Abstract
We present a new regularization approach for Diffusion Basis Functions fitting to estimate in vivo brain the axonal orientation from Diffusion Weighted Magnetic Resonance Images. That method assumes that the observed Magnetic Resonance signal at each voxel is a linear combination of a given diffusion basis functions; the aim of the approach is the estimation of the coefficients of the linear combination. An issue with the Diffusion Basis Functions method is the overestimation on the number of tensors (associated with different axon fibers) within a voxel due to noise, namely, the over fitting of the noisy signal. Our proposal overcomes such an overestimation problem. In additionally, we propose a metric to compare the performance of multi-fiber estimation algorithms. The metric is based on the Earth Mover’s Distance and allows us to compare in a single metric the orientation, size compartment and the number of axon bundles between two different estimations. The improvements of our two proposals is shown on synthetic and real experiments.
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Buxton, R.B.: Introduction to Functional Magnetic Resonance Imaging: Principles and Techniques, 1st edn. Cambridge University Press (2002)
Poldrack, R.A.: A structural basis for developmental dyslexia: Evidence from diffusion tensor imaging. In: Wolf, M. (ed.) Dyslexia, Fluency, and the Brain, pp. 213–233. York Press (2001)
Basser, P.J., Mattiello, J., Lebihan, D.: MR Diffusion Tensor Spectroscopy and Imaging. Biophysical Journal 66, 259–267 (1994)
Basser, P.J., Pierpaoli, C.: Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Magn. Reson. B 111 (1996)
Aranda, R., Rivera, M., Ramírez-Manzanares, A., Ashtari, M., Gee, J.C.: Massive Particles for Brain Tractography. In: Sidorov, G., Hernández Aguirre, A., Reyes García, C.A. (eds.) MICAI 2010, Part I. LNCS, vol. 6437, pp. 446–457. Springer, Heidelberg (2010)
Stejskal, E.O.: Use of Spin Echoes in a Pulsed Magnetic-Field Gradient to Study Anisotropic, Restricted Diffusion and Flow. The Journal of Chemical Physics 43, 3597–3603 (1965)
Ramírez-Manzanares, A., Rivera, M.: Basis tensor decomposition for restoring intra-voxel structure and stochastic walks for inferring brain connectivity in DT-MRI. Int. Journ. of Comp. Vis. 69, 77–92 (2006)
Bergmann, O., Kindlmann, G., Peled, S., Westin, C.F.: Two-tensor fiber tractography. In: IEEE 2007 International Symposium on Biomedical Imaging (ISBI), Washington D.C. (2007)
Malcolm, J.G., Michailovich, O., Bouix, S., Westin, C.F., Shenton, M.E., Rathi, Y.: A filtered approach to neural tractography using the watson directional function. Medical Image Analysis 14, 58–69 (2010)
Tuch, D.S., Reese, T.G., Wiegell, M.R., Makris, N., Belliveau, J.W., Wedeen, V.J.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn. Reson. Med. 48, 577–582 (2002)
Ramírez-Manzanares, A., Rivera, M., Vemuri, B.C., Carney, P., Mareci, T.: Diffusion basis functions decomposition for estimating white matter intravoxel fiber geometry. IEEE Trans. Med. Imag. 26, 1091–1102 (2007)
Ramírez-Manzanares, A., Rivera, M.: Basis pursuit based algorithm for intra-voxel recovering information in DW-MRI. In: Proc. IEEE Sixth Mexican International Conference on Computer Science (ENC 2005), Puebla, México, pp. 152–157 (2005)
Jian, B., Vemuri, B.: A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted MRI. IEEE Trans. Med. Imaging (2007)
Ramírez-Manzanares, A., Cook, P.A., Gee., J.C.: A comparison of methods for recovering intra-voxel white matter fiber architecture from clinical diffusion imaging scans. Med. Image Comput. Comput. Assist. Interv., 305–312 (2008)
Nocedal, J., Wright, S.J.: Numerical optimization. Springer, Heidelberg (1999)
Rubner, Y., Tomasi, C., Guibas, L.J.: The Earth Mover’s Distance as a Metric for Image Retrieval. International Journal of Computer Vision 40, 99–121 (2000)
Pele, O., Werman, M.: Fast and Robust Earth Mover’s Distances. In: 2009 IEEE 12th International Conference on Computer Vision, pp. 460–467. IEEE (2009)
Pele, O., Werman, M.: A linear Time Histogram Metric for Improved Sift Matching. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 495–508. Springer, Heidelberg (2008)
Le Bihan, D., Mangin, J.F., Poupon, C., Clark, C.A., Pappata, S., Molko, N., Chabriat, H.: Diffusion tensor imaging: Concepts and applications. J. Magn. Reson. Imaging 13, 534–546 (2001)
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Aranda, R., Rivera, M., Ramírez-Manzanares, A. (2011). Improved Diffusion Basis Functions Fitting and Metric Distance for Brain Axon Fiber Estimation. In: Ho, YS. (eds) Advances in Image and Video Technology. PSIVT 2011. Lecture Notes in Computer Science, vol 7088. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25346-1_4
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DOI: https://doi.org/10.1007/978-3-642-25346-1_4
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