Abstract
This work provides a new approach to estimate the parameters of a semi-parametric generalized linear model in the wavelet domain. The method is illustrated with the problem of detecting significant changes in fMRI signals that are correlated to a stimulus time course. The fMRI signal is described as the sum of two effects: a smooth trend and the response to the stimulus. The trend belongs to a subspace spanned by large scale wavelets. We have developed a scale space regression that permits to carry out the regression in the wavelet domain while omitting the scales that are contaminated by the trend. Experiments with fMRI data demonstrate that our approach can infer and remove drifts that cannot be adequately represented with low degree polynomials. Our approach results in a noticeable improvement by reducing the false positive rate and increasing the true positive rate.
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