Spatial inference methods for image analysis

从生物医学到环境研究，图像分析的一个中心问题是识别和 找出重要的影响。一个典型的例子是3D脑体积或2D皮质的图像分析 表面，使用解剖和功能成像。在1D功能数据（EEG）中也有很多例子 模式或解剖神经纤维），二维图像（显微镜）和二维空间数据（气候图）。这些 问题共享一个共同的数据结构，其中反复观察平滑函数或图像， 排列在精细的网格上。定位的目标是识别信号强的区域或 不同的条件或受试者组之间存在差异。 虽然有丰富的工具来分析成像数据，但重点主要集中在 在零假设下进行显著性检验和控制错误率，并受到实际应用的限制。 但是关于噪声场的不切实际的假设，损害了误差控制和统计功率。上 另一方面，函数数据分析方法正确地工作在非零均值模型下，但忽略了 平滑随机场理论的分析能力，它在图像分析中非常成功， 可以为功能数据带来类似的收益。 该提案的主要目标是开发新的空间推理方法，直接解决 非稀疏信号的估计和它们的空间不确定性的量化，以增加统计 功率，控制错误率，并获得适当的可解释的结果。在上一个赠款周期， 我们建立了峰检测的形式化误差控制方法。这次更新开发了位置 峰的不确定性和检测能力（目标1），并进一步发展置信带， 整个信号的空间置信区域（目标2）和信号超过 阈值（目标3）。提出了以平均值（效应幅度）和信噪比为目标的方法 比率（标准化平均值或效应量），允许在存在空间非线性时进行可解释的推断。 恒定方差，神经成像数据的特征。该提案提供了明确的空间定义， 推理，并支持平滑高斯随机场理论的方法，放弃平稳性 零均值假设这些方法经过严格验证，并用于绘制认知效果图 美国国立卫生研究院资助的大型青少年大脑认知发展（ABCD）研究中成瘾物质的使用。 该提案独特地汇集了图像和功能数据分析的想法，以提供更多 平滑信号和图像中重要效应的精确和可解释的空间定位。的 该提案中开发的方法提供了更准确的大脑和其他领域的映射， 更高的统计能力，以确定发生重要影响的位置， 理解和指导更有针对性的后续研究。

From biomedical to environmental research, a central problem in image analysis is to recognize and locate important effects. An archetypal example is image analysis of the 3D brain volume or the 2D cortical surface, using both anatomical and functional imaging. Examples also abound in 1D functional data (EEG patterns or anatomical neural fibers), 2D images (microscopy) and 2D spatial data (climate maps). These problems share a common data structure in which smooth functions or images are observed repeatedly and aligned on a fine grid. The goal of localization is to identify regions where the signal is strong or where differences exist between conditions or groups of subjects. While there is a rich collection of tools to analyze imaging data, the focus has been mainly on significance testing and controlling error rates under the null hypothesis and has been limited by practical but unrealistic assumptions about the noise field, compromising error control and statistical power. On the other hand, the functional data analysis approach rightly works under the non-zero mean model but ignores the analytical power of smooth random field theory, which has been so successful in image analysis and could enable similar gains for functional data. The main goal of this proposal is to develop new spatial inference methods that directly address the estimation of non-sparse signals and quantification of their spatial uncertainty, in order to increase statistical power, control error rates and obtain appropriately interpretable results. In the previous cycle of this grant, we established methodology for formal error control in peak detection. This renewal develops location uncertainty and detection power for peaks (Aim 1), and moves further to develop confidence bands and spatial confidence regions for the entire signal (Aim 2) and for excursion sets where the signal exceeds a threshold (Aim 3). Methods are proposed to target both the mean (effect magnitude) and the signal-to-noise ratio (standardized mean or effect size), allowing interpretable inference in the presence of spatially non- constant variance, characteristic of neuroimaging data. The proposal offers clear definitions of spatial inference, and supports the methodology with smooth Gaussian random field theory, forgoing the stationarity and zero-mean assumptions. These methods are rigorously validated and used to map the cognitive effects of addictive substance use in the large NIH-funded Adolescent Brain Cognitive Development (ABCD) study. This proposal uniquely brings together ideas from image and functional data analysis to provide more accurate and interpretable spatial localization of important effects in smooth signals and images. The methods developed in this proposal offer more accurate mapping of the brain and other domains, and higher statistical power to identify locations where important effects occur, enhancing scientific understanding and guiding better targeted follow-up studies.