Statistical Analysis Of Image Features

该项目的目的是开发统计方法，既可以考虑像素间的相关性，也可以应用全局图像变换方法来分析不相关的图像分量。典型的兴趣是调查在不同实验条件下从个体受试者获得的图像之间的差异，或者来自不同诊断组的受试者的平均图像之间的差异。基于傅立叶变换、小波变换和空间域中的高斯随机场理论，发展了三种不同的统计方法。在傅里叶域中，不同波数的统计量是不相关的，并且推理测试可以不受空间相关性的阻碍。这种方法提供了具有众所周知的属性和解释的严格的统计测试，但会导致空间上均匀的图像模糊，并且可能产生相对较差的空间定位。对于基于小波变换的分析，已经建立了严格的数学理论，该理论对小波系数进行参数统计检验，并通过仅对重要系数进行小波逆变换来估计局部图像差异。该方法提供了良好的空间定位和实现局部自适应图像平滑，但在解释测试结果和估计图像差异方面尚未积累太多经验。高斯随机场分析具有良好的空间局部化特性，并允许研究与外部变量(例如，年龄)的相关性，但它导致空间均匀的图像模糊，并且不提供(跨组或跨条件)图像差异的统计重建估计。这三种方法都被应用于正常受试者和酗酒者的正电子发射计算机断层扫描(PET)图像的分析，并在大体上相同的大脑区域发现了显著的差异。高斯随机场分析表明，在酒精患者的PET图像中，前额叶皮质的葡萄糖利用与年龄呈显着负相关。目前对这些主题的研究包括发展一维高斯随机场方法来分析fMRI时间序列数据。该方法可用于分析从实验中获取的fMRI数据，该实验旨在结合长基线条件(即，如实验所确定的足够长，以估计与所获取的数据相关联的方差)并转换到另一激活状态。它使用长基线数据来估计与来自图像内的体素的时间数据相关联的方差度量，并设置用于激活的统计上严格的阈值，尽管数据中存在已知的时间相关性。该分析技术正在用模拟和实验数据进行验证。此外，这种分析技术正在被纳入许多实验，其中包括一项旨在观察与正常受试者饮酒相关的大脑血流变化的实验。这为这项分析技术提供了一个理想的演示，基本上可以建立酒精摄入的反应曲线。最后，发展了基于传统傅立叶域时间序列分析的时间域统计分析，并在将fMRI血流研究中的信号定位到其他不那么严格和可推广的技术方面给出了类似的结果。这种分析方法有可能(1)定位fMRI的激活变化，(2)在没有相关噪声的情况下估计或重建激活的信号，(3)在不预先假设其结构的情况下局部估计血流动力学响应函数，以及(4)检测对多个输入刺激的多个响应。目前，这项技术既被用于研究简单的手指敲击数据，也被用于研究更复杂的实验设计。

The aim of this project is the development of statistical methods that either take into account interpixel correlation, or apply global image transform methods that permit an analysis of uncorrelated image components. Of typical interest is the investigation of differences between either images from individual subjects acquired under different experimental conditions, or between average images of subjects from different diagnostic groups. Three different statistical methods have been developed, based on the Fourier transform, the wavelet transform, and the theory of Gaussian random fields in the spatial domain. In the Fourier domain, the statistics at different wave numbers are uncorrelated and inference tests can be performed unencumbered by spatial correlations. This method provides for rigorous statistical tests with well-known properties and interpretations, but results in spatially uniform image blurring and may yield relatively poor spatial localization. For the wavelet-transform based analysis, a mathematically rigorous theory has been established that applies parametric statistical tests on wavelet coefficients and results in estimates of local image differences by inverse wavelet transform of only significant coefficients. The method provides for good spatial localization and the implementation of locally adaptive image smoothing, but there has not been much experience accumulated for the interpretation of test outcomes and estimates of image differences. Gaussian random field analysis has good spatial localization properties and permits the investigation of correlations with external variables (e.g., age), but it results in spatially uniform image blurring and does not provide for statistically reconstructed estimates of images differences (either across group or conditions). All three methods have been applied to the analysis of PET images from normal and alcoholic subjects and have identified significant differences in generally the same brain regions. Gaussian random field analysis was able to demonstrate in PET images from alcoholics a significant negative correlation of glucose utilization in the pre-frontal cortex with age. Current research on these topics includes the development of a 1-D Gaussian random field method to analyze fMRI time series data. This methodology can be used to analyze fMRI data acquired from experiments designed to incorporate a long (that is long enough, as determined experimentally, to estimate the variance associated with the acquired data) baseline condition and transition to another activated state. It uses the long baseline data to estimate the variance measure associated with the temporal data from a voxel within the image and sets a statistically rigorous threshold for activation in spite of the known temporal correlation in the data. This analysis technique is being validated with simulated and experimental data. Furthermore, this analysis technique is being incorporated into numerous experiments including one designed to look at the blood flow changes in the brain associated with alcoholic intake in normal subjects. This presents an ideal demonstration of this analysis technique to basically establish a response curve for alcohol intake. Finally, statistical analysis in the temporal domain based on traditional time series analysis in the Fourier domain have been developed and given similar results in terms of localization of the signal in fMRI blood flow studies to other less rigorous and generalizable techniques. This analysis methodology has the potential to (1) localize fMRI activation changes, (2) estimate or reconstruct the activated signal without the associated noise, (3) estimate the hemodynamic response function locally without prior assumptions as to its structure, and (4) detect multiple responses to multiple input stimuli. Currently this technique is being used to study both simple finger tap data as well as more complex experimental designs.