-1_15
URL : https://hal.archives-ouvertes.fr/inria-00423318

D. Carmo and M. , Riemannian geometry, Birkhauser, vol.36, p.45, 1992.
DOI : 10.1007/978-1-4757-2201-7

P. Douek, R. Turner, J. Pekar, N. Patronas, and D. Lebihan, MR Color Mapping of Myelin Fiber Orientation, Journal of Computer Assisted Tomography, vol.15, issue.6, pp.923-929, 1991.
DOI : 10.1097/00004728-199111000-00003
URL : https://hal.archives-ouvertes.fr/hal-00350066

J. Du, A. Goh, and A. Qiu, Diffeomorphic Metric Mapping of High Angular Resolution Diffusion Imaging based on Riemannian Structure of Orientation Distribution Functions'. Arxiv preprint arXiv, pp.1107-4763, 2011.

A. Einstein, Investigations on the Theory of the Brownian Movement, p.63, 1956.

D. Fick, P. Fillard, M. Descoteaux, A. Goh, S. Gouttard et al., Quantitative evaluation of 10 tractography algorithms on a realistic diffusion MR phantom, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science NeuroImage, vol.10, issue.211, pp.30-39, 1855.

P. Fillard, X. Pennec, V. Arsigny, and N. Ayache, Clinical DT-MRI Estimation, Smoothing, and Fiber Tracking With Log-Euclidean Metrics, IEEE Transactions on Medical Imaging, vol.26, issue.11, pp.1472-1482, 0200.
DOI : 10.1109/TMI.2007.899173
URL : https://hal.archives-ouvertes.fr/inria-00502645

P. Fletcher and S. Joshi, Riemannian geometry for the statistical analysis of diffusion tensor data, Signal Processing, vol.87, issue.2, pp.250-262, 2007.
DOI : 10.1016/j.sigpro.2005.12.018

P. Fletcher, C. Lu, S. Pizer, and S. Joshi, Principal geodesic analysis for the study of nonlinear statistics of shape'. Medical Imaging, IEEE Transactions on, vol.23, issue.187, pp.995-1005, 2004.

P. Fletcher, Statistical Variability in Nonlinear Spaces Application to Shape Analysis and DT-MRI, pp.51-99, 2004.

P. T. Fletcher, S. Venkatasubramanian, and S. Joshi, The geometric median on Riemannian manifolds with application to robust atlas estimation, NeuroImage, vol.45, issue.1, pp.143-152, 2009.
DOI : 10.1016/j.neuroimage.2008.10.052

L. R. Frank, Characterization of anisotropy in high angular resolution diffusion-weighted MRI, Magnetic Resonance in Medicine, vol.15, issue.6, pp.1083-1099, 2002.
DOI : 10.1002/mrm.10156

M. Fréchet, LesélémentsLes´Leséléments aléatoires de nature quelconque dans un espace distancié'. H. Poincaré, pp.215-310, 1948.

A. Ghosh, High Order Models in Diffusion MRI and Applications, p.234, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00645820

A. Ghosh, R. Deriche, and M. Moakher, Ternary Quartic approach for positive 4th order diffusion tensors revisited, 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp.618-621, 2009.
DOI : 10.1109/ISBI.2009.5193123
URL : https://hal.archives-ouvertes.fr/inria-00496873

A. Ghosh, M. Descoteaux, and R. Deriche, Riemannian Framework for Estimating Symmetric Positive Definite 4th Oder Diffusion Tensors, In: MICCAI, vol.66, pp.308-319, 2008.

A. Ghosh, E. Ozarslan, and R. Deriche, Challenges in Reconstructing the Propagator via a Cumulant Expansion of the One-Dimensional qspace MR Signal, p.146, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00496885

A. Ghosh, E. Tsigaridas, M. Descoteaux, P. Comon, B. Mourrain et al., 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, In: MICCAI, vol.66, pp.308-319, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00340600

A. Ghosh, D. Wassermann, R. D. Goh, A. , C. Lenglet et al., A Polynomial Approach for Maxima Extraction and Its Application to Tractography in HARDI, pp.723-734, 0200.
DOI : 10.1007/978-3-642-22092-0_59
URL : https://hal.archives-ouvertes.fr/inria-00610195

A. Goh, C. Lenglet, P. Thompson, and R. Vidal, Estimating Orientation Distribution Functions with Probability Density Constraints and Spatial Regularity, pp.877-885, 2009.
DOI : 10.1007/978-3-642-04268-3_108

A. Goh, C. Lenglet, P. Thompson, and R. Vidal, A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry, NeuroImage, vol.56, issue.3, pp.181-183, 0201.
DOI : 10.1016/j.neuroimage.2011.01.053

G. Gong, T. Jiang, C. Zhu, Y. Zang, Y. He et al., Side and handedness effects on the cingulum from diffusion tensor imaging, NeuroReport, vol.16, issue.15, pp.1701-101, 2005.
DOI : 10.1097/01.wnr.0000183327.98370.6a

I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, pp.140-165, 2007.

