Bullmore Ed, Fadili Jalal, Maxim Voichita, Sendur Levent, Whitcher Brandon, Suckling John, Brammer Michael, Breakspear Michael
Brain Mapping Unit and Wolfson Brain Imaging Centre, University of Cambridge, Addenbrooke's Hospital, Cambridge, UK.
Neuroimage. 2004;23 Suppl 1:S234-49. doi: 10.1016/j.neuroimage.2004.07.012.
The discrete wavelet transform (DWT) is widely used for multiresolution analysis and decorrelation or "whitening" of nonstationary time series and spatial processes. Wavelets are naturally appropriate for analysis of biological data, such as functional magnetic resonance images of the human brain, which often demonstrate scale invariant or fractal properties. We provide a brief formal introduction to key properties of the DWT and review the growing literature on its application to fMRI. We focus on three applications in particular: (i) wavelet coefficient resampling or "wavestrapping" of 1-D time series, 2- to 3-D spatial maps and 4-D spatiotemporal processes; (ii) wavelet-based estimators for signal and noise parameters of time series regression models assuming the errors are fractional Gaussian noise (fGn); and (iii) wavelet shrinkage in frequentist and Bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps. We conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fMRI data.
离散小波变换（DWT）被广泛用于多分辨率分析以及对非平稳时间序列和空间过程进行去相关或“白化”处理。小波自然适用于分析生物数据，比如人类大脑的功能磁共振成像，这类数据常常呈现出尺度不变性或分形特性。我们简要正式介绍一下DWT的关键特性，并回顾其在功能磁共振成像应用方面不断增加的文献。我们特别关注三个应用：（i）对一维时间序列、二维到三维空间图以及四维时空过程进行小波系数重采样或“小波套索”；（ii）对于假设误差为分数高斯噪声（fGn）的时间序列回归模型的信号和噪声参数，基于小波的估计器；（iii）在频率主义和贝叶斯框架下的小波收缩，以支持对空间扩展统计图进行多分辨率假设检验。我们得出结论，小波域是丰富的新概念和新技术来源，可增强对人类功能磁共振成像数据进行统计分析的能力。
