Bullmore Ed, Fadili Jalal, Breakspear Michael, Salvador Raymond, Suckling John, Brammer Michael
Brain Mapping Unit and Wolfson Brain Imaging Centre, University of Cambridge, Addenbrooke's Hospital, Cambridge, UK.
Stat Methods Med Res. 2003 Oct;12(5):375-99. doi: 10.1191/0962280203sm339ra.
Wavelets provide an orthonormal basis for multiresolution analysis and decorrelation or 'whitening' of nonstationary time series and spatial processes. Wavelets are particularly well suited to analysis of biological signals and images, such as human brain imaging data, which often have fractal or scale-invariant properties. We briefly define some key properties of the discrete wavelet transform (DWT) and review its applications to statistical analysis of functional magnetic resonance imaging (fMRI) data. We focus on time series resampling by 'wavestrapping' of wavelet coefficients, methods for efficient linear model estimation in the wavelet domain, and wavelet-based methods for multiple hypothesis testing, all of which are somewhat simplified by the decorrelating property of the DWT.
小波为多分辨率分析以及非平稳时间序列和空间过程的去相关或“白化”提供了一个正交归一基。小波特别适合分析生物信号和图像，例如人类脑成像数据，这些数据通常具有分形或尺度不变特性。我们简要定义离散小波变换（DWT）的一些关键特性，并回顾其在功能磁共振成像（fMRI）数据统计分析中的应用。我们专注于通过小波系数的“小波重采样”进行时间序列重采样、小波域中有效线性模型估计的方法以及基于小波的多重假设检验方法，所有这些方法都因DWT的去相关特性而有所简化。