R. Haberman, Elementary applied partial differential equations: with Fourier series and boundary value problems, p.12, 1987.

P. Hagmann, L. Jonasson, P. Maeder, J. Thiran, V. J. Wedeen et al., Understanding Diffusion MR Imaging Techniques: From Scalar Diffusion-weighted Imaging to Diffusion Tensor Imaging and Beyond, RadioGraphics, vol.26, issue.suppl_1, pp.205-223, 2006.
DOI : 10.1148/rg.26si065510

C. P. Hess, P. Mukherjee, E. T. Han, D. Xu, and D. B. Vigneron, Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis, Magnetic Resonance in Medicine, vol.54, issue.1, pp.104-117, 2006.
DOI : 10.1002/mrm.20931

T. Hosey, G. Williams, and R. Ansorge, Inference of multiple fiber orientations in high angular resolution diffusion imaging, Magnetic Resonance in Medicine, vol.56, issue.6, pp.1480-1489, 2005.
DOI : 10.1002/mrm.20723

S. A. Huettel, A. W. Song, and G. Mcgarthy, Functional magnetic resonance imaging, p.65, 2009.

S. Huzinaga, Gaussian???Type Functions for Polyatomic Systems. I, The Journal of Chemical Physics, vol.42, issue.4, pp.1293-96, 1965.
DOI : 10.1063/1.1696113

B. Jian and B. C. Vemuri, A Unified Computational Framework for Deconvolution to Reconstruct Multiple Fibers From Diffusion Weighted MRI, IEEE Transactions on Medical Imaging, vol.26, issue.11, pp.1464-1471, 2007.
DOI : 10.1109/TMI.2007.907552

B. Jian, B. C. Vemuri, E. Ozarslan, P. R. Carney, and T. H. Marecid, A novel tensor distribution model for the diffusion-weighted MR signal, NeuroImage, vol.37, issue.1, pp.164-176, 2007.
DOI : 10.1016/j.neuroimage.2007.03.074

F. Jiao, Y. Gur, C. Johnson, and S. Joshi, Detection of Crossing White Matter Fibers with High-Order Tensors and Rank-k Decompositions, pp.538-549, 2011.
DOI : 10.1007/978-3-642-22092-0_44

H. Johansen-berg and T. E. Behrens, Diffusion MRI: From quantitative measurement to In vivo neuroanatomy, p.73, 2009.

D. K. Jones, M. A. Horsfield, and A. Simmons, Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging, Magnetic Resonance in Medicine, vol.8, issue.3, pp.515-525, 1999.
DOI : 10.1002/(SICI)1522-2594(199909)42:3<515::AID-MRM14>3.0.CO;2-Q

H. Karcher, Riemannian center of mass and mollifier smoothing, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.509-541, 1977.
DOI : 10.1002/cpa.3160300502

W. Kendall, Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence, Proceedings of the London Mathematical Society, vol.3, issue.2, pp.371-418, 1990.
DOI : 10.1112/plms/s3-61.2.371

M. H. Khachaturian, J. J. Wisco, and D. S. Tuch, Boosting the sampling efficiency ofq-ball imaging using multiple wavevector fusion, Magnetic Resonance in Medicine, vol.45, issue.2, pp.289-296, 2007.
DOI : 10.1002/mrm.21090

C. G. Koay, L. Chang, J. D. Carew, C. Pierpaoli, and P. J. Basser, A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging, Journal of Magnetic Resonance, vol.182, issue.1, pp.115-125, 2006.
DOI : 10.1016/j.jmr.2006.06.020

B. Kreher, J. Schneider, I. Mader, E. Martin, J. Hennig et al., Multitensor approach for analysis and tracking of complex fiber configurations, Magnetic Resonance in Medicine, vol.51, issue.5, pp.1216-1225
DOI : 10.1002/mrm.20670

