Bagarinao E, Matsuo K, Nakai T, Sato S
Life Electronics Research Laboratory, National Institute of Advanced Industrial Science and Technology, Osaka, Japan.
Neuroimage. 2003 Jun;19(2 Pt 1):422-9. doi: 10.1016/s1053-8119(03)00081-8.
An algorithm using an orthogonalization procedure to estimate the coefficients of general linear models (GLM) for functional magnetic resonance imaging (fMRI) calculations is described. The idea is to convert the basis functions or explanatory variables of a GLM into orthogonal functions using the usual Gram-Schmidt orthogonalization procedure. The coefficients associated with the orthogonal functions, henceforth referred to as auxiliary coefficients, are then easily estimated by applying the orthogonality condition. The original GLM coefficients are computed from these estimates. With this formulation, the estimates can be updated when new image data become available, making the approach applicable for real-time estimation. Since the contribution of each image data is immediately incorporated into the estimated values, storing the data in memory during the estimation process becomes unnecessary, minimizing the memory requirements of the estimation process. By employing Cholesky decomposition, the algorithm is a factor of two faster than the standard recursive least-squares approach. Results of the analysis of an fMRI study using this approach showed the algorithm's potential for real-time application.
本文描述了一种使用正交化程序来估计功能磁共振成像（fMRI）计算中一般线性模型（GLM）系数的算法。其思路是使用常规的Gram-Schmidt正交化程序将GLM的基函数或解释变量转换为正交函数。与正交函数相关的系数，此后称为辅助系数，然后通过应用正交性条件轻松估计。原始的GLM系数从这些估计值中计算得出。采用这种公式，当有新的图像数据可用时，估计值可以更新，使得该方法适用于实时估计。由于每个图像数据的贡献立即纳入估计值中，因此在估计过程中无需将数据存储在内存中，从而将估计过程的内存需求降至最低。通过采用Cholesky分解，该算法比标准递归最小二乘法快两倍。使用这种方法对一项fMRI研究进行分析的结果表明了该算法在实时应用方面的潜力。
