神经成像的Riccati正则化精度矩阵
Riccati-regularized Precision Matrices for Neuroimaging
摘要：
图论在神经影像学中的引入为大脑连接的研究提供了宝贵的工具。这些方法需要定义一个图，这通常是通过估计大脑区域之间的有效连接，通过优化一个不适定的逆问题。大量的工作已经投入到稀疏连通图的提取方法的发展。本文旨在强调另一种方法的好处。我们研究了最近引入的低秩L2正则化矩阵，称为Riccati正则化精度矩阵。我们证明了他们的好处，皮层厚度图的分析和提取的功能性生物标志物从静息状态fMRI扫描。此外，我们还解释了如何通过随机投影进一步提高速度和结果质量。使用人类连接组计划数据集以及众多可能的扩展和应用获得的有希望的结果表明，Riccati精度矩阵可能有用地补充当前的稀疏方法。
英文摘要：
The introduction of graph theory in neuroimaging has pro- vided invaluable tools for the study of brain connectivity. These methods require the definition of a graph, which is typically derived by estimating the effective connectivity between brain regions through the optimization of an ill-posed inverse problem. Considerable efforts have been devoted to the development of methods extracting sparse connectivity graphs. The present paper aims at highlighting the benefits of an alternative ap- proach. We investigate low-rank L2 regularized matrices recently intro- duced under the denomination of Riccati regularized precision matrices. We demonstrate their benefits for the analysis of cortical thickness map and for the extraction of functional biomarkers from resting state fMRI scans. In addition, we explain how speed and result quality can be further improved with random projections. The promising results obtained using the Human Connectome Project dataset as well as the numerous possi- ble extensions and applications suggest that Riccati precision matrices might usefully complement current sparse approaches.
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