Double‐wavelet transform for multi‐subject resting state functional magnetic resonance imaging data

Conventional regions of interest (ROIs)—level resting state fMRI (functional magnetic resonance imaging) response analyses do not rigorously model the underlying spatial correlation within each ROI. This can result in misleading inference. Moreover, they tend to estimate the temporal covariance matrix with the assumption of stationary time series, which may not always be valid. To overcome these limitations, we propose a double‐wavelet approach that simplifies temporal and spatial covariance structure because wavelet coefficients are approximately uncorrelated under mild regularity conditions. This property allows us to analyze much larger dimensions of spatial and temporal resting‐state fMRI data with reasonable computational burden. Another advantage of our double‐wavelet approach is that it does not require the stationarity assumption. Simulation studies show that our method reduced false positive and false negative rates by properly taking into account spatial and temporal correlations in data. We also demonstrate advantages of our method by using resting‐state fMRI data to study the difference in resting‐state functional connectivity between healthy subjects and patients with major depressive disorder.