Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 4 scientific papers (total in 4 papers)

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

Full text: PDF file (172 kB)
References: PDF file   HTML file

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

Bibliographic databases:

Received: 28.08.2008

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}


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

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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  mathnet  crossref  crossref  mathscinet  isi
    2. Sakhanenko L., “Numerical Issues in Estimation of Integral Curves From Noisy Diffusion Tensor Data”, Stat. Probab. Lett., 82:6 (2012), 1136–1144  crossref  mathscinet  zmath  isi  scopus
    3. Sakhanenko L., “Rate Acceleration For Estimators of Integral Curves From Diffusion Tensor Imaging (Dti) Data”, Stat. Probab. Lett., 107 (2015), 286–295  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:233
    Full text:102
    References:37

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021