P. Kuchel, A. Coy, and P. Stilbs, NMR ???diffusion-diffraction??? of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics, Magnetic Resonance in Medicine, vol.5, issue.5, pp.637-643, 1997.
DOI : 10.1002/mrm.1910370502

L. Bihan and D. , Looking into the functional architecture of the brain with diffusion MRI, Nature Reviews Neuroscience, vol.4, issue.6, pp.469-480, 2003.
DOI : 10.1038/nrn1119
URL : https://hal.archives-ouvertes.fr/hal-00349696

G. Lebanon, Metric learning for text documents, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.4, pp.497-508, 2006.
DOI : 10.1109/TPAMI.2006.77

D. Lebihan, E. Breton, D. Lallemand, P. Grenier, E. Cabanis et al., MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders, Radiology, vol.61, pp.401-407, 1986.

C. Lenglet, Geometric and Variational Methods for Diffusion Tensor MRI Processing, p.101, 2006.
URL : https://hal.archives-ouvertes.fr/tel-00457463

C. Lenglet, J. Campbell, M. Descoteaux, G. Haro, P. Savadjiev et al., Mathematical methods for diffusion MRI processing, Mathematical Methods for Diffusion MRI Processing, pp.111-122, 2009.
DOI : 10.1016/j.neuroimage.2008.10.054

C. Lenglet, M. Rousson, R. Deriche, B. Lenglet, C. et al., DTI segmentation by statistical surface evolution, IEEE Transactions on Medical Imaging, vol.25, issue.6, pp.685-700, 2006.
DOI : 10.1109/TMI.2006.873299
URL : https://hal.archives-ouvertes.fr/inria-00070183

J. Li, Y. Liu, W. Qin, J. Jiang, Z. Qiu et al., Age of Onset of Blindness Affects Brain Anatomical Networks Constructed Using Diffusion Tensor Tractography, Cerebral Cortex, vol.23, issue.3, p.228, 2012.
DOI : 10.1093/cercor/bhs034

X. Li, W. Hu, Z. Zhang, X. Zhang, M. Zhu et al., Visual tracking via incremental log-Euclidean Riemannian subspace learning'. In: Computer Vision and Pattern Recognition, CVPR 2008. IEEE Conference on, pp.1-8, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01485545

Y. Li, Y. Liu, J. Li, W. Qin, K. Li et al., Brain Anatomical Network and Intelligence, PLoS Computational Biology, vol.24, issue.5, pp.1000395-1000396, 2009.
DOI : 10.1371/journal.pcbi.1000395.s009

F. Lin, C. Yu, T. Jiang, K. Li, C. Zhu et al., Discriminative analysis of relapsing neuromyelitis optica and relapsing???remitting multiple sclerosis based on two-dimensional histogram from diffusion tensor imaging, NeuroImage, vol.31, issue.2, pp.543-549, 2006.
DOI : 10.1016/j.neuroimage.2005.12.051
URL : https://hal.archives-ouvertes.fr/inria-00123576

C. Liu, R. Bammer, B. Acar, and M. E. Moseley, Characterizing non-gaussian diffusion by using generalized diffusion tensors, Magnetic Resonance in Medicine, vol.42, issue.5, pp.925-937, 2004.
DOI : 10.1002/mrm.20071

C. Liu, R. Bammer, and M. E. Moseley, Generalized Diffusion Tensor Imaging (GDTI): A Method for Characterizing and Imaging Diffusion Anisotropy Caused by Non-Gaussian Diffusion, Israel Journal of Chemistry, vol.44, issue.1-2, pp.145-154, 2003.
DOI : 10.1560/HB5H-6XBR-1AW1-LNX9

P. Mahalanobis, On the generalized distance in statistics, Proceedings of the National Institute of Science, pp.49-53, 1936.

