The aim of many Functional Magnetic Resonance Imaging (FMRI)
experiments is to locate regions of the brain that are activated by
a specific visual, audial, or cognitive task. Voxel-wise
determination of activation is a common method for locating active
regions. Because the decision is made for each (of a large number
of) voxels, finding an activation threshold is a
multiple-comparisons problem. We propose using modifications of the
Benjamini and Hochberg (1995) procedure (BH) that account for the
fact that observed images are strongly spatially correlated; the
proposed procedures control the expected proportion of false
positives among the voxels declared to be activated. The methods,
Enhanced FDR (EFDR) by Shen at al. (2002) and EFDR fused with PAT
procedure, transform the map of dependent test statistics to the
wavelet domain and test the activation hypotheses. EFDR enhances
FDR by reducing the number of hypotheses being tested. EFDR
represents spatial map of the test statistics sparsely in the
wavelet domain and selects an optimal set of hypotheses to be tested
using a criterion based on generalized degrees of freedom. The PAT
method thresholds the wavelet coefficients using ``pvalue-driven''
threshold. Transforming the non-zero wavelet coefficients back via
the inverse discrete-wavelet transformation produces a final image
that indicates presence of a signal and also gives an idea about its
location and magnitude. To examine the effectiveness of the new
procedures on FMRI data, we performed a simulation involving
artificial-activation data sets, consisting of noise plus a signal
componenent; the noise component was determined by statistical
properties of real noise data sets from 3 subjects.
This is joint work with N. Cressie and T. J. Santner.