{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T02:55:14Z","timestamp":1776221714398,"version":"3.50.1"},"reference-count":99,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,5,4]],"date-time":"2016-05-04T00:00:00Z","timestamp":1462320000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Comput Vis"],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s11263-016-0909-2","type":"journal-article","created":{"date-parts":[[2016,5,4]],"date-time":"2016-05-04T00:43:30Z","timestamp":1462322610000},"page":"272-299","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Riemannian Bayesian Framework for Estimating Diffusion Tensor Images"],"prefix":"10.1007","volume":"120","author":[{"given":"Kai","family":"Krajsek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marion I.","family":"Menzel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanno","family":"Scharr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,5,4]]},"reference":[{"issue":"3","key":"909_CR1","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.nurt.2007.05.011","volume":"4","author":"A\u00a0L Alexander","year":"2007","unstructured":"Alexander, A\u00a0. L., Lee, J\u00a0. E., Lazar, M., & Field, A\u00a0. S. (2007). Diffusion tensor imaging of the brain. Neurotherapeutics: The Journal of the American Society for Experimental NeuroTherapeutics, 4(3), 316\u2013329.","journal-title":"Neurotherapeutics: The Journal of the American Society for Experimental NeuroTherapeutics"},{"key":"909_CR2","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1002\/mrm.1910360222","volume":"36","author":"AH Andersen","year":"1996","unstructured":"Andersen, A. H. (1996). The Rician distribution of noisy MRI data. Magnetic Resonance in Medicine, 36, 331\u2013333.","journal-title":"Magnetic Resonance in Medicine"},{"issue":"4","key":"909_CR3","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1016\/j.neuroimage.2008.05.053","volume":"42","author":"JL Andersson","year":"2008","unstructured":"Andersson, J. L. (2008). Maximum a posteriori estimation of diffusion tensor parameters using a Rician noise model: Why, how and but. Neuroimage, 42(4), 1340\u201356.","journal-title":"Neuroimage"},{"key":"909_CR4","doi-asserted-by":"crossref","unstructured":"Arsigny, V., Fillard, P., Pennec, X., & Ayache, N. (2005). Fast and simple calculus on tensors in the log-Euclidean framework. In Proceedings of the 8th International Conference on Medical Image Computing and Computer-Assisted Intervention\u2019, pp.\u00a0115\u2013122.","DOI":"10.1007\/11566465_15"},{"issue":"2","key":"909_CR5","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1002\/mrm.20965","volume":"56","author":"V Arsigny","year":"2006","unstructured":"Arsigny, V., Fillard, P., Pennec, X., & Ayache, N. (2006). Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine, 56(2), 411\u2013421.","journal-title":"Magnetic Resonance in Medicine"},{"key":"909_CR6","first-page":"345","volume":"4","author":"C Atkinson","year":"1981","unstructured":"Atkinson, C., & Mitchell, A. (1981). Raos distance measure. The Indian Journal of Statistics, 4, 345\u2013365.","journal-title":"The Indian Journal of Statistics"},{"issue":"3","key":"909_CR7","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1006\/jmrb.1996.0086","volume":"111","author":"PJ Basser","year":"1996","unstructured":"Basser, P. J., & Pierpaoli, C. (1996). Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. Journal of Magnetic Resonance, Series B, 111(3), 209\u2013219.","journal-title":"Journal of Magnetic Resonance, Series B"},{"issue":"1","key":"909_CR8","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1002\/mrm.20334","volume":"53","author":"PG Batchelor","year":"2005","unstructured":"Batchelor, P. G., Moakher, M., Atkinson, D., Calamante, F., & Connelly, A. (2005). A rigorous framework for diffusion tensor calculus. Magnetic Resonance in Medicine, 53(1), 221\u2013225.","journal-title":"Magnetic Resonance in Medicine"},{"issue":"5","key":"909_CR9","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1118\/1.596304","volume":"15","author":"MA Bernstein","year":"1989","unstructured":"Bernstein, M. A., Thomasson, D. M., & Perman, W. H. (1989). Improved detectability in low signal-to-noise ratio magnetic resonance images by means of a phase-corrected real reconstruction. Medical Physics, 15(5), 813\u2013817.","journal-title":"Medical