图像分析中偏移集组合的空间置信区域
Spatial Confidence Regions for Combinations of Excursion Sets in Image Analysis
摘要：
成像数据中偏移集的分析对于神经成像、气候学和宇宙学等广泛的科学学科是必不可少的。尽管越来越多的文献，很少有关于在同一空间区域，但反映了不同的研究条件下采样的过程的比较。给定一组渐近高斯随机场，每个对应于一个不同的研究条件下获得的样本，这项工作的目的是提供有关所有字段的偏移集的交集或并集的置信声明。这样的空间区域是自然感兴趣的，因为它们直接对应于“所有随机场超过预定阈值？或者“至少一个随机场在哪里超过预定阈值？".为了评估目前的空间变异的程度，我们开发了一种方法，提供了一个所需的信心，子集和超集的空间区域定义的逻辑连接（即集合交集）或分离（即集合工会），没有任何假设的依赖关系的不同领域之间。该方法通过广泛的模拟验证，并证明使用任务功能磁共振成像数据集，以确定与激活共同的工作记忆任务的四个变体的大脑区域。
英文摘要：
The analysis of excursion sets in imaging data is essential to a wide range of scientific disciplines such as neuroimaging, climatology and cosmology. Despite growing literature, there is little published concerning the comparison of processes that have been sampled across the same spatial region but which reflect different study conditions. Given a set of asymptotically Gaussian random fields, each corresponding to a sample acquired for a different study condition, this work aims to provide confidence statements about the intersection, or union, of the excursion sets across all fields. Such spatial regions are of natural interest as they directly correspond to the questions "all random fields exceed a predetermined threshold?", or "Where does at least one random field exceed a predetermined threshold?". To assess the degree of spatial variability present, we develop a method that provides, with a desired confidence, subsets and supersets of spatial regions defined by logical conjunctions (i.e. set intersections) or disjunctions (i.e. set unions), without any assumption on the dependence between the different fields. The method is verified by extensive simulations and demonstrated using a task-fMRI dataset to identify brain regions with activation common to four variants of a working memory task.
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