Abstract
Diffusion MRI is a noninvasive imaging modality that allows for the estimation and visualization of white matter connectivity patterns in the human brain. However, due to the low signal-to-noise ratio (SNR) nature of diffusion data, deriving useful statistics from the data is adversely affected by different sources of measurement noise. This is aggravated by the fact that the sampling distribution of the statistic of interest is often complex and unknown. In situations as such, the bootstrap, due to its distribution-independent nature, is an appealing tool for the estimation of the variability of almost any statistic, without relying on complicated theoretical calculations, but purely on computer simulation. In this work, we present new bootstrap strategies for variability estimation of diffusion statistics in association with noise. In contrast to the residual bootstrap, which relies on a predetermined data model, or the repetition bootstrap, which requires repeated signal measurements, our approach, called the non-local bootstrap (NLB), is non-parametric and obviates the need for time-consuming multiple acquisitions. The key assumption of NLB is that local image structures recur in the image. We exploit this self-similarity via a multivariate non-parametric kernel regression framework for bootstrap estimation of uncertainty. Evaluation of NLB using a set of high-resolution diffusion-weighted images, with lower than usual SNR due to the small voxel size, indicates that NLB is markedly more robust to noise and results in more accurate inferences.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation 4(2), 490–530 (2005)
Chung, S., Lu, Y., Henry, R.G.: Comparison of bootstrap approaches for estimation of uncertainties of DTI parameters. NeuroImage 33(2), 531–541 (2006)
Coupé, P., Yger, P., Prima, S., Hellier, P., Kervrann, C., Barillot, C.: An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images. IEEE Transaction on Medical Imaging 27, 425–441 (2008)
Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Transactions on Image Processing 16(8), 2080–2095 (2007)
Davison, A., Hinkley, D.: Bootstrap Methods and their Application. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press (1997)
Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probablilty. Chapman and Hall (1994)
Fan, J., Gijbels, I.: Local Polynomial Modelling and Its Applications. Monographs on Statistics and Applied Probablilty. Chapman and Hall (1996)
Friman, O., Farnebäck, G., Westin, C.F.: A Bayesian approach for stochastic white matter tractography. IEEE Transactions on Medical Imaging 25, 965–977 (2006)
Härdle, W.: Applied Nonparametric Regression. Cambridge University Press (1992)
Härdle, W., Bowman, A.W.: Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands. Journal of the American Statistical Association 83(401), 102–110 (1988)
Härdle, W., Müller, M.: Multivariate and semiparametric kernel regression. In: Schimek, M.G. (ed.) Smoothing and Regression: Approaches, Computation, and Application. Wiley & Sons, Inc., Hoboken (2000)
Haroon, H.A., Morris, D.M., Embleton, K.V., Alexander, D.C., Parker, G.J.M.: Using the model-based residual bootstrap to quantify uncertainty in fiber orientations from Q-ball analysis. IEEE Transaction on Medical Imaging 28(4), 535–550 (2009)
Jbabdi, S., Woolrich, M., Andersson, J., Behrens, T.: A Bayesian framework for global tractography. NeuroImage 37(1), 116–129 (2007)
Jeurissen, B., Leemans, A., Tournier, J.D., Sijbers, J.: Can residual bootstrap reliably estimate uncertainty in fiber orientation obtained by spherical deconvolution from diffusion-weighted MRI? In: Proceedings 14th Annual Meeting of the Organization of Human Brain Mapping (2008)
Jeurissen, B., Leemans, A., Jones, D.K., Tournier, J.D., Sijbers, J.: Probabilistic fiber tracking using the residual bootstrap with constrained spherical deconvolution. Human Brain Mapping 32(3), 461–479 (2011)
Johansen-Berg, H., Behrens, T.E. (eds.): Diffusion MRI — From Quantitative Measurement to In-Vivo Neuroanatomy. Elsevier (2009)
Jones, D.: Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. Magnetic Resonance in Medicine 49(1), 7–12 (2003)
Lazar, M., Alexander, A.L.: Bootstrap white matter tractography (BOOT-TRAC). NeuroImage 24(2), 524–532 (2005)
Manjón, J., Carbonell-Caballero, J., Lull, J., García-Martí, G., Martí-Bonmatí, L., Robles, M.: MRI denoising using non-local means. Medical Image Analysis 12(4), 514–523 (2008)
Manjón, J., Coupé, P., Martí-Bonmatí, L., Collins, D., Robles, M.: Adaptive non-local means denoising of MR images with spatially varying noise levels. Journal of Magnetic Resonance Imaging 31(1), 192–203 (2010)
Nadaraya, E.: On estimating regression. Theory of Probability and its Applications 9(1), 141–142 (1964)
Porter, D.A., Heidemann, R.M.: High resolution diffusion-weighted imaging using readout-segmented echo-planar imaging, parallel imaging and a two-dimensional navigator-based reacquisition. Magnetic Resonance in Medicine 62(2), 468–475 (2009)
Ruppert, D., Wand, M.: Multivariate locally weighted least squares regression. The Annals of Statistics 22(3), 1346–1370 (1994)
Shi, F., Yap, P.T., Gao, W., Lin, W., Gilmore, J., Shen, D.: Altered structural connectivity in neonates at genetic risk for schizophrenia: A combined study using morphological and white matter networks. NeuroImage 62(3), 1622–1633 (2012)
Silverman, B.: Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probablilty. Chapman and Hall (1998)
Watson, G.: Smooth regression analysis. Sankhyā: The Indian Journal of Statistics Series A 26(4), 359–372 (1964)
Wee, C.Y., Yap, P.T., Li, W., Denny, K., Browndyke, J.N., Potter, G.G., Welsh-Bohmer, K.A., Wang, L., Shen, D.: Enriched white matter connectivity networks for accurate identification of MCI patients. NeuroImage 54(3), 1812–1822 (2010)
Wee, C.Y., Yap, P.T., Zhang, D., Denny, K., Browndyke, J.N., Potter, G.G., Welsh-Bohmer, K.A., Wang, L., Shen, D.: Identification of MCI individuals using structural and functional connectivity networks. NeuroImage 59(3), 2045–2056 (2012)
Yap, P.T., Fan, Y., Chen, Y., Gilmore, J., Lin, W., Shen, D.: Development trends of white matter connectivity in the first years of life. PLoS ONE 6(9), e24678 (2011)
Yap, P.T., Wu, G., Shen, D.: Human brain connectomics: Networks, techniques, and applications. IEEE Signal Processing Magazine 27(4), 131–134 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yap, PT., An, H., Chen, Y., Shen, D. (2013). The Non-Local Bootstrap – Estimation of Uncertainty in Diffusion MRI. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds) Information Processing in Medical Imaging. IPMI 2013. Lecture Notes in Computer Science, vol 7917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38868-2_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-38868-2_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38867-5
Online ISBN: 978-3-642-38868-2
eBook Packages: Computer ScienceComputer Science (R0)