Scale space searches for a periodic signal in fMRI data with spatially varying hemodynamic response

We propose a simple method for testing for a periodic signal in fMRI data where the hemodynamic response function is spatially varying with possibly different lags at different voxels. At each voxel, the test is based on the power of the spectrum at a frequency that matches the signal, divided by an estimator of the variance to produce a χ image with 2 degrees of freedom. We then apply scale space methods to search for signals of different width by smoothing the data with different Gaussian spatial filters, then searching over scale as well as location. The resulting scale space image is thresholded at a level chosen to control the false positive rate using a new result for the P-value of the maximum of scale space χ fields.