Improved activation detection via complex-valued AR(p) modeling of fMRI

A complex-valued model with AR(p) errors is proposed as an alternative to the more common Gaussian-assumed magnitude-only AR(p) model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and are compared in terms of activation detection and false discovery rates for simulated and experimental data. For simulated data, the complexvalued AR(p) model likelihood-ratio activation statistic show superior power of activation detection at low signal-to-noise ratios and lower false discovery rates. Also, when applied to an experimental data set, the activation map produced by the complex-valued AR(p) model more clearly identifies the primary activation regions. Our results advocate the use of the complex-valued data and the Gaussian AR(p) model as a more efficient and reliable tool in fMRI experiments over the current practice of using only the magnitude dataset.