Physics"},{"issue":"2","key":"909_CR10","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1148\/radiology.161.2.3763909","volume":"161","author":"DL Bihan","year":"1986","unstructured":"Bihan, D. L., Breton, E., Lallemand, D., Grenier, P., Cabanis, E., & Laval-Jeantet, M. (1986). MR imaging of intravoxel incoherent motions: Application to diffusion and perfusion in neurologic disorders. Radiology, 161(2), 401\u2013407.","journal-title":"Radiology"},{"issue":"4","key":"909_CR11","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1002\/jmri.1076","volume":"13","author":"DL Bihan","year":"2001","unstructured":"Bihan, D. L., Mangin, J., Poupon, C., Clark, C., Pappata, S., Molko, N., et al. (2001). Diffusion tensor imaging: Concepts and applications. Journal of Magnetic Resonance Imaging, 13(4), 534\u2013546.","journal-title":"Journal of Magnetic Resonance Imaging"},{"key":"909_CR12","first-page":"556","volume":"4485","author":"B Burgeth","year":"2007","unstructured":"Burgeth, B., Didas, S., Florack, L., & Weickert, J. (2007). A generic approach to the filtering of matrix fields with singular PDEs. In Scale-Space and Variational Methods in Image Processing, 4485, 556\u2013567.","journal-title":"In Scale-Space and Variational Methods in Image Processing"},{"key":"909_CR13","doi-asserted-by":"crossref","unstructured":"Burgeth, B., Didas, S., & Weickert, J. (2009). A general structure tensor concept and coherence-enhancing diffusion filtering for matrix fields. Visualization and Processing of Tensor Fields, Mathematics and Visualization Springer, Berlin (pp. 305\u2013323).","DOI":"10.1007\/978-3-540-88378-4_15"},{"issue":"6","key":"909_CR14","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1109\/TPAMI.1986.4767851","volume":"8","author":"J Canny","year":"1986","unstructured":"Canny, J. (1986). A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6), 679\u2013698.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"2","key":"909_CR15","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.sigpro.2006.02.049","volume":"87","author":"CA Castano-Moraga","year":"2007","unstructured":"Castano-Moraga, C. A., Lenglet, C., Deriche, R., & Ruiz-Alzola, J. (2007). A Riemannian approach to anisotropic filtering of tensor fields. Signal Processing, 87(2), 263\u2013276.","journal-title":"Signal Processing"},{"issue":"1","key":"909_CR16","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1023\/B:JMIV.0000011324.14508.fb","volume":"20","author":"C Chefd\u2019hotel","year":"2004","unstructured":"Chefd\u2019hotel, C., Tschumperl\u00e9, D., Deriche, R., & Faugeras, O. (2004). Regularizing flows for constrained matrix-valued images. Journal of Mathematical Imaging and Vision, 20(1), 147\u2013162.","journal-title":"Journal of Mathematical Imaging and Vision"},{"issue":"2","key":"909_CR17","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1002\/mrm.20582","volume":"54","author":"B Chen","year":"2005","unstructured":"Chen, B., & Hsu, E. W. (2005). Noise removal in magnetic resonance diffusion tensor imaging. Magnetic Resonance in Medicine, 54(2), 393\u2013401.","journal-title":"Magnetic Resonance in Medicine"},{"key":"909_CR18","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2307\/1971304","volume":"122","author":"R Cohen","year":"1985","unstructured":"Cohen, R. (1985). The immersion conjecture for differentiable manifolds. The Annals of Mathematics, 122, 237\u2013328.","journal-title":"The Annals of Mathematics"},{"key":"909_CR19","doi-asserted-by":"crossref","unstructured":"Constantinides, C., Atalar, E., & McVeigh, E. (1997). Signal-to-noise measurements in magnitude images from NMR phased arrays. Magnetic Resonance in Medicine 38, 852\u2013857. Erratum in Magn. Reson. Med., 52, (2004), p. 219.","DOI":"10.1109\/IEMBS.1997.754578"},{"key":"909_CR20","doi-asserted-by":"crossref","unstructured":"Coulon, O., Alexander, D.\u00a0C., & Arridge, S.\u00a0R. (2001). A regularization scheme for diffusion tensor magnetic resonance images. In Proceedings of the 17th International Conference on Information Processing in Medical Imaging, pp.\u00a092\u2013105.","DOI":"10.1007\/3-540-45729-1_8"},{"key":"909_CR21","volume-title":"Methods of mathematical physics","author":"R Courant","year":"1953","unstructured":"Courant, R., & Hilbert, D. (1953). Methods of mathematical physics (Vol. 1). New York: Interscience."