Activation detection in fMRI using a maximum energy ratio statistic obtained by adaptive spatial filtering
An adaptive spatial filtering method is proposed that takes into account contextual information in fMRI activation detection. This filter replaces the time series of each voxel with a weighted average of time series of a small neighborhood around it. The filter coefficients at each voxel are derived so as to maximize a test statistic designed to indicate the presence of activation. This statistic is the ratio of the energy of the filtered time series in a signal subspace to the energy of the residuals. It is shown that the filter coefficients and the maximum energy ratio can be found through a generalized eigenproblem. This approach equates the filter coefficients to the elements of an eigenvector corresponding to the largest eigenvalue of a specific matrix, while the largest eigenvalue itself becomes the maximum energy ratio that can be used as a statistic for detecting activation. The distribution of this statistic under the null hypothesis is derived by a nonparametric permutation technique in the wavelet domain. Also, in this paper we introduce a new set of basis vectors that define the signal subspace. The space spanned by these basis vectors covers a wide range of possible hemodynamic response functions (HRF) and is applicable to both event related and block design fMRI signal analysis. This approach circumvents the need for a priori assumptions about the exact shape of the HRF. Resting-state experimental fMRI data were used to assess the specificity of the method, showing that the actual false-alarm rate of the proposed method is equal or less than its expected value. Analysis of simulated data and motor task fMRI datasets from six volunteers using the method proposed here showed an improved sensitivity as compared to a conventional test with a similar statistic applied to spatially smoothed data.