R. Mair, P. Sen, M. H. ¨-urlimann, S. Patz, D. Cory et al., The Narrow Pulse Approximation and Long Length Scale Determination in Xenon Gas Diffusion NMR Studies of Model Porous Media, Journal of Magnetic Resonance, vol.156, issue.2, pp.202-212, 2002.
DOI : 10.1006/jmre.2002.2540

J. Marcinkiewicz, Sur une propri???t??? de la loi de Gau???, Mathematische Zeitschrift, vol.29, issue.1, pp.612-618, 1939.
DOI : 10.1007/BF01210677

S. Maybank, Detection of image structures using the Fisher information and the Rao metric, IEEE transactions, pp.1579-1589, 2004.
DOI : 10.1109/TPAMI.2004.122

T. Mcgraw, B. Vemuri, R. Yezierski, and T. Mareci, Segmentation of High Angular Resolution Diffusion MRI Modeled as a Field of von Mises-Fisher Mixtures, p.214, 2006.
DOI : 10.1007/11744078_36

K. Merboldt, W. , and J. Frahm, Self-diffusion NMR imaging using stimulated echoes, Journal of Magnetic Resonance (1969), vol.64, issue.3, pp.479-486, 1985.
DOI : 10.1016/0022-2364(85)90111-8

S. Merlet, J. Cheng, A. Ghosh, and R. Deriche, Spherical Polar Fourier EAP and odf reconstruction via compressed sensing in diffusion mri, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp.189-227, 0191.
DOI : 10.1109/ISBI.2011.5872425
URL : https://hal.archives-ouvertes.fr/inria-00585694

W. Mio, D. Badlyans, and X. Liu, A Computational Approach to Fisher Information Geometry with Applications to Image Analysis, pp.18-33, 2005.
DOI : 10.1007/11585978_2

M. Moakher, A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices, SIAM Journal on Matrix Analysis and Applications, vol.26, issue.3, pp.735-747, 2005.
DOI : 10.1137/S0895479803436937

S. Mori, Introduction to Diffusion Tensor Imaging, p.72, 2007.

M. Moseley, Y. Cohen, J. Mintorovitch, J. Kucharczyk, J. Tsuruda et al., Diffusion-weighted MR imaging of anisotropic water diffusion in cat central nervous system., Radiology, vol.176, issue.2, pp.439-445, 1990.
DOI : 10.1148/radiology.176.2.2367658

E. Ozarslan, C. Koay, and P. Basser, Simple harmonic oscillator based estimation and reconstruction for one-dimensional q-space mr, Magnetic Resonance in Medicine, pp.35-95, 2008.

¨. Ozarslan, E. , C. Koay, T. Shepherd, S. Blackband et al., Simple harmonic oscillator based reconstruction and estimation for three-dimensional q-space mri, International Society for Magnetic Resonance in Medicine (ISMRM). p. 1396. 74, pp.92-95, 2009.

¨. Ozarslan, E. , and T. H. Mareci, Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging, Magnetic Resonance in Medicine, vol.48, issue.5, pp.955-965, 2003.
DOI : 10.1002/mrm.10596

¨. Ozarslan, E. , N. Shemesh, C. Koay, Y. Cohen et al., Nuclear magnetic resonance characterization of general compartment size distributions, New Journal of Physics, vol.13, issue.1, p.228, 2011.
DOI : 10.1088/1367-2630/13/1/015010

¨. Ozarslan, E. , T. Shepherd, C. Koay, S. Blackband et al., Temporal scaling characteristics of diffusion as a new MRI contrast: Findings in rat hippocampus, NeuroImage, vol.60, issue.2, p.228, 2012.
DOI : 10.1016/j.neuroimage.2012.01.105

E. Ozarslan, T. M. Shepherd, B. C. Vemuri, S. J. Blackband, and T. H. Mareci, Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT), NeuroImage, vol.31, issue.3, pp.1086-1103, 2006.
DOI : 10.1016/j.neuroimage.2006.01.024

¨. Ozarslan, E. , B. Vemuri, and T. Mareci, Generalized scalar measures for diffusion MRI using trace, variance, and entropy, Magnetic Resonance in Medicine, vol.40, issue.4, pp.866-876, 2005.
DOI : 10.1002/mrm.20411

B. Pelletier, Kernel density estimation on Riemannian manifolds, Statistics & Probability Letters, vol.73, issue.3, pp.297-304, 2005.
DOI : 10.1016/j.spl.2005.04.004

X. Pennec, X. Bibliography-pennec, P. Fillard, and N. Ayache, Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements, Journal of Mathematical Imaging and Vision, vol.20, issue.10, pp.127-154, 0200.
DOI : 10.1007/s10851-006-6228-4
URL : https://hal.archives-ouvertes.fr/inria-00614994

C. Pierpaoli and P. Basser, Toward a quantitative assessment of diffusion anisotropy, Magnetic Resonance in Medicine, vol.222, issue.6, pp.893-906, 1996.
DOI : 10.1002/mrm.1910360612

C. Poupon, Détection des faisceaux de fibres de la substance blanche pour l'´ etude de la connectivité anatomique cérébrale, p.72, 1999.

