Luo Huaien, Puthusserypady Sadasivan
Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore.
IEEE Trans Biomed Eng. 2007 Sep;54(9):1621-30. doi: 10.1109/TBME.2007.902591.
The assumption of noise stationarity in the functional magnetic resonance imaging (fMRI) data analysis may lead to the loss of crucial dynamic features of the data and thus result in inaccurate activation detection. In this paper, a Bayesian approach is proposed to analyze the fMRI data with two nonstationary noise models (the time-varying variance noise model and the fractional noise model). The covariance matrices of the time-varying variance noise and the fractional noise after wavelet transform are diagonal matrices. This property is investigated under the Bayesian framework. The Bayesian estimator not only gives an accurate estimate of the weights in general linear model, but also provides posterior probability of activation in a voxel and, hence, avoids the limitations (i.e., using only hypothesis testing) in the classical methods. The performance of the proposed Bayesian methods (under the assumption of different noise models) are compared with the ordinary least squares (OLS) and the weighted least squares (WLS) methods. Results from the simulation studies validate the superiority of the proposed approach to the OLS and WLS methods considering the complex noise structures in the fMRI data.
在功能磁共振成像（fMRI）数据分析中，假设噪声平稳可能会导致数据关键动态特征的丢失，从而导致激活检测不准确。本文提出了一种贝叶斯方法，用于分析具有两种非平稳噪声模型（时变方差噪声模型和分数噪声模型）的fMRI数据。时变方差噪声和分数噪声经小波变换后的协方差矩阵为对角矩阵。在贝叶斯框架下研究了这一特性。贝叶斯估计器不仅能准确估计一般线性模型中的权重，还能提供体素中激活的后验概率，从而避免了经典方法中的局限性（即仅使用假设检验）。将所提出的贝叶斯方法（在不同噪声模型假设下）的性能与普通最小二乘法（OLS）和加权最小二乘法（WLS）进行了比较。模拟研究结果验证了考虑fMRI数据中复杂噪声结构时，所提出方法相对于OLS和WLS方法的优越性。
