Space-time separability in functional MRI: Asymptotic power analysis of a new test procedure

Space-time separability has been assumed and applied to most of data analysis methods in functional magnetic resonance imaging (FMRI). We developed a procedure for testing space and time separability in the framework of the parametric cepstrum. In this paper, the asymptotic power of the proposed space-time separability test is analyzed. The analysis shows two important properties of the proposed test. The asymptotic power function involves cepstral coefficients only in the non-separable region (parameters of interest). And the non-centrality parameter of the asymptotic power function is a scaled Euclidean metric between the logarithms of a non- separable power spectral density (PSD) and a separable PSD.