Abstract
Spatial regularization is a technique that exploits the dependence between nearby regions to locally pool data, with the effect of reducing noise and implicitly smoothing the data. Most of the currently proposed methods are focused on minimizing a cost function, during which the regularization parameter must be tuned in order to find the optimal solution. We propose a fast Markov chain Monte Carlo (MCMC) method for diffusion tensor estimation, for both 2D and 3D priors data. The regularization parameter is jointly with the tensor using MCMC. We compare FA (fractional anisotropy) maps for various b-values using three diffusion tensor estimation methods: least-squares and MCMC with and without spatial priors. Coefficient of variation (CV) is calculated to measure the uncertainty of the FA maps calculated from the MCMC samples, and our results show that the MCMC algorithm with spatial priors provides a denoising effect and reduces the uncertainty of the MCMC samples.
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References
Aboitiz, F., Scheibel, A.B., Fisher, R.S., Zaidel, E.: Fiber composition of the human corpus callosum. Brain Res. 598(1), 143–153 (1992)
Amestoy, P.R., Davis, T.A., Duff, I.S.: An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 17(4), 886–905 (1996)
Behrens, T.E., Berg, H.J., Jbabdi, S., Rushworth, M., Woolrich, M.: Probabilistic diffusion tractography with multiple fibre orientations: what can we gain? Neuroimage 34(1), 144–155 (2007)
Chung, S., Lu, Y., Henry, R.G.: Comparison of bootstrap approaches for estimation of uncertainties of DTI parameters. NeuroImage 33(2), 531–541 (2006)
Demiralp, C., Laidlaw, D.H.: Generalizing diffusion tensor model using probabilistic inference in Markov random fields. In: MICCAI CDMRI Workshop (2011)
Glasser, M.F., Sotiropoulos, S.N., Wilson, J.A., Coalson, T.S., Fischl, B., Andersson, J.L., Xu, J., Jbabdi, S., Webster, M., Polimeni, J.R., et al.: The minimal preprocessing pipelines for the human connectome project. Neuroimage 80, 105–124 (2013)
Graessner, J.: Diffusion-Weighted Imaging (DWI). MAGNETON Flash, pp. 6–9 (2011)
King, M.D., Gadian, D.G., Clark, C.A.: A random effects modelling approach to the crossing-fibre problem in tractography. NeuroImage 44(3), 753–768 (2009)
Koay, C.G.: Least squares approaches to diffusion tensor estimation. Diffus. MRI, 272 (2010)
Martín-Fernández, M., Josá-Estépar, R.S., Westin, C.-F., Alberola-López, C.: A novel Gauss-Markov random field approach for regularization of diffusion tensor maps. In: Moreno-Díaz, R., Pichler, F. (eds.) EUROCAST 2003. LNCS, vol. 2809, pp. 506–517. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45210-2_46
Martín-Fernández, M., Westin, C.-F., Alberola-López, C.: 3D bayesian regularization of diffusion tensor MRI using multivariate Gaussian Markov random fields. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 351–359. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30135-6_43
Papandreou, G., Yuille, A.L.: Gaussian sampling by local perturbations. In: Advances in Neural Information Processing Systems, pp. 1858–1866 (2010)
Penny, W., Flandin, G., Trujillo-Barreto, N.: Bayesian comparison of spatially regularised general linear models. Hum. Brain Mapp. 28(4), 275–293 (2007)
Penny, W.D., Trujillo-Barreto, N.J., Friston, K.J.: Bayesian fMRI time series analysis with spatial priors. Neuroimage 24(2), 350–362 (2005)
Poupon, C., Mangin, J.-F., Clark, C.A., Frouin, V., Régis, J., Le Bihan, D., Bloch, I.: Towards inference of human brain connectivity from MR diffusion tensor data. Med. Image Anal. 5(1), 1–15 (2001)
Raj, A., Hess, C., Mukherjee, P.: Spatial HARDI: improved visualization of complex white matter architecture with Bayesian spatial regularization. Neuroimage 54(1), 396–409 (2011)
Rue, H., Held, L.: Gaussian Markov Random Fields: Theory and Applications. CRC Press, Boca Raton (2005)
Sidén, P., Eklund, A., Bolin, D., Villani, M.: Fast Bayesian whole-brain fMRI analysis with spatial 3D priors. Neuroimage 146, 211–225 (2017)
Van Essen, D. C., Smith, S. M., Barch, D. M., Behrens, T. E., Yacoub, E., Ugurbil, K., Consortium, W.-M. H., et al: The WU-Minn human connectome project: an overview. Neuroimage 80, 62–79 (2013)
Walker-Samuel, S., Orton, M., Boult, J.K., Robinson, S.P.: Improving apparent diffusion coefficient estimates and elucidating tumor heterogeneity using Bayesian adaptive smoothing. Magnet. Reson. Med. 65(2), 438–447 (2011)
Wang, Z., Vemuri, B.C., Chen, Y., Mareci, T.: A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from DWI. In: Taylor, C., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 660–671. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45087-0_55
Wegmann, B., Eklund, A., Villani, M.: Bayesian heteroscedastic regression for diffusion tensor imaging. In: Modeling, Analysis, and Visualization of Anisotropy. Springer (2017)
Acknowledgements
This research was supported by the Information Technology for European Advancement (ITEA) 3 Project BENEFIT (better effectiveness and efficiency by measuring and modelling of interventional therapy) and the Swedish Research Council (grant 2015-05356, “Learning of sets of diffusion MRI sequences for optimal imaging of micro structures” and grant 2013-5229 “Statistical analysis of fMRI data”).
Data collection and sharing for this project was provided by the Human Connectome Project (HCP; Principal Investigators: Bruce Rosen, M.D., Ph.D., Arthur W. Toga, Ph.D., Van J. Weeden, MD). HCP funding was provided by the National Institute of Dental and Craniofacial Research (NIDCR), the National Institute of Mental Health (NIMH), and the National Institute of Neuro-logical Disorders and Stroke (NINDS). HCP data are disseminated by the Laboratory of Neuro Imaging at the University of Southern California.
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Gu, X., Sidén, P., Wegmann, B., Eklund, A., Villani, M., Knutsson, H. (2017). Bayesian Diffusion Tensor Estimation with Spatial Priors. In: Felsberg, M., Heyden, A., Krüger, N. (eds) Computer Analysis of Images and Patterns. CAIP 2017. Lecture Notes in Computer Science(), vol 10424. Springer, Cham. https://doi.org/10.1007/978-3-319-64689-3_30
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DOI: https://doi.org/10.1007/978-3-319-64689-3_30
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