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Generalized Wishart Processes for Interpolation Over Diffusion Tensor Fields

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Advances in Visual Computing (ISVC 2015)

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Abstract

Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive tool for watching the microstructure of fibrous nerve and muscle tissue. From dMRI, it is possible to estimate 2-rank diffusion tensors imaging (DTI) fields, that are widely used in clinical applications: tissue segmentation, fiber tractography, brain atlas construction, brain conductivity models, among others. Due to hardware limitations of MRI scanners, DTI has the difficult compromise between spatial resolution and signal noise ratio (SNR) during acquisition. For this reason, the data are often acquired with very low resolution. To enhance DTI data resolution, interpolation provides an interesting software solution. The aim of this work is to develop a methodology for DTI interpolation that enhance the spatial resolution of DTI fields. We assume that a DTI field follows a recently introduced stochastic process known as a generalized Wishart process (GWP), which we use as a prior over the diffusion tensor field. For posterior inference, we use Markov Chain Monte Carlo methods. We perform experiments in toy and real data. Results of GWP outperform other methods in the literature, when compared in different validation protocols.

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References

  1. Basser, P., Mattiello, J., Le Bihan, D.: Estimation of the effective self-diffusion tensor from the nmr spin echo. J. Magn. Reson. 103, 247–254 (1994)

    Article  Google Scholar 

  2. Yang, F., Zhu, Y.M., Luo, J.H., Robini, M., Liu, J., Croisille, P.: A comparative study of different level interpolations for improving spatial resolution in diffusion tensor imaging. IEEE J. Biomed. Health Inform. 18, 1317–1327 (2014)

    Article  Google Scholar 

  3. Fletcher, P., Joshi, S.: Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Process. 87, 250–262 (2007)

    Article  MATH  Google Scholar 

  4. Bi, C., Takahashi, S., Fujishiro, I.: Interpolating 3D diffusion tensors in 2D planar domain by locating degenerate lines. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Chung, R., Hammoud, R., Hussain, M., Kar-Han, T., Crawfis, R., Thalmann, D., Kao, D., Avila, L. (eds.) ISVC 2010, Part I. LNCS, vol. 6453, pp. 328–337. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Barmpoutis, A., Vemuri, B., Shepherd, T., Forder, J.: Tensor splines for interpolation and approximation of dt-mri with applications to segmentation of isolated rat hippocampi. IEEE Trans. Med. Imaging 26, 1537–1546 (2007)

    Article  Google Scholar 

  6. Hotz, I., Sreevalsan-Nair, J., Hamann, B.: Tensor field reconstruction based on eigenvector and eigenvalue interpolation. In: Scientific Visualization: Advanced Concepts, pp. 110–123 (2010)

    Google Scholar 

  7. Pajevic, S.: A continuous tensor field approximation of discrete dt-mri data for extracting microstructural and architectural features of tissue. J. Magn. Reson. 154, 85–100 (2002)

    Article  Google Scholar 

  8. Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-euclidean metrics for fast and simple calculus on diffusion tensors. Magn. Res. Med. 56, 411–421 (2006)

    Article  Google Scholar 

  9. Kindlmann, G., Estepar, R., Niethammer, M., Haker, S., Westin, C.: Geodesic-loxodromes for diffusion tensor interpolation and difference measurement. Med. Image Comput. Comput. Assist. Interv. 10, 1–9 (2007)

    Google Scholar 

  10. Yang, F., Zhu, Y.M., Magnin, I., Luo, J.H., Croisille, P., Kingsley, P.: Feature-based interpolation of diffusion tensor fields and application to human cardiac dt-mri. Med. Image Anal. 16, 459–481 (2012)

    Article  Google Scholar 

  11. Chang, I.S., Shun-Ren, X.: Diffusion tensor interpolation profile control using non-uniform motion on a riemannian geodesic. Comput. Electron. 13, 90–98 (2012)

    Google Scholar 

  12. Wilson, A., Ghahramani, Z.: Generalised wishart processes. In: UAI 2011, pp. 736–744 (2011)

    Google Scholar 

  13. Tanner, J., Stejskal, E.: Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Physiol. 42, 288–292 (1965)

    Article  Google Scholar 

  14. Basser, P.: Inferring microstructural features and the physiological state of tissues from diffusion weighted images. NMR Biomed. 8, 333–344 (1995)

    Article  Google Scholar 

  15. Lin-Chin, C., Jones, D., Pierpaoli, C.: RESTORE: robust estimation of tensors by outlier rejection. Magn. Reson. Med. 53, 1088–1095 (2005)

    Article  Google Scholar 

  16. Murray, I., Adams, R., Mackay, D.: Elliptical slice sampling. JMLR 9, 541–548 (2010)

    Google Scholar 

  17. Barmpoutis, A., Vemuri, B.: A unified framework for estimating diffusion tensors of any order with symmetric positive-definite constraints. In: Proceedings of ISBI 2010: IEEE International Symposium on Biomedical Imaging, pp. 1385–1388 (2010)

    Google Scholar 

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Acknowledgments

H.D. Vargas Cardona is funded by Colciencias under the program: formación de alto nivel para la ciencia, la tecnología y la innovación - Convocatoria 617 de 2013. This research has been developed under the project financed by Colciencias with code 1110-657-40687.

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Correspondence to Hernán Darío Vargas Cardona .

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Cardona, H.D.V., Álvarez , .A., Orozco, Á.A. (2015). Generalized Wishart Processes for Interpolation Over Diffusion Tensor Fields. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2015. Lecture Notes in Computer Science(), vol 9475. Springer, Cham. https://doi.org/10.1007/978-3-319-27863-6_46

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  • DOI: https://doi.org/10.1007/978-3-319-27863-6_46

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