C. Poupon, B. Rieul, I. Kezele, M. Perrin, F. Poupon et al., New diffusion phantoms dedicated to the study and validation of high-angular-resolution diffusion imaging (HARDI) models, Magnetic Resonance in Medicine, vol.52, issue.6, pp.1276-1283, 2008.
DOI : 10.1002/mrm.21789

V. Prckovska, A. Roebroeck, W. Pullens, A. Vilanova, and B. Ter-haar-romeny, Optimal Acquisition Schemes in High Angular Resolution Diffusion Weighted Imaging, pp.9-17, 2008.
DOI : 10.1007/978-3-540-85990-1_2

L. Qi, G. Yu, and E. Wu, Higher Order Positive Semidefinite Diffusion Tensor Imaging, SIAM Journal on Imaging Sciences, vol.3, issue.3, pp.416-433, 2010.
DOI : 10.1137/090755138

C. Rao, Information and the Accuracy Attainable in the Estimation of Statistical Parameters, Bull. Calcutta Math. Soc, vol.37, issue.54, pp.81-91, 1945.
DOI : 10.1007/978-1-4612-0919-5_16

A. Read, Linear interpolation of histograms, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.425, issue.1-2, pp.357-360, 1999.
DOI : 10.1016/S0168-9002(98)01347-3

D. Ritchie and G. Kemp, Protein docking using spherical polar Fourier correlations, Proteins: Structure, Function, and Genetics, vol.3, issue.2, pp.178-194, 2000.
DOI : 10.1002/(SICI)1097-0134(20000501)39:2<178::AID-PROT8>3.0.CO;2-6
URL : https://hal.archives-ouvertes.fr/inria-00434273

A. Schwartzman, Random Ellipsoids And False Discovery Rates: Statistics For Diffusion Tensor Imaging Data, p.100, 2006.

N. Shu, J. Li, K. Li, C. Yu, and T. Jiang, Abnormal diffusion of cerebral white matter in early blindness, Human Brain Mapping, vol.27, issue.Part 7, pp.220-227, 2009.
DOI : 10.1002/hbm.20507

L. Skovgaard, A Riemannian geometry of the multivariate normal model'. Scandinavian journal of statistics pp, pp.211-223, 1984.

O. Söderman and B. Jönsson, Restricted Diffusion in Cylindrical Geometry, Journal of Magnetic Resonance, Series A, vol.117, issue.1, pp.94-97, 1995.
DOI : 10.1006/jmra.1995.0014

M. Spivak, A comprehensive introduction to differential geometry, p.44, 1999.

A. Srivastava, I. Jermyn, and S. Joshi, Riemannian Analysis of Probability Density Functions with Applications in Vision, 2007 IEEE Conference on Computer Vision and Pattern Recognition, pp.1-8, 2007.
DOI : 10.1109/CVPR.2007.383188

E. Stejskal and J. Tanner, Spin Diffusion Measurements: Spin Echoes in the Presence of a Time???Dependent Field Gradient, The Journal of Chemical Physics, vol.42, issue.1, pp.288-292, 1965.
DOI : 10.1063/1.1695690

R. Subbarao and P. Meer, Nonlinear Mean Shift over Riemannian Manifolds, International Journal of Computer Vision, vol.22, issue.11, pp.1-20, 2009.
DOI : 10.1007/s11263-008-0195-8

D. Taylor and M. Bushell, The spatial mapping of translational diffusion coefficients by the NMR imaging technique'. Physics in medicine and biology 30, 1985.

C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), pp.839-846, 1998.
DOI : 10.1109/ICCV.1998.710815

J. Tournier, F. Calamante, and A. Connelly, Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution, NeuroImage, vol.35, issue.4, pp.1459-1472, 2007.
DOI : 10.1016/j.neuroimage.2007.02.016

J. Tournier, F. Calamante, D. Gadian, and A. Connelly, Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution, NeuroImage, vol.23, issue.3, pp.1176-1185, 2004.
DOI : 10.1016/j.neuroimage.2004.07.037

A. Tristántrist´tristán-vega and S. Aja-fernándezfern´fernández, DWI filtering using joint information for DTI and HARDI, Medical Image Analysis, vol.14, issue.2, pp.205-218, 2010.
DOI : 10.1016/j.media.2009.11.001

