Estimability of Spatio-temporal Activation in fMRI

Event-related functional magnetic resonance imaging (fMRI) is considered as an estimation and reconstruction problem. A linear model of the fMRI system based on the Fourier sampler (k-space) approximation is introduced and used to examine what parameters of the activation are estimable, i.e. can be accurately reconstructed in the noisefree limit. Several possible spatio-temporal representations of the activation are decomposed into null and measurement components. A causal representation of the activation using generalized Laguerre polynomials is introduced.