},{"key":"909_CR22","unstructured":"Cox, R., & Glen, D. (2006). Efficient, robust, nonlinear, and guaranteed positive definite diffusion tensor estimation. International Society for Magnetic Resonance in Medicine, (p. 349)."},{"key":"909_CR23","unstructured":"Dunham, W. (1990). Cardano and the solution of the cubic. Journey through Genius: The Great Theorems of Mathematics, (pp. 133\u2013154)."},{"issue":"2","key":"909_CR24","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1118\/1.595484","volume":"11","author":"W Edelstein","year":"1984","unstructured":"Edelstein, W., Bottomley, P., & Pfeifer, L. (1984). A signal-to-noise calibration procedure for NMR imaging systems. Medical Physics, 11(2), 180\u2013185.","journal-title":"Medical Physics"},{"issue":"3","key":"909_CR25","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1097\/00004728-198306000-00001","volume":"7","author":"W Edelstein","year":"1983","unstructured":"Edelstein, W., Bottomley, P., & Smith, H. H. L. (1983). Signal, noise, and contrast in NMR imaging. Journal of Computer Assisted Tomography, 7(3), 391\u2013401.","journal-title":"Journal of Computer Assisted Tomography"},{"issue":"1","key":"909_CR26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12883-015-0525-8","volume":"16","author":"BL Edlow","year":"2016","unstructured":"Edlow, B. L., Copen, W. A., Izzy, S., Bakhadirov, K., van der Kouwe, A., Glenn, M. B., et al. (2016). Diffusion tensor imaging in acute-to-subacute traumatic brain injury: A longitudinal analysis. BMC Neurology, 16(1), 1\u201311.","journal-title":"BMC Neurology"},{"issue":"1","key":"909_CR27","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s11263-006-6854-8","volume":"69","author":"C Feddern","year":"2006","unstructured":"Feddern, C., Weickert, J., Burgeth, B., & Welk, M. (2006). Curvature-driven PDE methods for matrix-valued images. International Journal of Computer Vision, 69(1), 93\u2013107.","journal-title":"International Journal of Computer Vision"},{"key":"909_CR28","doi-asserted-by":"crossref","unstructured":"Fillard, P., Arsigny, V., Ayache, N. & Pennec, X. (2005). A Riemannian framework for the processing of tensor-valued images. In First International Workshop of Deep Structure, Singularities, and Computer Vision, pp.\u00a0112\u2013123.","DOI":"10.1007\/11577812_10"},{"issue":"11","key":"909_CR29","doi-asserted-by":"crossref","first-page":"1472","DOI":"10.1109\/TMI.2007.899173","volume":"26","author":"P Fillard","year":"2007","unstructured":"Fillard, P., Pennec, X., Arsigny, V., & Ayache, N. (2007). Clinical DT-MRI estimation, smoothing, and fiber tracking with log-Euclidean metrics. IEEE Transaction on Medical Imaging, 26(11), 1472\u20131482.","journal-title":"IEEE Transaction on Medical Imaging"},{"key":"909_CR30","unstructured":"Fletcher, P. T., & Joshi, S. (2004). Principle geodesic analysis on symmetric spaces: Statistics of diffusion tensors. Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis, ECCV Workshops CVAMIA and MMBIA 2004, pp.\u00a087\u201398."},{"issue":"2","key":"909_CR31","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.sigpro.2005.12.018","volume":"87","author":"PT Fletcher","year":"2007","unstructured":"Fletcher, P. T., & Joshi, S. (2007). Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Processing, 87(2), 250\u2013262.","journal-title":"Signal Processing"},{"key":"909_CR32","first-page":"189","volume-title":"Visualization and processing of tensors and higher order descriptors for multi-valued data\u2019, mathematics and visualization","author":"L Florack","year":"2014","unstructured":"Florack, L., & Fuster, A. (2014). Riemann-Finsler geometry for diffusion weighted magnetic resonance imaging. In C.-F. Westin, A. Vilanova, & B. Burgeth (Eds.), Visualization and processing of tensors and higher order descriptors for multi-valued data\u2019, mathematics and visualization (pp. 189\u2013208). Berlin, Heidelberg: Springer."},{"key":"909_CR33","unstructured":"F\u00f6rstner, W., & Moonen, B. (1999). A metric for covariance matrices, Techical Report, Number 1999. Department of Geodesy and Geoinformatics, Stuttgart University."