Analyzing fMRI experiments with structural adaptive smoothing procedures.

Data from functional magnetic resonance imaging (fMRI) consist of time series of brain images that are characterized by a low signal-to-noise ratio. In order to reduce noise and to improve signal detection, the fMRI data are spatially smoothed. However, the common application of a Gaussian filter does this at the cost of loss of information on spatial extent and shape of the activation area. We suggest to use the propagation-separation procedures introduced by Polzehl, J., Spokoiny, V. (2006). Propagation-separation approach for local likelihood estimation. Probab. Theory Relat. Fields, in print. instead. We show that this significantly improves the information on the spatial extent and shape of the activation region with similar results for the noise reduction. To complete the statistical analysis, signal detection is based on thresholds defined by random field theory. Effects of adaptive and non-adaptive smoothing are illustrated by artificial examples and an analysis of experimental data.