NEW STATISTICAL METHODS FOR MEDICAL SIGNALS AND IMAGES

医学和生物数据通常以数字化信号和图像的形式出现；例如，磁共振图像，心电图痕迹，甚至蛋白质的折叠路径。随着仪器数据采集成为常规，这些图像、信号或路径的序列通常与其他协变量测量一起被收集，从而产生基本测量单位或响应是高维对象的数据集。该项目继续侧重于开发建模和理解这些数据的技术，这些数据明确考虑并确实利用固有的空间或时间相关性，并在适当时将其与协变量或类别标签信息联系起来。为了研究协方差结构，该项目提出了“稀疏”形式的主成分和判别分析，它们可能对不一定是光滑形式的局部现象更敏感，或者更适合于不规则观测数据。在适当的基上相应的二次正则化方法形成了自然的比较衬托，并且还将在某些应用中得到发展。对于均值的估计，该项目将研究稀疏经验贝叶斯方法来估计非光滑的局部现象。这项工作的大部分将在现有和新的合作中与医学成像、心脏病学和其他专业的研究人员进行，例如癌症、心脏病和大脑测绘。

Medical and biological data often come in the form of digitized signals and images; for example, magnetic resonance images, electrocardiogram traces and even the folding paths of proteins. As instrumental data acquisition becomes routine, sequences of such images, signals or paths are collected, often along with other covariate measurements, resulting in datasets where the basic unit of measurement, or response, is a high-dimensional object. The project continues to focus on developing techniques for modelling and understanding such data that explicitly take into account, and indeed exploit inherent spatial or temporal correlation, and when appropriate, relate it to covariate or class label information. To study covariance structure, the project proposes "sparse" forms of principal components and discriminant analysis that may be more sensitive to either local phenomena of not necessarily smooth form or that are more adapted to irregularly observed data. Corresponding quadratically regularized methods in appropriate bases form a natural foil for comparison, and will also be developed in certain applications. For estimation of means, the project will examine sparse empirical Bayes methods for estimating non smooth local phenomena. Much of this work will be carried out in existing and new collaborations with researchers in medical imaging, cardiology and other specialties, working for example on cancer, heart disease and brain mapping.