Integral curves of noisy vector fields and statistical problems in diffusion tensor imaging: nonparametric kernel estimation and hypotheses testing

Annals of Statistics

Volumn 35, Issue 4, 2007, Pages 1576-1607

  Koltchinskii, Vladimir ^a   Sakhanenko, Lyudmila ^b   Cai, Songhe ^c  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

^c UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Diffusion tensor imaging; Functional central limit theorem; Integral curves; Kernel regression estimator; Vector fields

Indexed keywords

EID: 50449088822     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000073     Document Type: Article

References (20)

1. BASSER, P. J., PAJEVIC, S., PIERPAOLI, C. and ALDROUBI, A. (2002). Fiber tract following in the human brain using DT-MRI data. IEICE Trans. Information and Systems E85-D 15-21.
2. BASSER, P. J., PAJEVIC, S., PIERPAOLI, C., DUDA, J. and ALDROUBI, A. (2000). In vivo fiber tractography using DT-MRI data. Magnetic Resonance in Med. 44 625-632.
3. CHUNG, M. K., LAZAR, M., ALEXANDER, A. L., LU, Y. and DAVIDSON, R. (2003). Probabilistic connectivity measure in diffusion tensor imaging via anisotropic kernel smoothing. Technical report, Univ. Wisconsin-Madison.
4. EFROMOVICH, S. (1999). Nonparametric Curve Estimation. Methods, Theory and Application. Springer, New York.
5. FAN, J. and GIJBELS, I. (1996). Local Polynomial Modelling and its Applications. Chapman and Hall, London.
6. GÖSSL, C., FAHRMEIR, L., PÜTZ, B., AUER, L. M. and AUER, D. P. (2002). Fiber tracking from DTI using linear state space models: Detectability of the pyramidal tract. NeuroImage 16 378-388.
7. GUYE, M., PARKER, G. J. M., SYMMS, M., BOULBY, P., WHEELER-KINGSHOTT, C. A. M., SALEK-HADDADI, A., BARKER, G. J. and DUNCAN, J. S. (2003). Combined functional MRI and tractography to demonstrate the connectivity of the human primary motor cortex in vivo. NeuroImage 19 1349-1360.
8. HILLE, E. (1969). Lectures on Ordinary Differential Equations. Addison-Wesley, Reading, MA.
9. IBRAGIMOV, I. and HAS'MINSKII, R. (1981). Statistical Estimation. Asymptotic Theory. Springer, New York.
10. JONES, D. K. (2003). Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. Magnetic Resonance in Med. 49 7-12.
11. KOLTCHINSKII, V., SAKHANENKO, L. and CAI, S. (2005). Integral curves of noisy vector fields and statistical problems in diffusion tensor imaging: Nonparametric kernel estimation and hypotheses testing. Technical report. Available at www.stt.msu.edu/~luda/diffusion4fwpics. pdf.
12. O'DONNELL, L., HAKER, S. and WESTIN, C.-F. (2002). New approaches to estimation of white matter connectivity in diffusion tensor MRI: Elliptic PDEs and geodesics in a tensor warped space. Image Computing and Computer-Assisted Intervention MICCAI 2002. Lecture Notes in Comput. Sci. 2488 459-466.
13. PAJEVIC, S., ALDROUBI, A. and BASSER, P. J. (2002). A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue. J. Magnetic Resonance 154 85-100.
14. PARKER, G. J. M., BARKER, G. J. and BUCKLEY, D. L. (2002). A probabilistic index of connectivity (PICo) determined using a Monte Carlo approach to streamlines. ISMRM Workshop on Diffusion MRI (Biophysical Issues) Saint-Malo, France 245-255.
15. PARKER, G. J. M., STEPHAN, K. E., BARKER, G. J., ROWE, J. B., MACMANUS, D. G., WHEELER-KINGSHOTT, C. A. M. ET AL. (2002). Initial demonstration of in vivo tracing of axonal projections in the macaque brain and comparison with the human brain using diffusion tensor imaging and fast marching tractography. NeuroImage 15 797-809.
16. PARKER, G. J. M., WHEELER-KINGSHOTT, C. A. M. and BARKER, G. J. (2002). Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging. IEEE Trans. Medical Imaging 21 505-512.
17. POLZEHL, J. and SPOKOINY, V. (2001). Functional and dynamic magnetic resonance imaging using vector adaptive weights smoothing. Appl. Statist. 50 485-501.
18. POUPON, C., CLARK, C. A., FROUIN, V., RÉGIS, J., BLOCH, I., LE BIHAN, D. and MANGIN, J.-F. (2000). Regularization of diffusion-based direction maps for the tracking of brain white matter fascicles. NeuroImage 12 184-195.
19. SHAFIE, K., SIGAL, B., SIEGMUND, D. and WORSLEY, K. J. (2003). Rotation space random fields with an application to fMRI data. Ann. Statist. 31 1732-1771.
20. WEINSTEIN, D., KINDLMANN, G. and LUNDBERG, E. (1999). Tensorlines: Advection-diffusion based propagation through diffusion tensor fields. In Proc. Visualization'99 249-253. IEEE, Piscataway, NJ.