},{"key":"909_CR34","volume-title":"Matrix computations","author":"G Golub","year":"1996","unstructured":"Golub, G., & Loan, C. V. (1996). Matrix computations (3rd ed.). Baltimore, MD: Johns Hopkins.","edition":"3"},{"key":"909_CR35","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1002\/mrm.1910340618","volume":"34","author":"H Gudbjartsson","year":"1995","unstructured":"Gudbjartsson, H., & Patz, S. (1995). The Rician distribution of noisy MRI data. Magnetic Resonance in Medicine, 34, 910\u2013914.","journal-title":"Magnetic Resonance in Medicine"},{"issue":"3","key":"909_CR36","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11263-008-0196-7","volume":"85","author":"Y Gur","year":"2009","unstructured":"Gur, Y., Pasternak, O., & Sochen, N. (2009). Fast GL(n)-invariant framework for tensors regularization. International Journal of Computer Vision, 85(3), 211\u2013222.","journal-title":"International Journal of Computer Vision"},{"key":"909_CR37","first-page":"83","volume-title":"Mathematical methods for signal and image analysis and representation\u2019, Vol.\u00a041 of computational imaging and vision","author":"Y Gur","year":"2012","unstructured":"Gur, Y., Pasternak, O., & Sochen, N. (2012). SPD tensors regularization via Iwasawa decomposition. In L. Florack, R. Duits, G. Jongbloed, M.-C. Lieshout, & L. Davies (Eds.), Mathematical methods for signal and image analysis and representation\u2019, Vol.\u00a041 of computational imaging and vision (pp. 83\u2013100). London: Springer."},{"key":"909_CR38","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/11567646_2","volume":"3752","author":"Y Gur","year":"2005","unstructured":"Gur, Y., & Sochen, N. (2005). Denoising tensors via Lie group flows. In Variational Geometric, and Level Set Methods in Computer Vision, 3752, 13\u201324.","journal-title":"In Variational Geometric, and Level Set Methods in Computer Vision"},{"key":"909_CR39","doi-asserted-by":"crossref","unstructured":"Gur, Y., & Sochen, N.\u00a0A. (2007). Fast invariant Riemannian DT-MRI regularization. In Proc. of IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA), Rio de Janeiro, Brazil, pp.\u00a01\u20137.","DOI":"10.1109\/ICCV.2007.4409142"},{"key":"909_CR40","volume-title":"Robust statistics: The approach based on influence functions","author":"FR Hampel","year":"1986","unstructured":"Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (1986). Robust statistics: The approach based on influence functions. New York: Wiley."},{"issue":"2\u20134","key":"909_CR41","first-page":"283","volume":"23","author":"S Hartmann","year":"2003","unstructured":"Hartmann, S. (2003). Computational aspects of the symmetric eigenvalue problem of second order tensors. Technische Mechanik, 23(2\u20134), 283\u2013294.","journal-title":"Technische Mechanik"},{"issue":"3","key":"909_CR42","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1006\/jmre.2001.2400","volume":"156","author":"K Hasan","year":"2001","unstructured":"Hasan, K., Basser, P., Parker, D., & Alexander, A. (2001). Analytical computation of the eigenvalues and eigenvectors in DT-MRI. Journal of Magnetic Resonance, 156(3), 41\u201347.","journal-title":"Journal of Magnetic Resonance"},{"key":"909_CR43","volume-title":"Differential geometry Lie groups and symmetric spaces","author":"S Helgason","year":"1978","unstructured":"Helgason, S. (1978). Differential geometry Lie groups and symmetric spaces. New York: Academic press."},{"key":"909_CR44","unstructured":"Henkelman, R. (1985). Measurement of signal intensities in the presence of noise in MR images, Medical Physics, 12(2), 232\u2013233. Erratum in, 13, (1986) 544."},{"key":"909_CR45","first-page":"71","volume":"24","author":"D Hoult","year":"1976","unstructured":"Hoult, D., & Richards, R. (1976). The SNR of the NMR experiment. Journal of Magnetic Resonance, 24, 71\u201385.","journal-title":"Journal of Magnetic Resonance"},{"key":"909_CR46","volume-title":"Robust statistics. Wiley series in propability and mathematical statistics","author":"PJ Huber","year":"1981","unstructured":"Huber, P. J. (1981). Robust statistics. Wiley series in propability and mathematical statistics. New York: Wiley."