Aston John A D, Gunn Roger N, Hinz Rainer, Turkheimer Federico E
Institute of Statistical Science, Academia Sinica, 128 Academia Road, Sec 2, Taipei 11529, Taiwan.
Neuroimage. 2005 Mar;25(1):159-68. doi: 10.1016/j.neuroimage.2004.10.037. Epub 2005 Jan 5.
Neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model. This allows inferences to be made about the signal estimates and resulting conclusions to be drawn about the underlying data. It can often be advantageous to interrogate temporal models after spatial transformation of the data into the wavelet domain. Wavelet bases provide a multiresolution decomposition of the spatial data dimension and an ensuing reduction in spatial correlation. However, widespread acceptance of these wavelet techniques has been hampered by the limited ability to reconstruct both parametric and error estimates into the image domain after analysis of temporal models in the wavelet domain. This paper introduces a derivation and a fast implementation of a method for the calculation of the variance of the parametric images obtained from wavelet filters. The technique is proposed for a class of estimators that have been shown to be useful in neuroimaging studies. The techniques are demonstrated for both functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) data sets.
神经影像学研究不仅非常重视对源自时间模型的潜在参数的估计，还重视对其标准误差的估计。这使得能够对信号估计进行推断，并对基础数据得出结论。在将数据进行空间变换到小波域之后审视时间模型通常是有利的。小波基提供了空间数据维度的多分辨率分解，并随之降低了空间相关性。然而，在小波域对时间模型进行分析之后，将参数估计和误差估计重建到图像域的能力有限，这阻碍了这些小波技术的广泛应用。本文介绍了一种从小波滤波器获得的参数图像方差计算方法的推导和快速实现。该技术是针对一类已被证明在神经影像学研究中有用的估计器提出的。针对功能磁共振成像（fMRI）和正电子发射断层扫描（PET）数据集展示了这些技术。
