Tensor Regressions and Applications in Neuroimaging Data Analysis

快速发展的医学成像技术正在产生大量复杂的成像数据，并对新的统计方法提出了前所未有的要求。研究人员的目标是将先进的统计建模与现代计算技术相结合，以解决医学成像分析中一些最具挑战性的问题。研究人员提出了一个新的统计框架，并为张量回归开发了相应的理论和算法，即，使用多维数组/张量形式的图像协变量进行回归。他们在张量回归的背景下研究了各种正则化方案，以稳定估计，改善风险属性，并重建稀疏信号。他们还在张量回归框架内开发科学应用的方法，包括大脑区域和连接模式识别，基于成像的疾病诊断和多种成像模式分析。该项目为一系列成像数据问题提供了系统的解决方案，也提供了一类新的统计回归方法。现代科学中最有趣的问题之一是了解人类的大脑，包括普通人群和那些患有神经精神和神经退行性疾病的人。先进的医学成像技术提供了强大的工具来帮助解决这个问题，产生前所未有的规模和复杂性的成像数据。研究人员的目标是开发一系列新的统计方法，理论和高度可扩展的算法，用于分析大量医学成像数据。拟议的研究预计将在两个方面做出重大贡献：及时响应神经影像数据分析日益增长的需求和挑战，以及开发一个全新的广泛的统计框架和相关方法，有助于统计学科的发展。

Rapidly advancing medical imaging technologies are producing massive amounts of complex imaging data, and are imposing unprecedented demands for new statistical methodology. The investigators aim to integrate advanced statistical modeling with modern computational techniques to address some most challenging questions arising from medical imaging analysis. The investigators propose a novel statistical framework and develop accompanying theory and algorithms for tensor regression, i.e., regression with image covariates that are in the form of multidimensional arrays / tensors. They study a variety of regularization schemes in the context of tensor regression to stabilize estimation, improve risk property, and reconstruct sparse signals. They also develop methodology within the tensor regression framework for scientific applications including brain region and connectivity pattern identification, imaging based disease diagnosis, and multiple imaging modalities analysis. The project offers a systematic solution to a family of imaging data problems, and also provides a new class of statistical regression methods.One of the most intriguing questions in modern science is to understand human brains, both those of general population and those with neuropsychiatric and neurodegenerative disorders. Advanced medical imaging technologies provide powerful tools to help address the question, producing imaging data of unprecedented size and complexity. The investigators aim to develop a host of novel statistical methods, theories, and highly scalable algorithms for the analysis of massive medical imaging data. The proposed research is expected to make significant contributions on two fronts: timely response to the growing needs and challenges of neuroimaging data analysis, and development of an utterly new and broad statistical framework and the associated methodology that contributes to the advance of the statistical discipline.