Table of Contents Author Guidelines Submit a Manuscript
International Journal of Biomedical Imaging
Volume 2012 (2012), Article ID 192730, 9 pages
http://dx.doi.org/10.1155/2012/192730
Research Article

Fast and Analytical EAP Approximation from a 4th-Order Tensor

ATHENA Research Team, INRIA Sophia Antipolis Méditerranée, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France

Received 20 July 2012; Accepted 2 December 2012

Academic Editor: Carl-Fredrik Westin

Copyright © 2012 Aurobrata Ghosh and Rachid Deriche. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Özarslan 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. 50, no. 5, pp. 955–965, 2003. View at Publisher · View at Google Scholar · View at Scopus
  2. E. Özarslan, B. C. Vemuri, and T. H. Mareci, “Fiber orientation mapping using generalized diffusion tensor imaging,” in Proceedings of the 2nd IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI '10), pp. 1036–1039, April 2004. View at Publisher · View at Google Scholar · View at Scopus
  3. E. Özarslan, B. C. Vemuri, and T. H. Mareci, “Generalized scalar measures for diffusion MRI using trace, variance, and entropy,” Magnetic Resonance in Medicine, vol. 53, no. 4, pp. 866–876, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. D. S. Tuch, T. G. Reese, M. R. Wiegell, N. Makris, J. W. Belliveau, and J. Van Wedeen, “High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity,” Magnetic Resonance in Medicine, vol. 48, no. 4, pp. 577–582, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. P. J. Basser, J. Mattiello, and D. Lebihan, “Estimation of the effective self-diffusion tensor from the NMR spin echo,” Journal of Magnetic Resonance, Series B, vol. 103, no. 3, pp. 247–254, 1994. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Barmpoutis, B. Jian, and B. C. Vemuri, “Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI,” in Proceedings of the Information Processing in Medical Imaging (IPMI '07), pp. 308–319, 2007.
  7. A. Barmpoutis, M. S. Hwang, D. Howland, J. R. Forder, and B. C. Vemuri, “Regularized positive-definite fourth order tensor field estimation from DW-MRI,” NeuroImage, vol. 45, no. 1, pp. S153–162, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Ghosh, R. Deriche, and M. Moakher, “Ternary quartic approach for positive 4th order diffusion tensors revisited,” in Proceedings of the IEEE International Symposium on Biomedical Imaging: From Nano to Macro, (ISBI '09), pp. 618–621, July 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Ghosh, M. Descoteaux, and R. Deriche, “Riemannian framework for estimating symmetric positive definite 4th order diffusion tensors,” in Proceedings of the 14th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI '08), pp. 858–865, 2008.
  10. A. Barmpoutis and B. C. Vemuri, “Unified framework for estimating diffusion tensors of any order with symmetric positive-definite constraints,” in Proceedings of the 7th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, (ISBI '10), pp. 1385–1388, April 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. L. Qi, G. Yu, and E. X. Wu, “Higher order positive semidefinite diffusion tensor imaging,” SIAM Journal on Imaging Sciences, vol. 3, no. 3, pp. 416–433, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. A. Fuster, J. van de Sande, L. Astola, C. Poupon, J. Velterop, and B. M. ter Haar Romeny, “Fourth-order tensor invariants in high angular resolution diffusion imaging,” in Proceedings of the 14th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI '11), G. H. Zhang and N. Adluru, Eds., pp. 54–63, 2011.
  13. A. Ghosh, T. Papadopoulo, and R. Deriche, “Biomarkers for HARDI: 2nd and 4th order tensor invariants,” in Proceedings of the IEEE International Symposium on Biomedical Imaging (ISBI), Barcelona, Spain, 2012. View at Publisher · View at Google Scholar
  14. T. Schultz, A. Fuster, A. Ghosh, L. Florack, R. Deriche, and L. H. Lim, “Higher-order tensors in diffusion imaging: a survey,” in Visualization and Processing of Tensors and Higher Order Descriptors For Multi-Valued Data, B. Burgeth, A. Bartroli, and C. F. Westin, Eds., Springer, New York, NY, USA, 2013. View at Google Scholar
  15. V. Wedeen, T. G. Reese, D. Tuch et al., “Mapping fiber orientation spectra in cerebral white matter with fourier-transform diffusion mri,” in Proceedings of the 8th Scientific Meeting and Exhibition of the International Society for the Magnetic Resonance in Medecine, vol. 8, p. 82, 2000.
  16. D. S. Tuch, “Q-ball imaging,” Magnetic Resonance in Medicine, vol. 52, no. 6, pp. 1358–1372, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Descoteaux, E. Angelino, S. Fitzgibbons, and R. Deriche, “Regularized, fast, and robust analytical Q-ball imaging,” Magnetic Resonance in Medicine, vol. 58, no. 3, pp. 497–510, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. K. M. Jansons and D. C. Alexander, “Persistent angular structure: new insights from diffusion magnetic resonance imaging data,” Inverse Problems, vol. 19, no. 5, pp. 1031–1046, 2003. View at Publisher · View at Google Scholar · View at Scopus
  19. J. D. Tournier, F. Calamante, D. G. Gadian, and A. Connelly, “Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution,” NeuroImage, vol. 23, no. 3, pp. 1176–1185, 2004. View at Publisher · View at Google Scholar · View at Scopus
  20. E. Özarslan, 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, no. 3, pp. 1086–1103, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, Oxford, UK, 1993.
  22. 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. 43, no. 1-2, pp. 145–154, 2003. View at Publisher · View at Google Scholar · View at Scopus
  23. 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, no. 2, pp. 269–286, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Anwander, M. Tittgemeyer, D. Y. Von Cramon, A. D. Friederici, and T. R. Knösche, “Connectivity-based parcellation of Broca's area,” Cerebral Cortex, vol. 17, no. 4, pp. 816–825, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. T. G. Reese, O. Heid, R. M. Weisskoff, and V. J. Wedeen, “Reduction of eddy-current-induced distortion in diffusion MRI using a twice-refocused spin echo,” Magnetic Resonance in Medicine, vol. 49, no. 1, pp. 177–182, 2003. View at Publisher · View at Google Scholar · View at Scopus
  26. P. A. Cook, Y. Bai, N. S. Gilani et al., “Camino: open-source diffusion-MRI reconstruction and processing,” in Proceedings of the 14th Scientific Meeting of the International Society for Magnetic Resonance in Medicine, p. 2759, May 2006.