A. Tristántrist´tristán-vega, C. Westin, and S. Aja-fernándezfern´fernández, Estimation of fiber Orientation Probability Density Functions in High Angular Resolution Diffusion Imaging, NeuroImage, vol.47, issue.2, pp.638-650, 2009.
DOI : 10.1016/j.neuroimage.2009.04.049

A. Tristántrist´tristán-vega, C. Westin, and S. Aja-fernándezfern´fernández, A new methodology for the estimation of fiber populations in the white matter of the brain with the Funk???Radon transform, NeuroImage, vol.49, issue.2, pp.1301-1315, 2010.
DOI : 10.1016/j.neuroimage.2009.09.070

D. Tschumperlé and R. Deriche, Variational frameworks for DT-MRI estimation, regularization and visualization, Proceedings Ninth IEEE International Conference on Computer Vision, p.72, 2003.
DOI : 10.1109/ICCV.2003.1238323

D. Tuch, R. Weisskoff, J. Belliveau, and V. Wedeen, High angular resolution diffusion imaging of the human brain, Proceedings of the 7th Annual Meeting of ISMRM, p.74, 1999.

D. S. Tuch, Diffusion MRI of Complex Tissue Structure, p.83, 2002.

D. S. Tuch, T. G. Reese, M. R. Wiegell, N. Makris, J. W. Belliveau et al., High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity, Magnetic Resonance in Medicine, vol.147, issue.4, pp.577-582, 2002.
DOI : 10.1002/mrm.10268

E. A. Von-dem-hagen, R. M. Wang, Q. , T. Su, Y. Zhou et al., Orientational diffusion reflects fiber structure within a voxel, Magnetic Resonance in Medicine, vol.33, issue.3, pp.454-459, 2002.
DOI : 10.1002/mrm.10250

Z. Wang and B. C. Vemuri, DTI segmentation using an information theoretic tensor dissimilarity measure, IEEE Transactions on Medical Imaging, vol.24, issue.10, pp.1267-1277, 2005.
DOI : 10.1109/TMI.2005.854516

D. Wassermann, M. Descoteaux, and R. Deriche, Diffusion Maps Clustering for Magnetic Resonance Q-Ball Imaging Segmentation, International Journal of Biomedical Imaging, vol.4191, issue.3, pp.1-12, 2008.
DOI : 10.1109/TMI.2005.854516
URL : https://hal.archives-ouvertes.fr/inria-00429948

V. Wedeen, T. Reese, D. Tuch, M. Weigel, J. Dou et al., Mapping fiber orientation spectra in cerebral white matter with Fourier transform diffusion MRI, Proceedings of the International Society of Magnetic Resonance in Medicine, pp.82-83, 2000.

V. J. Wedeen, P. Hagmann, W. I. Tseng, T. G. Reese, and R. M. Weisskoff, Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging, Magnetic Resonance in Medicine, vol.118, issue.6, pp.1377-1386, 2005.
DOI : 10.1002/mrm.20642

Y. Weldeselassie, A. Barmpoutis, and M. Atkins, Symmetric Positive-Definite Cartesian Tensor Orientation Distribution Functions (CT-ODF), p.78, 2010.
DOI : 10.1007/978-3-642-15705-9_71

C. Westin, S. Maier, H. Mamata, A. Nabavi, F. Jolesz et al., Processing and visualization for diffusion tensor MRI, Medical Image Analysis, vol.6, issue.2, pp.93-108, 2002.
DOI : 10.1016/S1361-8415(02)00053-1

W. Wootters, Statistical distance and Hilbert space, Physical Review D, vol.23, issue.2, pp.357-53, 1981.
DOI : 10.1103/PhysRevD.23.357

Y. Wu and A. L. Alexander, Hybrid diffusion imaging, NeuroImage, vol.36, issue.3, pp.617-629, 0200.
DOI : 10.1016/j.neuroimage.2007.02.050

Y. Wu, A. S. Field, and A. L. Alexander, Computation of Diffusion Function Measures in q -Space Using Magnetic Resonance Hybrid Diffusion Imaging, IEEE Transactions On Medical Imaging, vol.27, issue.88, pp.858-865, 2008.

C. Yu, J. Li, Y. Liu, W. Qin, Y. Li et al., White matter tract integrity and intelligence in patients with mental retardation and healthy adults, NeuroImage, vol.40, issue.4, pp.1533-1541, 2008.
DOI : 10.1016/j.neuroimage.2008.01.063