A GLOBAL OPTIMAL CONVERGENCE RATE IN A MODEL FOR THE DIFFUSION TENSOR IMAGING
A GLOBAL OPTIMAL CONVERGENCE RATE IN A MODEL FOR THE DIFFUSION TENSOR IMAGING
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DOI：
10.1137/s0040585x97984619
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发表时间：
2011-01-01
影响因子：
0.6
通讯作者：
Sakhanenko, L.
中科院分区：
文献类型：
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作者：
Sakhanenko, L.
在他们最近的工作Koltchinskii，Sakhanenko和蔡[安。统计。35（2007），pp. 1576-1607]提出并研究了基于相应梯度向量场的噪声数据的积分曲线的估计器。这个估计问题的动机是扩散张量成像，一种流行的大脑成像技术。最近Sakhanenko [理论Probab。应用程序、54（2009），pp. 166-177]证明了这些估计在极大极小意义下具有逐点最优收敛速度。在这项工作中，我们表明，这些估计是收敛速度最优的最小意义上的积分L-p-范数，1
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