A GLOBAL OPTIMAL CONVERGENCE RATE IN A MODEL FOR THE DIFFUSION TENSOR IMAGING

被引：5

作者：

Sakhanenko, L. ^{[1
]}

机构：

[1] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2011年 / 55卷 / 01期

关键词：

integral curve; optimal rate of convergence; diffusion tensor imaging;

D O I：

10.1137/S0040585X97984619

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In their recent work Koltchinskii, Sakhanenko, and Cai [Ann. Statist., 35 (2007), pp. 1576-1607] proposed and studied estimators for integral curves based on noisy data of the corresponding gradient vector field. That estimation problem was motivated by diffusion tensor imaging, a popular brain imaging technique. Recently Sakhanenko [Theory Probab. Appl., 54 (2009), pp. 166-177] showed that those estimates have pointwise optimal convergence rate in a minimax sense. In this work we show that these estimators are convergence rate-optimal in the minimax sense with respect to the integral L-p-norm, 1 <= p <= infinity. This result closes up a gap in the research on the optimal convergence rates for these estimators.

引用

收藏

页码：77 / 90

页数：14

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