},{"issue":"6","key":"909_CR47","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1002\/mrm.21734","volume":"60","author":"HK Jeong","year":"2008","unstructured":"Jeong, H. K., & Anderson, A. W. (2008). Characterizing fiber directional uncertainty in diffusion tensor MRI. Magnetic Resonance in Medicine, 60(6), 1408\u20131421.","journal-title":"Magnetic Resonance in Medicine"},{"issue":"2","key":"909_CR48","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1214\/009053604000001273","volume":"33","author":"IH Jermyn","year":"2005","unstructured":"Jermyn, I. H. (2005). Invariant Bayesian estimation on manifolds. Annals of Statistics, 33(2), 583\u2013605.","journal-title":"Annals of Statistics"},{"key":"909_CR49","doi-asserted-by":"crossref","unstructured":"Karcher, H. (1977). Riemannian center of mass and mollifier smoothing. Communications on Pure and Applied Mathematics, 30, 509\u2013541.","DOI":"10.1002\/cpa.3160300502"},{"key":"909_CR50","volume-title":"Fundamentals of statistical processing, volume I: Estimation theory","author":"SM Kay","year":"1993","unstructured":"Kay, S. M. (1993). Fundamentals of statistical processing, volume I: Estimation theory. New Jerssey: Prentice Hall Signal Processing Series."},{"issue":"3","key":"909_CR51","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.jmr.2006.01.016","volume":"179","author":"CG Koay","year":"2006","unstructured":"Koay, C. G., & Basser, P. J. (2006). Analytically exact correction scheme for signal extraction from noisy magnitude MR signals. Journal of Magnetic Resonance, 179(3), 317\u2013322.","journal-title":"Journal of Magnetic Resonance"},{"key":"909_CR52","doi-asserted-by":"crossref","unstructured":"Krajsek, K., Menzel, M.\u00a0I., & Scharr, H. (2009). Riemannian Bayesian estimation of diffusion tensor images. In IEEE International Conference on Computer Vision, pp.\u00a02327\u20132334.","DOI":"10.1109\/ICCV.2009.5459431"},{"key":"909_CR53","doi-asserted-by":"crossref","unstructured":"Krajsek, K., Menzel, M.\u00a0I., Zwanger, M., & Scharr, H. (2008). Riemannian anisotropic diffusion for tensor valued images. In European Conference on Computer Vision, pp.\u00a0326\u2013339.","DOI":"10.1007\/978-3-540-88693-8_24"},{"key":"909_CR54","doi-asserted-by":"crossref","unstructured":"Krajsek, K., & Mester, R. (2006). The edge preserving Wiener filter for scalar and tensor valued images. In Proceedings of the 28th DAGM-Symposium, pp.\u00a091\u2013100.","DOI":"10.1007\/11861898_10"},{"key":"909_CR55","doi-asserted-by":"crossref","unstructured":"Krajsek, K. & Scharr, H. (2012). A Riemannian approach for estimating orientation distribution function (ODF) images from high-angular resolution diffusion imaging (HARDI), In IEEE Conference on Computer Vision and Pattern Recognition, pp.\u00a01019\u20131026.","DOI":"10.1109\/CVPR.2012.6247779"},{"key":"909_CR56","doi-asserted-by":"crossref","unstructured":"Landman, B.\u00a0A., Bazin, P.\u00a0L., & Prince, J.\u00a0L. (2007a). Diffusion tensor estimation by maximizing Rician likelihood. In IEEE International Conference on Computer Vision, pp.\u00a01\u20138.","DOI":"10.1109\/ICCV.2007.4409140"},{"key":"909_CR57","doi-asserted-by":"crossref","unstructured":"Landman, B., Bazin, P., & Prince, J. (2007b). Robust diffusion tensor estimation by maximizing Rician likelihood, In \u2018MMBIA08\u2019, pp.\u00a01\u20138.","DOI":"10.1109\/ICCV.2007.4409140"},{"issue":"3","key":"909_CR58","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s10851-006-6897-z","volume":"25","author":"C Lenglet","year":"2006","unstructured":"Lenglet, C., Rousson, M., Deriche, R., & Faugeras, O. (2006). Statistics on the manifold of multivariate normal distributions: Theory and application to diffusion tensor MRI processing. Journal of Mathematical Imaging and Vision, 25(3), 423\u2013444.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"909_CR59","doi-asserted-by":"crossref","unstructured":"Lenglet, C., Rousson, M., Deriche, R., Faugeras, O., Lehericy, S., & Ugurbil, K. (2005). A Riemannian approach to diffusion tensor images segmentation. In \u2018IPMI\u2019, pp.\u00a0591\u2013602.","DOI":"10.1007\/11505730_49"},{"key":"909_CR60","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1088\/0022-3735\/13\/1\/013","volume":"13","author":"J Libove","year":"1980","unstructured":"Libove, J., & Singer, J. R. (1980). Resolution and signal-to-noise relationships in NMR imaging in the human body. Journal of Physics: Section E: Scientific Instruments, 13, 38\u201343.","journal-title":"Journal of Physics: Section E: Scientific Instruments"},{"key":"909_CR61","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1002\/mrm.1910360327","volume":"36","author":"A Macovski","year":"1996","unstructured":"Macovski, A. (1996). Noise in MRI. Magnetic Resonance in Medicine, 36, 494\u2013497.","journal-title":"Magnetic Resonance in Medicine"},{"key":"909_CR62","doi-asserted-by":"crossref","unstructured":"Martin-Fernandez, M., San-Jose, R., Westin, C.