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 Teor. Veroyatnost. i Primenen., 2009, Volume 54, Issue 1, Pages 170–180 (Mi tvp2553)

Lower Bounds for Accuracy of Estimation in Diffusion Tensor Imaging

L. A. Sakhanenko

University of New Mexico

Abstract: A vector field is observed at random locations with additive noise. The corresponding integral curve is to be estimated based on the data. The focus of the current paper is to obtain lower bounds for the functions of deviations between true and estimated integral curves. In particular, we show that the estimation procedure in [Koltchinskii, Sakhanenko, and Cai, Ann. Statist., 35 (2007), pp. 1576–1607] yields estimates, which have the optimal rate of convergence in a minimax sense. Overall, this work is motivated by diffusion tensor imaging, which is a modern brain imaging technique. The integral curves are used to model axonal fibers in the brain. In medical research, it is important to estimate and map these fibers. The paper addresses statistical aspects pertinent to such an estimation problem.

Keywords: local asymptotic normality, optimal rate of convergence, diffusion tensor imaging

DOI: https://doi.org/10.4213/tvp2553

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English version:
Theory of Probability and its Applications, 2010, 54:1, 168–177

Bibliographic databases:

Citation: L. A. Sakhanenko, “Lower Bounds for Accuracy of Estimation in Diffusion Tensor Imaging”, Teor. Veroyatnost. i Primenen., 54:1 (2009), 170–180; Theory Probab. Appl., 54:1 (2010), 168–177

Citation in format AMSBIB
\Bibitem{Sak09} \by L.~A.~Sakhanenko \paper Lower Bounds for Accuracy of Estimation in Diffusion Tensor Imaging \jour Teor. Veroyatnost. i Primenen. \yr 2009 \vol 54 \issue 1 \pages 170--180 \mathnet{http://mi.mathnet.ru/tvp2553} \crossref{https://doi.org/10.4213/tvp2553} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2766654} \zmath{https://zbmath.org/?q=an:05771299} \transl \jour Theory Probab. Appl. \yr 2010 \vol 54 \issue 1 \pages 168--177 \crossref{https://doi.org/10.1137/S0040585X97984085} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000276689500013} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77749338829} 

• http://mi.mathnet.ru/eng/tvp2553
• https://doi.org/10.4213/tvp2553
• http://mi.mathnet.ru/eng/tvp/v54/i1/p170

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. L. A. Sakhanenko, “Global rate optimality in a model for diffusion tensor imaging”, Theory Probab. Appl., 55:1 (2011), 77–90
2. Sakhanenko L., “Numerical Issues in Estimation of Integral Curves From Noisy Diffusion Tensor Data”, Stat. Probab. Lett., 82:6 (2012), 1136–1144
3. Sakhanenko L., “Rate Acceleration For Estimators of Integral Curves From Diffusion Tensor Imaging (Dti) Data”, Stat. Probab. Lett., 107 (2015), 286–295
4. Carmichael O. Sakhanenko L., “Estimation of Integral Curves From High Angular Resolution Diffusion Imaging (Hardt) Data”, Linear Alg. Appl., 473:SI (2015), 377–403
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