NeuroImage
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Long-memory noise is common to many areas of signal processing and can seriously confound estimation of linear regression model parameters and their standard errors. Classical autoregressive moving average (ARMA) methods can adequately address the problem of linear time invariant, short-memory errors but may be inefficient and/or insufficient to secure type 1 error control in the context of fractal or scale invariant noise with a more slowly decaying autocorrelation function. Here we introduce a novel method, called wavelet-generalized least squares (WLS), which is (to a good approximation) the best linear unbiased (BLU) estimator of regression model parameters in the context of long-memory errors. ⋯ Compared to ordinary least squares and ARMA-based estimators, WLS is shown to be more efficient and to give excellent type 1 error control. The method is also applied to some real (neurophysiological) data acquired by functional magnetic resonance imaging (fMRI) of the human brain. We conclude that wavelet-generalized least squares may be a generally useful estimator of regression models in data complicated by long-memory or fractal noise.
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Gradient-echo echo-planar imaging is a standard technique in functional magnetic resonance imaging (fMRI) experiments based on the blood oxygenation level-dependent (BOLD) effect. A major problem is the occurrence of susceptibility gradients near air/tissue interfaces. As a consequence, the detection of neuronal activation may be greatly compromised in certain brain areas, especially in the temporal lobes and in the orbitofrontal cortex. ⋯ It is shown that these gradients influence the effective echo time TE and may reduce considerably the local BOLD sensitivity, even in the case of acceptable image intensities. A compensation method is proposed and tested in an fMRI experiment based on a hypercapnic challenge. The results suggest that the compensation method allows for the detection of activation in brain areas which are usually unavailable for BOLD studies.