-F., & Alberola-Lopez, C. (2003). A novel Gauss-Markov random field approach for regularization of diffusion tensor maps. In Ninth International Conference on Computer Aided Systems Theory (EUROCAST\u201903), pp.\u00a0506\u2013517.","DOI":"10.1007\/978-3-540-45210-2_46"},{"issue":"4","key":"909_CR63","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1118\/1.597004","volume":"20","author":"G McGibney","year":"1993","unstructured":"McGibney, G., & Smith, M. (1993). An unbiased signal-to-noise ratio measure for magnitude resonance images. Medical Physics, 20(4), 1077\u20131078.","journal-title":"Medical Physics"},{"key":"909_CR64","doi-asserted-by":"crossref","unstructured":"Melonakos, J., Mohan, V., Niethammer, M., Smith, K., Kubicki, M., & Tannenbaum, A. (2007). Finsler tractography for white matter connectivity analysis of the cingulum bundle. International Conference on Medical Image Computing and Computer-assisted Intervention (pp. 36\u201343). Berlin, Heidelberg: Springer.","DOI":"10.1007\/978-3-540-75757-3_5"},{"key":"909_CR65","unstructured":"Menzel, M.\u00a0I. (2002). Multi-nuclear NMR on contaminated Sea Ice, Ph.D. Thesis, RWTH Aachen, Germany."},{"issue":"3","key":"909_CR66","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1137\/S0895479803436937","volume":"26","author":"M Moakher","year":"2005","unstructured":"Moakher, M. (2005). A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM Journal on Matrix Analysis and Applications, 26(3), 735\u2013747.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"909_CR67","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1115\/1.3171840","volume":"53","author":"K Morman","year":"1986","unstructured":"Morman, K. (1986). The generalized strain measure with application to nonhomogeneous deformations in rubber-like solids. Journal of Applied Mechanics, 53, 726\u2013728.","journal-title":"Journal of Applied Mechanics"},{"issue":"3","key":"909_CR68","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.neurobiolaging.2006.01.009","volume":"28","author":"MJ M\u00fcller","year":"2007","unstructured":"M\u00fcller, M. J., Greverus, D., Weibrich, C., Dellani, P. R., Scheurich, A., Stoeter, P., et al. (2007). Diagnostic utility of hippocampal size and mean diffusivity in amnestic MCI. Neurobiology of Aging, 28(3), 398\u2013403.","journal-title":"Neurobiology of Aging"},{"issue":"10","key":"909_CR69","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/83.791966","volume":"8","author":"R Nowak","year":"1999","unstructured":"Nowak, R. (1999). Wavelet-based Rician noise removal for magnetic resonance imaging. IEEE Transactions on Image Processing, 8(10), 1408\u20131419.","journal-title":"IEEE Transactions on Image Processing"},{"issue":"1","key":"909_CR70","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1109\/TNS.1983.4332357","volume":"30","author":"D Ortendahl","year":"1983","unstructured":"Ortendahl, D., Crooks, L., & Kaufman, L. (1983). A comparison of the noise characteristics of projection reconstruction and two-dimensional Fourier transformations in NMR imaging. IEEE Transactions on Nuclear Science, 30(1), 692\u2013696.","journal-title":"IEEE Transactions on Nuclear Science"},{"key":"909_CR71","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1002\/mrm.1910010304","volume":"1","author":"D Ortendahl","year":"1984","unstructured":"Ortendahl, D., Hylton, N. M., Kaufman, L., & Crooks, L. (1984). Resolution and signal-to-noise relationships in NMR imaging in the human body. Magnetic Resonance in Medicine, 1, 316\u2013338.","journal-title":"Magnetic Resonance in Medicine"},{"key":"909_CR72","unstructured":"Pennec, X. (1999). Probabilities and statistics on Riemannian manifolds: Basic tools for geometric measurements. In IEEE Workshop on Nonlinear Signal and Image Processing (NSIP99), pp.\u00a0194\u2013198."},{"issue":"1","key":"909_CR73","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10851-006-6228-4","volume":"25","author":"X Pennec","year":"2006","unstructured":"Pennec, X. (2006). Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements. Journal of Mathematical Imaging and Vision, 25(1), 127\u2013154.","journal-title":"Journal of Mathematical Imaging and Vision"},{"issue":"1","key":"909_CR74","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s11263-005-3222-z","volume":"66","author":"X Pennec","year":"2006","unstructured":"Pennec, X., Fillard, P., & Ayache, N. (2006). A Riemannian framework for tensor computing. International Journal of Computer Vision, 66(1), 41\u201366.","journal-title":"International Journal of Computer Vision"},{"key":"909_CR75","first-page":"81","volume":"37","author":"C Rao","year":"1945","unstructured":"Rao, C. (1945). Information and the accuracy attainable in the estimation of statistical parameters. Journal of the Royal Society of Statistics, 37, 81\u201389.","journal-title":"Journal of the Royal Society of Statistics"},{"key":"909_CR76","unstructured":"Rice, S. (1944). Mathematical analysis of random noise, Bell System Technical Journal (Reprinted by N. Wax Selected Papers on Noise and Stochastic Processes, Dover Publications 1954) 23 and 24."},{"key":"909_CR77","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1002\/mrm.1910160203","volume":"16","author":"P Roemer","year":"1990","unstructured":"Roemer, P., Edelstein, W., Hayes, C., Souza, S., & Mueller, O. (1990). The NMR phased array. Magnic Resonance in Medicine, 16, 192\u2013225.","journal-title":"Magnic Resonance in Medicine"},{"key":"909_CR78","unstructured":"Scharr, H. (2000). Optimal operators in digital image processing. Ph.D Thesis, Interdisciplinary Center for Scientific Computing, University of Heidelberg."},{"key":"909_CR79","doi-asserted-by":"crossref","unstructured":"Scharr, H., Black, M. J., & Haussecker, H. W. (2003). Image statistics and anisotropic diffusion. IEEE International Conference on Computer Vision, pp.\u00a0840\u2013847.","DOI":"10.1109\/ICCV.2003.1238435"},{"issue":"2","key":"909_CR80","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1104\/pp.106.089250","volume":"144","author":"TWJ Scheenen","year":"2007","unstructured":"Scheenen, T. W. J., Vergeldt, F. J., Heemskerk, A. M., & As, H. V. (2007). Intact plant magnetic resonance imaging to study dynamics in long-distance sap flow and flow-conducting surface area. Plant Physiology, 144(2), 1157\u20131165.","journal-title":"Plant Physiology"},{"issue":"3","key":"909_CR81","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1002\/mrm.10728","volume":"51","author":"J Sijbers den","year":"2004","unstructured":"den Sijbers, J., & Dekker, A. J. (2004). Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magnetic Resonance in Medicine, 51(3), 586\u2013594.","journal-title":"Magnetic Resonance in Medicine"},{"issue":"3","key":"909_CR82","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/42.712125","volume":"17","author":"J Sijbers","year":"1998","unstructured":"Sijbers, J., den Dekker, A., Scheunders, P., & Dyck, D. V. (1998). Maximum-likelihood estimation of Rician distribution parameters. IEEE Transactions on Medical Imaging, 17(3), 357\u2013361.","journal-title":"IEEE Transactions on Medical Imaging"},{"key":"909_CR83","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1088\/0031-9155\/52\/5\/009","volume":"52","author":"J Sijbers","year":"2007","unstructured":"Sijbers, J., Poot, D., den Dekker, A. J., & Pintjens, W. (2007). Automatic estimation of the noise variance from the histogram of a magnetic resonance image. Physics in Medicicine and Biology, 52, 1335\u20131348.","journal-title":"Physics in Medicicine and Biology"},{"key":"909_CR84","unstructured":"Skovgaard, L. (1981). A Riemannian geometry of the multivariate normal model, Technical Report 81\/3. Statistical Research Unit, Danish Medical Research Council, Danish Social Science Research Council."},{"key":"909_CR85","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1063\/1.1695690","volume":"42","author":"E Stejskal","year":"1965","unstructured":"Stejskal, E., & Tanner, J. (1965). Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient. Journal of Chemical Physics, 42, 288\u2013292.","journal-title":"Journal of Chemical Physics"},{"key":"909_CR86","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717921","volume-title":"Inverse problem theory and model parameter estimation","author":"A Tarantola","year":"2005","unstructured":"Tarantola, A. (2005). Inverse problem theory and model parameter estimation (1st ed.). New Delhi: SIAM.","edition":"1"},{"key":"909_CR87","first-page":"159","volume":"50","author":"A Tarantola","year":"1982","unstructured":"Tarantola, A., & Valette, B. (1982). Inverse problems = quest for information. Journal of Geophysics, 50, 159\u2013170.","journal-title":"Journal of Geophysics"},{"key":"909_CR88","doi-asserted-by":"crossref","unstructured":"Tschumperl\u00e9, & D. Deriche, R. (2001). Diffusion tensor regularization with constraints preservation. In IEEE Conference on Computer Vision and Pattern Recognition, pp.\u00a0948\u2013953.","DOI":"10.1109\/CVPR.2001.990631"},{"issue":"3","key":"909_CR89","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1023\/A:1020870207168","volume":"50","author":"D Tschumperl\u00e9","year":"2002","unstructured":"Tschumperl\u00e9, D., & Deriche, R. (2002). Orthonormal vector sets regularization with PDEs and applications. International Journal of Computer Vision, 50(3), 237\u2013252.","journal-title":"International Journal of Computer Vision"},{"key":"909_CR90","doi-asserted-by":"crossref","unstructured":"Wang, Y., & Lei, T. (1994). Statistical analysis of MR imaging and its applications in image modeling. In Proceedings of the IEEE International Conference on Image Processing and Neural Networks, pp.\u00a0866\u2013870.","DOI":"10.1109\/ICIP.1994.413438"},{"key":"909_CR91","unstructured":"Weickert, J. (1996). Anisotropic diffusion in image processing. Ph.D. Thesis, University of Kaiserslautern."},{"issue":"2\u20133","key":"909_CR92","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1023\/A:1008009714131","volume":"31","author":"J Weickert","year":"1999","unstructured":"Weickert, J. (1999a). Coherence-enhancing diffusion filtering. International Journal of Computer Vision, 31(2\u20133), 111\u2013127.","journal-title":"International Journal of Computer Vision"},{"key":"909_CR93","unstructured":"Weickert, J. (1999b). Nonlinear diffusion filtering. Handbook of Computer Vision and Applications, pp.\u00a0423\u2013450."},{"key":"909_CR94","doi-asserted-by":"crossref","unstructured":"Weickert, J., & Brox, T. (2002). Diffusion and regularization of vector- and matrix-valued images. Inverse Problems, Image Analysis, and Medical Imaging Contemporary Mathematics, pp.\u00a0251\u2013268.","DOI":"10.1090\/conm\/313\/05378"},{"key":"909_CR95","doi-asserted-by":"crossref","unstructured":"Westin, C., & Knutsson, H. (2003). Tensor field regularization using normalized convolution. Computer Aided Systems Theory, pp.\u00a0564\u2013572.","DOI":"10.1007\/978-3-540-45210-2_51"},{"key":"909_CR96","doi-asserted-by":"crossref","first-page":"220","DOI":"10.2307\/1969265","volume":"45","author":"H Whitney","year":"1944","unstructured":"Whitney, H. (1944). The self-intersections of a smooth n-manifold in 2n-space. Annals of Mathematics, 45, 220\u2013246.","journal-title":"Annals of Mathematics"},{"issue":"3","key":"909_CR97","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1002\/(SICI)1522-2594(199903)41:3<631::AID-MRM29>3.0.CO;2-Q","volume":"41","author":"J Wood","year":"1999","unstructured":"Wood, J., & Johnson, M. (1999). Wavelet packet denoising of magnetic resonance images: Importance of Rician noise at low SNR. Magnetic Resonance in Medicine, 41(3), 631\u2013635.","journal-title":"Magnetic Resonance in Medicine"},{"key":"909_CR98","doi-asserted-by":"crossref","unstructured":"Z\u00e9ra\u00ef, M., & Moakher, M. (2007a). Riemannian curvature-driven flows for tensor-valued data. In International Conference on Scale Space and Variational Methods in Computer Vision, pp.\u00a0592\u2013602.","DOI":"10.1007\/978-3-540-72823-8_51"},{"key":"909_CR99","unstructured":"Z\u00e9ra\u00ef, M., & Moakher, M. (2007b). Riemannian level-set methods for tensor-valued data, CoRR."}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-016-0909-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11263-016-0909-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-016-0909-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T04:09:46Z","timestamp":1567829386000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11263-016-0909-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,4]]},"references-count":99,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["909"],"URL":"https:\/\/doi.org\/10.1007\/s11263-016-0909-2","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,4]]}}}