An exploration of spatial similarities in temporal noise spectra in fMRI measurements

In this paper, we describe a method to evaluate similarities in estimated temporal noise spectra of functional Magnetic Resonance Imaging (fMRI) time series. Accurate noise spectra are needed for reliable activation detection in fMRI. Since these spectra are a-priori unknown, they have to be estimated from the fMRI data. A noise model can be estimated for each voxel separately, but when noise spectra of neighboring voxels are (almost) equal, the power of the activation detection test can be improved by estimating the noise model from a set of neighboring voxels. In this paper, a method is described to evaluate the similarity of noise spectra of neighboring voxels. Noise spectrum similarities are studied in simulation as well as experimental fMRI datasets. The parameters of the model describing the voxel time series are estimated by a Maximum Likelihood (ML) estimator. The similarity of the ML estimated noise processes is assessed by the Model Error (ME), which is based on the Kullback Leibler divergence. Spatial correlations in the fMRI data reduce the ME between the noise spectra of (neighboring) voxels. This undesired effect is quantified by simulation experiments where spatial correlation is introduced. By plotting the ME as a function of the distance between voxels, it is observed that the ME increases as a function of this distance. Additionally, by using the theoretical distribution of the ME, it is observed that neighboring voxels indeed have similar noise spectra and these neighbors can be used to improve the noise model estimate.